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GUIDANCE MATERIALS

AS13006 Process Control Methods

Appendix D

Revised

2018-OCT-09

INTRODUCTION

The following guidance supports AS13006. Within AS13006 this guidance is referenced from appendix D. Many of the graphics in this guidance are produced using Minitab software – a recognized statistical software application.

TABLE OF CONTENTS 1. BENEFITS OF STATISTICAL PROCESS CONTROL (SPC) ................................................................................... 3 1.1. Background ............................................................................................................................................................ 3

1.2. Benefits .................................................................................................................................................................. 3

1.3. Resistance to SPC ................................................................................................................................................. 3

2. PROCESS CONTROL METHODS ............................................................................................................................ 6

2.1. Error/Mistake Proofing ........................................................................................................................................... 6 2.2. Control Charts for Variable Data ............................................................................................................................ 7

2.3. Run Charts with Non-Statistical Limits ................................................................................................................. 10

2.4. Pre-Control Charts ............................................................................................................................................... 12

2.5. Life/Usage Control................................................................................................................................................ 15

2.6. Control Charts for Attribute Data .......................................................................................................................... 16

2.7. Visual Process Check & Checklist ....................................................................................................................... 22 2.8. First Piece Check ................................................................................................................................................. 23

2.9. Test Piece Evaluation .......................................................................................................................................... 24

3. PROCESS CAPABILITY INDICES .......................................................................................................................... 25

3.1. Fundamentals for Variable data ........................................................................................................................... 25

3.2. Process Stability in Practice ................................................................................................................................. 29

3.3. Process Capability for Attribute Data ................................................................................................................... 32 4. GUIDANCE FOR NON-NORMAL DATA ................................................................................................................. 35

4.1. Using Control Charts with Non-Normal Data ....................................................................................................... 39

4.2. Capability Analysis for Non-Normal data ............................................................................................................. 42

5. COMMON SOURCES OF VARIATION ................................................................................................................... 45

6. SCENARIOS REQUIRING SPECIFIC ANALYSIS METHODS ............................................................................... 46




6.1. Assessing Control and Capability of Multiple Variable Features ......................................................................... 46

6.2. Assessing Control and Capability of Variable Data by Process or Part Family ................................................... 53

7. COMPUTER BASED SYSTEMS AND SOFTWARE ............................................................................................... 58

8. METHODS AND FORMULAE .................................................................................................................................. 59

9. AS13006 PROCESS CONTROL MATURITY REVIEW .......................................................................................... 65




1. BENEFITS OF STATISTICAL PROCESS CONTROL (SPC)

1.1. Background

The overall objective of Statistical Process Control (SPC) is to operate processes economically with minimum disruption due to stoppages and non-conformances.

The term ‘statistical control’ can be considered from two perspectives:

• The use of statistical tools – and others, within a closed loop system to manage process variation.

• The state of statistical control, when a process behaves in a random and predictable way within its natural range.

It is hard to see how a state of statistical control can be achieved without the use of process control techniques. Processes have a tendency to behave in an unstable manner unless they are managed into a state of control; and to be effective this management needs to be early (in cycle / point of process) as opposed to after the event (e.g., final inspection).

Statistical Process Control techniques are not new, being originally used in the early 1920’s. Some other techniques, such as mistake proofing go back much further.

Industry uses process control extensively to control quality. The benefits are easy to see; total cost of quality is reduced and the process can be depended on to consistently deliver conforming product.

SPC tools have the following objectives:

a. To increase knowledge of the process.

b. To steer the process to behave in the desired way, often towards a specific target.

c. To reduce product/process variation, or in other ways improve performance.

With correct process control, end of line inspection moves from being an exercise of sorting good and bad product to one of routine validation of goodness ‘as expected’.

For SPC to be most effective it needs to operate within an inherently stable environment. The relevant Foundational Activities (refer to AS13006) should be in place and managed, to underpin the control strategy. Without these fundamentals in place SPC will fail.

1.2. Benefits

Financial benefits of Process Control and SPC tools come from:

• Reduced costs due to scrap, screening, rework, repair, downtime, and material outages.

• Reduced costs incurred during the total lifecycle of the product

• Cost saving through reduced inspection levels.

• Customer loyalty and retention.

• Improved product design through the feedback of manufacturing capability information

• The ability to maintain a process to a target value where deviation from the target results in some loss (typically in performance) – a concept known as Taguchi’s Loss Function

• More immediate problem resolution.

1.3. Resistance to SPC




SPC is sometimes seen as an automotive/mass production tool. This assumption is incorrect. Considering the quality revolution that automotive has undergone in its history it is worth reflecting on, and learning from, the automotive application of process control rather than creating a counter argument against its use.

Resistance to implementing SPC techniques is not uncommon. Common reasons given for not implementing are:

a. “We already inspect everything we make”

Over reliance on ‘end of line’ inspection leads to quality becoming an exercise of ‘sorting product good from bad’. It is not possible to reach a level of 100% conformance through inspection alone; all that can be done is to react to non- conforming product, and investigate. The approach drives a culture of firefighting and results in higher product non-conformance than would be the case had ‘point of process’ statistical control been in place. SPC benefits both the supplier and the customer.

b. “SPC is not suitable for low volume manufacture”

Management of variation is not exclusive to high volume. Most manufacturing problems have variation at their source; and most low volume operations have high consequence of failure, whether that be cost or time to replace or rework defective items. A rigorous process control strategy, inputs, parameters, and setup standards is vital to maintain conformance. These items can be controlled before the operation is performed using statistical or non-statistical techniques to prevent non-conformance rather than managing after the event.

c. “SPC is only suitable for simple products”

Complex products tend to have large numbers of characteristics. One may argue against running SPC on all of these characteristics. Strategies can be employed that enable proper selection of ‘controlling’ characteristics (input or output) that give indication of the health of a process. These characteristics are included in the control strategy. Variation studies can be performed on feature groups collectively to reduce the burden of analysis (see 6.1 - Assessing Control and Capability of Multiple Variable Features).

NOTE: On some products, sources of variation exist that affect the variation between features ‘within part’. For example, groups of features in large components affected by distortion and material stress relief during processing can display characteristics of ‘out of round’. This type of behavior can be better understood using ‘Between/Within’ charting strategies. This type of behavior is typically difficult to detect using traditional inspection output such as CMM reports or single feature by feature analysis. (see 6.1 - Assessing Control and Capability of Multiple Variable Features).

d. “SPC is not suitable for high product mix situations”

For high product mix situations, it is often useful to focus on characteristics that are common to the process rather than measure and monitor separate products by different mechanisms. Short run or part family approaches may be used in which the deviation from target is monitored (see 6.2 - Assessing Control and Capability of Variable Data by Process or Part Family)

SPC analysis allows the manufacturer to see if differences between products are evident, thereby prioritizing improvement.

e. “We have tried SPC before and failed”

There are many pitfalls in SPC deployment and criticism of it is often based on historic issues and past experience of poor deployment. Causes of issues in deployment of SPC can be due to:

• Poor engagement of those recording and monitoring the data.

• Failure to do anything useful with the data (e.g., failure to investigate and correct special causes).

• Failure to development an adequate control strategy (e.g., SPC not being ‘closed loop’ and timely)

• SPC done in isolation, with inadequate attention given to the ‘fundamentals’

• Failing to develop the SPC approach as experience grows.




f. “SPC is only useful once we have 30 data points”

It is true that confidence in the accuracy of control limits and capability indices is higher as more data is gathered, but to wait for an arbitrary number of points before review may result in a missed opportunity for improvement. This is not to say that process tampering (making unnecessary adjustments), is to be encouraged, but obvious issues may be seen with relatively few data points, e.g., a process that is running significantly off target may be corrected without initial need for control limits, but once on target control limits can be used to recognize when corrections are necessary, thus keeping the process stable. Initial assessment may be as simple as using a run chart or Pre-control chart in the early stages of production.

g. “SPC is only applicable to variable measurements”

SPC can be used to monitor rate, frequency, proportion, and count for attribute type characteristics and defects. The benefit of monitoring these attributes through control charts is that change in the rate, frequency or incidence of the attributes can trigger positive (and prescriptive) action rather than relying on subjective ‘gut feel’ decisions or no action at all.

Attributes that can be monitored statistically are for example:

• Proportion of defective parts

• Number of attribute defects (either per batch or per item)

• Rate of rare event type defects (similar to mean time between failure for machinery)

Knowledge is also an enabler to success. The following publications contain additional information (technical and non-technical) relating to the application of statistical methods for quality improvement and control:

• Advanced Product Quality Planning (APQP), Automotive Industry Action Group (AIAG), ISBN 1605341371

• Statistical Process Control (SPC), Automotive Industry Action Group (AIAG), ISBN 1605341088

• Implementing Six Sigma 2nd Edition, Breyfogle 2003. ISBN 0-471-26572-1

• Understanding Variation - The Key to Managing Chaos. Donald J. Wheeler. Published by SPC Press, ISBN: 0-945320-53-1

• “Poka-Yoke”, by Productivity Press, ISBN 0-915299-31-3

• “Mistake Proofing for Operators: The ZQC System”, by Productivity Press, ISBN 1-56327-127-3




2. PROCESS CONTROL METHODS

The following sections expand on the Process Control Methods in AS13006 – Table 1 – Process Control Methods

2.1. Error/Mistake Proofing

Error proofing is the use of an automatic device or method that either makes error impossible or makes its occurrence immediately apparent. Error proofing should be chosen when the process is at risk of human error. The process risk analysis (PFMEA) should identify where human error is likely (occurrence), where it has a high impact (severity) or may not be easily detected (detection). Safety related risks often require mistake proofed solutions.

Error proofing devices can take four forms. The hierarchy of these are:

1. Elimination – design the product or process hardware in such a way that an error is not possible.

2. Control – prevent an error being made by detecting it before it has an effect

3. Signal – provide an immediate and obvious warning to prevent or highlight an error.

4. Facilitation – methods of guidance that make error less likely

NOTE: Error proofing methods are not industry specific. Some industrial sectors have a particularly well developed mistake-proofing culture often extending into product as well as process design. The automotive industry is very well known for its use of error proofing both from the manufacturing processes to the operation of the final product.

Examples:

• Guide Pins used to assure a one-way fit of a tool, fixture or part to prevent incorrect orientation.

• An alarm used to alert an operator that a machine cycle has been attempted with a misaligned tool. The operator can take action to correct the problem.

• A limit switch used to detect correct placement of a work piece.

• Counters can be used to help an operator track the correct number of components needed in an assembly.

• A checklist used to assure all key steps are completed by the operator to prevent missing something that could cause an escape and/or defect. This approach is also described further in 2.7 - Visual Process Check & Checklist.

• Use of machine probing as either a control during manufacturing to check a size before final cut or as a signal after final cut to detect an anomaly or identify that an adjustment may be needed.

• Use of a Stopper Gate (physical barrier) affixed to a Fan Compressor assembly fixture to ensure an oil fill tube is installed in the correct port when there are multiple ports to choose from.

• Asymmetrical design of a nameplate that assures it is installed in only one possible orientation preventing backwards or upside down installation.

• A left/right two button hand operated system with foot switch operation to ensure hands are free prior to cycling a forging press.

• Automated weighing of a part or batch to ensure part is completely processed or batch is complete and present before moving to the next operation.

To ensure error proofing devices are robust, it is good practice to check that the failure of the device does not cause a problem (test to see what happens if the device fails to detect the error). Depending on the result (and the criticality of failure), revisit the design and maintenance requirements of the device and improve it.




If it is not possible to have an automated error proofing device, some of the other methods included in this standard may offer some level of protection.

For further reading on the subject of Error/Mistake-Proofing the following may be referred to:

• “Poka-Yoke”, by Productivity Press, ISBN 0-915299-31-3

• “Mistake-Proofing for Operators: The ZQC System”, by Productivity Press, ISBN 1-56327-127-3

2.2. Control Charts for Variable Data

This section outlines 4 recognized control charts for variable data and provides guidance as to when they may be used. The list is not exhaustive. There are many more types of control charts not covered here that may be used for specific situations.

Figure 2.2-1 and Table 2.2-1 outline the basis for variable control chart selection.

Figure 2.2-1: VARIABLE CONTROL CHART SELECTION

Table 2.2-1. VARIABLE CONTROL CHARTS

Chart Its use

Xbar and R

Xbar and S

Monitoring and control of characteristics on products being produced at a volume where typically a sample (subgroup) will be taken periodically to maintain quality.

Example: From a high volume process, five parts per hour are sampled from the line and measured. The average and range is plotted to understand if the process has changed (due to moving off target or through an increase in variation).

Can also be used for multiple similar products where it can used to plot ‘deviation from target’ thus avoiding the need for multiple charts.

The X bar chart displays the average of the subgroup. The R or S chart displays the variation within the subgroup (either the Range or Standard Deviation).

An X-Bar and R chart is used for subgroups of 3 to 8.




Chart Its use

An X-Bar and S chart is used when subgroup size exceeds 8

NOTE: The variation within the subgroups is assumed to be representative of the overall variation (no between batch effects expected). When this assumption is not met the process may appear out of control when in fact it is not. Consult an experienced practitioner if this appears to be the case.

Individual and Moving Range

(I-MR or X-MR)

Monitoring and control of characteristics on individual products being produced from continuous processes at a rate where subgrouping of data is not feasible.

Monitoring and control of process characteristics.

Can also be used for short run applications where there is product mix with similar characteristics (may be known as part families). In this situation the variability for all parts should be similar; used to monitor part families.

The Individuals chart displays the actual measured value (or deviation from target)

The Moving Range chart plots the difference between consecutive points (short-term variation)

NOTE: The variation from item to item is assumed to be representative of the overall process variation (no batching effects or systemic drifts/wear expected). When this assumption is not met the process may appear out of control when in fact it is stable. Consult a process control specialist if this appears to be the case.

I-MR-R/S Xbar-MR-R/S Also known as Between/ Within control chart or ‘Three Way’ chart

Characteristics where the variation within the subgroup is not representative of the overall variation between them, usually the case when monitoring processes with ‘batching’ effects or multiple characteristics (a group of identical features) within a part are studied where the assumptions for an Xbar/R or S chart are not met.

The subgroup average is plotted on the Xbar chart

The variation between consecutive subgroup averages is plotted on the Moving Range chart.

The Variation within the subgroup is plotted on the R or S chart.

NOTE: Higher subgroup sizes may lead to higher sensitivity to ‘special causes’ on R and S charts. Expected patterns within parts and batches can sometimes show signals that have no practical significance. Guidance may be sought from an experienced SPC practitioner if this appears to be the case.

There are eight industry standard tests for statistical control; to determine if the process data contains evidence of special causes of variation.

A process can be judged to be in statistical control (i.e., only common causes of variation present) when there is an absence of the patterns shown in Figure 2.2-3. An example of a stable process is shown in Figure 2.2-2. It should be noted when seeking to improve a process that the more tests used, the more signals will be detected. It may be worth using a selected few when starting out using SPC.

For process control purposes manufacturers often select the most appropriate tests for the process being operated, taking into account the actions that would be needed when they occur. Tests most frequently used by operators are Test 1 and 5 (Figure 2.2-3) however software applications make the use of all tests relatively simple.




Figure 2.2-2: PROCESS SHOWING NO SIGNS OF SPECIAL CAUSE VARIATION

Figure 2.2-3: TESTS FOR SPECIAL CAUSE VARIATION

2825221 91 61 31 0741Observation

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alue

_X

UCL

LCL

2825221 91 61 31 0741Observation

Mov

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Rang

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__MR

UCL

LCL=0

I-MR Chart of 'in control' process.




2.3. Run Charts with Non-Statistical Limits

This section outlines the control of characteristics subject to systematic (predictable) drift where operation of traditional statistical control limits provides little benefit when compared to the characteristics’ ‘loss function’ and the cost and other implications of adjustment or reset.

Some processes have characteristics that naturally drift in a certain direction as the process runs. These processes when viewed on commonly used control charts tend to break tests for out of control condition long before the drift becomes a meaningful issue.

Processes where this behaviour may exist naturally are chemical etching (concentration changes), investment casting slurry control (through evaporation) and in some cases machining cutting tools (if they exhibit significant wear/drift with use).

An approach to manage this variation is to set limits on a time series chart. This limit will be set such that it detects drifts to avoid problems, but not so soon as it becomes uneconomic to adjust. This type of control is generally only useful when operated at the process rather than at an end of line inspection.

With appropriately set limits this method can be used effectively to control quality even using simpler measurement systems than downstream measurement equipment such as a CMM.

NOTE: Some processes have recommended standards that use such controls. For example, ARP4992 “Periodic Testing for Processing Solutions” provides recommended guidelines for establishing at test plan for solutions used in processing of metals such as electro-polish, anodizing, and conversion coatings and can be applied to other similar processes.

The following six step approach can be used:

1. Determine the variable to be monitored

2. If the variable is an input or process variable, study, and quantify its relationship to the process outputs.

3. Establish the optimal process limits to be applied. In most cases this should be done using process data, to best ensure the limits are not too wide to allow a non-conformance.

4. Establish the adjustment to be made when the limit is reached. For example, this may be to adjust towards a lower limit, or an optimal setting, or in the case of a cutting tool, replace it. This reaction will be documented in the Control Plan and process instructions.

5. Operate the process and plot the measurements

6. If the process limit is reached, adjust/set the process (see step four). Confirm the adjustment has had the desired effect. If so continue. If not take action to understand why.

Figure 2.3-1 demonstrates how a chart of this type may be used. The process drifts upwards so a lower limit is not discussed within this example (for simplicity). It may however be wise to have one to mitigate other risks.




Figure 2.3-1 – RUN CHART WITH NON-STATISTICAL LIMITS

Process improvements can be made using the data from the run chart, for example in the following ways:

• Use process data and related process output to determine tighter reaction limits

• Incorporation of automatic adjustments to the process to tighten the adjustment interval. This will decrease the spread between the limits.

• Make changes to the process or tools that decrease the rate of change of the process variable being controlled.

• Optimise the initial location for the process to increase the time between adjustments.

Features controlled in the way described should typically have a relatively flat ‘loss function’ when compared to the cost of reset or adjustment. The design authority should be consulted where implications of process drift is not understood.

Process Capability

Processes with systematic drift and infrequent ‘large adjustments’ may produce distorted capability analysis. There are two reasons for this.

1. The within subgroup range is typically small relative to the overall variation, resulting in Cp metrics being overly optimistic and not representative of the spread of the process.

2. The distribution of the data may not fit a distribution well enough to make accurate capability predictions. Both Cp and Pp derived capability may be inaccurate and alternative methods (e.g., Non-normal methods such as Johnson Transformation, Box-Cox Transformation (see 4. Guidance for Non-Normal Data) may be required. If these methods do not help then the process performance may need to be characterized by other means.

201 81 61 41 21 08642

1 0.075

1 0.050

1 0.025

1 0.000

9.975

9.950

Index

Dia

met

er

USL = 1 0.065

LSL = 9.935

Process Limit = 1 0.04

Process set-point = 9.96

set-point'is reset to 'processreached processWhen limit is

Diameter




2.4. Pre-Control Charts

Background

The use of Pre-Control dates back to the 1950s when it was developed by an employee of the Rath and Strong consultancy group. The merits of its use are often debated, with some favoring and some opposing its use. There are definitely valid arguments for and against which should be considered.

Pre-Control is a method for monitoring and controlling the process within specification limits. It may be particularly useful when applied to process (outputs or parameters) that have a tendency to drift but for which the process is not overly sensitive to small changes. For example, a measurement taken on a ground feature where the grinding wheel wears over time.

Pre-Control may also be useful where it is important to maintain a capable process centered or ‘on target’, when detection of process ‘special causes’ are less important.

Pre-Control uses a chart that monitors items by classifying the measurements into colored zones (Red, Yellow, or Green). Decisions are made whether to adjust or stop the process based on where in these zones the measurements lie.

The advantages of Pre-Control are its simplicity and that it drives a behaviour towards on-target thinking.

NOTE: It is commonplace for the bands to be set as follows (see Figure 2.4-1):

• Green – the central 50% of the tolerance band (or 50% tolerance around a specific target)

• Yellow – outer quartiles (or remainder) of the tolerance band.

• Red – outside the tolerance.

Where tolerance is unilateral the chart will have a single green, yellow, and red zone (see Figure 2.4-2).

Method

Following setup, a qualification phase runs according to a predefined ruleset to ensure the process is ‘on target’. Typically, qualification is passed after five consecutive units are produced in the Green zone.

3 styles of Pre-Control exist:

1. Classical Pre-Control: Rules based around sampling two consecutive items periodically from a production run:

• Single item in Yellow – continue to run (but check subsequent item)

• Both items in Yellow – stop and investigate. Correct the process

• Single item in Red – stop and investigate. Correct the process

2. Two Stage Pre-Control: based on a single item being sampled periodically.

• A single measurement in the yellow zone triggers measurement of additional items.

• A single Red will trigger process to be stopped and corrected.

3. Modified Pre-Control:

• A standard control chart with colored zones applied as described for Classical Precontrol (but to control limits, not tolerances).




With the exception of modified Pre-control, the limits and rules are not statistically derived. Opponents argue there is a risk of process tampering (over-control), if applying Pre-Control to an incapable process; or missing special causes that would be detected by statistical control charts. It is therefore not advisable to use Pre-Control on processes with poor capability or in situations where small changes in process need to be recognized.

Figure 2.4-1 – PRE-CONTROL CHART FOR BILATERAL TOLERANCE

Figure 2.4-2. – PRE-CONTROL CHART FOR UNILATERAL TOLERANCE

NOTE: If analyzing the capability of a process that uses Pre-Control methods, a statistical control chart should be constructed to ensure the process is stable prior to analysis of capability and communication of capability indices such as Cp/Cpk.

Despite the concern of an unstable process on capability, a measure of goodness such as extended period in Green zone on a Pre-Control Chart may serve as satisfactory evidence of capability to meet customer requirements if the customer permits this. This is more likely for minor characteristics than for KCs or special characteristics such as those categorized as Major or Critical.

For further reading on the subject of Pre-Control refer to Implementing Six Sigma (2nd Edition) – Breyfogle 2003. ISBN 0-471-26572-1)

Pre-Control Example:

An aerospace manufacturer produces a Fuel Air Bracket (see Figure 2.4-3) with a key feature having an engineering tolerance of 0.386 +/- 0.005 inches. The central 50% of the total tolerance (+/- 0.0025 inches) defines the green zone).

Figure 2.4-3 – FUEL AIR BRACKET EXAMPLE

KEY




The engineer defines the zones on the Pre-Control chart. The edges of the green zone are known as Upper and Lower Pre-Control limits (UPC and LPC).

UPC limit = 0.386 + 0.0025 = 0.3885 inches

LPC limit = 0.386 - 0.0025 = 0.3835 inches.

The control method selected is two stage Pre-Control.

Set-Up Procedure

Following successful setup the process operator runs five parts and records the dimensions of the features being controlled. If all five parts fall within the green zone on the Pre-Control chart (UPC = 0.3885 inches and LPC = 0.3835 inches) the setup is judged to be targeted properly and sample measurements are taken at a frequency of 20% (check every 5th part). This measurement frequency is for the purpose of maintaining process control, and does not relate to product inspection frequency.

Executing the Pre-Control Monitoring Technique

The 10th piece comes up for inspection. It has a measured value of 0.387 inches. This is within the Pre-Control (UPC and LPC) limits, and the operator continues with production. The next piece to be inspected is the 15th. Its measurement is 0.3854 inches, well within the Pre-Control limits so the operator continues. The 20th part measures 0.3892 inches. This value is outside the UPC limit. The reaction plan referenced in the Control Plan determines that the operator now measures the next part produced, in this case the 21st. This part measures 0.3867 inches, again outside the UPC limit. The operator stops the process and investigates according to the prescribed reaction plan.

Pre-Control Rule 1: If the measured value is within the green zone (Pre-Control limits UPC and LPC) the operator may continue to check every 5th part (apply a 20% monitoring frequency).

Pre-Control Rule 2: When two consecutive measured values fall outside the same Pre-Control limit (UPC and LPC), the operator should react making an appropriate process adjustment. The reaction plan reference in the Control Plan (refer to AS13004) should describe the actions required.

Pre-Control Rule 3: When one measurement violates one Pre-Control limit and the following part violates the opposite Pre-Control limit, the variability may have increased. The operator should investigate the cause engaging support if needed (e.g., Quality/Manufacturing Engineer). The reaction plan referenced in the Control Plan (refer to AS13004) should describe the actions required.




2.5. Life/Usage Control

Processes may have factors that are dynamic in nature and change through use or over time. Such processes may require control methods that prevent the process (or its factors) reaching a condition that will adversely affect the product of the process. Such controls can be placed on, e.g. chemicals, wearable items such as cutting tools, and other consumables.

The control criteria for life/usage controls may be defined in many ways. Control is often not simply a question of ‘how old’. Examples of control criteria are: number of parts processed, total running time, number of cycles, once opened use by date, weight of parts processed, and surface area processed.

Examples of control application include:

• A cutting tool has a maximum operating time. The tool life is recorded on a machine readable chip. The machine program includes code that checks the life of the tool prior to use. When cutting tips are replaced and the tool is set a pre-setting operation resets the readable chip to zero.

• A peening operation has media that is controlled based on the total equipment running time. A timer is installed on the equipment to indicate how close the process is to a media change. In addition to this method of control, the process also has assessment for media quality and uses test pieces to qualify the process for correct operation.

• The concentration of a chemical etch bath is routinely maintained with an auto-dosing system. However once a month the entire system is emptied, cleaned out, and refilled. To keep the planning of this control simple this is done at a defined time regardless of use – for example the morning of the first Monday in every month.

A life/usage limit may also incorporate a check and reset. For example a wearable item may be tested after a number of cycles and found to have not reached a point where change is required. The tool may be returned for use for a defined number of cycles. It should be noted that this does not imply the tool will be run to the point of failure.

The life/usage limits should ideally be determined to maximize the process quality. Statistical studies and experiments will allow the life to be optimized for other factors such as cost. These studies may be performed on test pieces and scaled to the production process. The life/usage limits should be validated however usually at process qualification

NOTE: These guidelines and examples do not replace specific process standards or customer requirements that may exist to govern the life/usage controls.




2.6. Control Charts for Attribute Data

Attributes are characteristics, or conditions characterized as present or not-present or counted. A number of charts may be used depending on the attribute being studied.

NOTE: Process control via attributes is less effective than variable methods. Some checking methods may provide attribute data despite being variable in their nature. An example is hole size, that may be checked via variable methods or attribute (e.g., plug gauge). If an attribute method were selected based on its speed and simplicity, it should be on the basis that the process is proven capable, because an attribute go/no-go gauge will not give early warning of emerging issues, the way a variable gauge does. A robust control strategy in the case of hole size may be to use a variable tool measurement device such as a presetter to assure the quality of the tool, and an attribute style plug gauge as a quick conformance check but with a periodic sample taken from production for variable measurement.

Figure 2.6-1 and Table 2.6-1 outline the basis for attribute control chart selection.

Figure 2.6-1 – ATRIBUTE CONTROL CHART SELECTION




Table 2.6-1 – ATTRIBUTE CONTROL CHARTS

Scenario When to use Control type (which chart) Example

A process that observes discrete values, such as pass/fail, go/no-go, present/absent, or conforming/ non-conforming. For example a circuit card could consist of a number of solder joints that either conform or do not conform to a set standard

Appropriate: When it is important to control the number or % of defects over a given time period, lot to lot, or unit to unit such as measuring improvement over time, when go/no-go gauges are employed or when visual inspections are used. Not Appropriate: Cannot be used for establishing process control or process capability in the same way as variables data due to the scale not being continuous. Measures of performance and stability can be undertaken with a view to directing improvement activities but true process control needs to be done through process variables, inputs, and foundational activities Not appropriate for rare events.

P-chart Plot the percent defective – classifying product as good or bad with changing or constant subgroup size

Plot the monthly percent defective rate of a critical supplier; plot the On Time Delivery performance of a critical supplier

NP-chart Plot the number defective – classifying parts as good or bad with constant subgroup size

A machining cell produces fuel control valves in standard lot sizes of 50. Final Inspection performs a 100% inspection of the product and plots the number of valves that are determined to be nonconforming.

C-chart Plot the count of defects based where the same area of opportunity (constant subgroup size) exists

An aerospace manufacturer produces one type of heat exchanger for a customer. After vacuum braze a leak check is performed. A c-chart is used to plot the number of leaks requiring weld repair.

U-chart Plot Defects Per Unit (DPU) based on counts and varying or constant area of opportunity (changing or constant subgroup size) the defects come from

An aerospace manufacturer operating Production Part Approval Process (PPAP) tracks the DPU on a monthly basis for all the inspected PPAP packages. An accompanying Pareto Diagram suggests the categories driving the DPU rate are poor PFMEAs, part marking errors and poorly written Control Plans. Projects are established to address these issues in order to reduce the overall DPU rate shown on the u-chart.




Examples:

P Chart Example:

Figure 2.6-2 – P CHART OF DEFECTIVES

Example: the non-conformities from a series of batches of 50 parts are monitored by the manufacturer on a P-Chart (Figure 2.6-2). The manufacturer observes an overall defective rate of 2.2%. The manufacturer concludes from the control chart that – despite the variability from batch to batch - the rate of defectives is statistically stable over time.

Figure 2.6-3 – P CHART WITH VARYING SAMPLE SIZES

2825221 91 61 31 0741

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UCL=0.08423

LCL=0

P Chart of Defective(%)

34312825221 91 61 31 0741

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Sample

Prop

ortio

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_P=0.8873

UCL=0.9429

LCL=0.8317

1

11

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1

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1

Tests are performed with unequal sample sizes.

P Chart of % Yield




Example: A manufacturer monitors the yield % in their goods produced per week on a P Chart (Figure 2.6-3). The weekly output varies. The manufacturer concludes that the process yield is not stable over time and seeks to understand the cause of the ‘bad’ weeks.

C Chart Example:

Figure 2.6-4 – C CHART

Example: A manufacturer produces a similar quantity of product each day. The number of defects noted from a visual inspection area is plotted on a C Chart (Figure 2.6-4) in order to understand the process performance and behaviour over time. In this case the supplier notes a run of improved performance between days 12 and 22, and an increase in defects on day 30. In reaction to the defect rate on day 30 the manufacturer launches a problem solving activity.

NOTE: The use of nP charts and U charts are not illustrated in this document. Implementing Six Sigma – Breyfogle 2003. ISBN 0-471-26572-1 may be referred to for explanation and examples of their use.

The tests for special causes of variation for attribute control charts are as follows:

• One or more points beyond a control limit

• A run of eight or more points on the same side of the center line

• Six points in a row increasing or decreasing

• Fourteen points in a row alternating up and down

It is considered good practice to use a Pareto chart to support attribute methods to allow further prioritization and insight on the defects/defectives within the attributes plotted.

Use of variable methods for attributes -

In some scenarios, attribute data may be monitored quite adequately using variables control charts. For example the Right First Time measure of a manufacturing operation whilst based on an attribute (good/bad), may be expressed as a ratio and plotted on a simple individuals control chart. In many cases an Individuals chart is simpler to interpret and construct than attributes charts. Also of consideration is the sample sizes used, that when large may result in tighter

2825221 91 61 31 0741

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1

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22

C Chart of Visual defects per period




control limits that result in the majority of data showing as ‘out of control especially when defective items occur naturally in clusters. The individuals chart may help put the process in a better perspective.

A note on rare events –

For rare/infrequent events, attribute control charts can give less definitive results. The absence of events/defects/failures for example will have an adverse effect on the control limits and averages. In these cases a time between failures may be a more useful measure to track. Mean Time Between Failure (MTBF) is a commonly used measure of equipment reliability for example.

Figure 2.6-5 – C CHART

Example – A manufacturer plots the failures of a machine tool, counting how many failures were experienced over a 100 day period (Figure 2.6-5). The chart is not very informative.

91817161514131211 11

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C Chart of failures per day




Figure 2.6-6 – INDIVIDUALS CONTROL CHART

Example: The manufacturer plots the time between failures for the data on an Individuals chart (Figure 2.6-6). The chart is much more informative. The average days between failures of 7.7 days and the control limits can help guide the manufacturer on equipment reliability and maintenance activity planning.

1 0987654321

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Indi

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alue

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UCL=16.27

LCL=-0.87

Individuals chart of time between failures




2.7. Visual Process Check & Checklist

A visual process check provides positive confirmation of goodness either prior to allowing a process to run, or during its operation.

The process checks need to become part of routine operation. The personnel conducting the check will ideally understand the importance of the check and also understand the reaction if the check fails against the criteria. In many cases the check will confirm that a particular step of the sequence has been done correctly.

The checks may be conducted by a single person, however on important items or high consequence failure items the method may use two persons who jointly confirm that the correct condition is achieved. An example of this approach is the standard pre-flight checks that are undertaken by pilot and co-pilot when preparing for a flight. One pilot calls out the check, the other performs the check and confirms as correct, and then the first records the check on a checklist before proceeding.

An example is shown in Figure 2.7-1

To increase robustness, a “double scrutiny”, and/or “buddy check” may involve two personnel to positively confirm an action or result of a check; or the check may be performed by someone independent of the operation.

A single person check may have some inherent risks of error. A preferred approach is automation or error proofing devices, (see 2.1 – Error/Mistake Proofing). Prior to finalizing the check it is advisable to confirm the PFMEA risk level – as the method of control relates to the detection score in the PFMEA (refer to AS13004).

Pre-Operation Process Checklist Note to operator: Use this checklist prior to execution of the process operation and sign off each item below.

Part No: 123456-78 Process operation number: 110

Run date: 08/12/2016 Process step name: Machine air holes in Fuel/Air bracket

Check item number

Check item Result of check (Pass/Fail)

Reaction (if Fail) Sign off (initial and date)

1 Health/Safety check Stop and isolate equipment. Contact cell leader

2 Work instructions are latest version Contact Manufacturing

Engineer – obtain instructions

3 Machine asset care checks complete and correct Raise issue with cell leader

4 Gages in calibration Contact Quality engineer

5 Fixture damage check Contact Manufacturing Engineer

6 CNC programme correct (as per instruction) Contact Manufacturing

Engineer

7 FOD check Raise issue with cell leader

8 Etc

Figure 2.7-1 - PROCESS CHECKLIST FORMAT EXAMPLE




2.8. First Piece Check

The objective of a first piece check is to validate the set-up and quality of a process prior to the full production run. Alongside other controls it serves to verify and confirm the integrity of the production system (man, machine, fixture, tool, NC program, etc.) at a point in time, and hence to avoid economic damage of non-conformance (through timely action to ensure process conformance).

Prerequisite to a first piece check should be the adherence and confirmation that all other foundational control requirements are met (e.g., calibration, machine tool diagnostics, tooling within prescribed life limits, acceptable parameter settings, consumables level, etc.) typically approved through positive confirmation (see 2.7)

As a general rule, all manufacturing processes can be subject to first piece inspection.

It may be called out in a control strategy:

• Whenever a new production lot is started

• Following maintenance/repairs of measurement systems and production equipment, as well as after software updates of production equipment control systems

• At a defined interval (e.g., at the start of each shift)

• When tools used to produce the component contour are replaced, (e.g., diamond rolls, profiled grinding/cutting wheels, etc.)

First-piece checking/inspection may be independent from the production method in a number of ways:

• Inspection by an operator other than the person having performed the operation (two person rule); thus avoiding risks due to bias and other human factors

• Inspection using another inspection tool or inspection method (where possible); thus avoiding/highlighting measurement discrepancies

If independent inspection is to be used the method should be at least as good as the production method, free from bias and have adequate resolution to make the decisions valid. Tighter limits may apply to first piece checks and this should be considered when evaluating such measurement equipment.

In order that the process is correctly judged as sufficiently good to continue additional criteria may be applied. Such criteria should have a rational and/or scientific basis for its application. For instance a process capability study or designed experiments.

Example 1: a machined dimension with a known adequate level of capability, achieved at first part check may be deemed sufficient if within 50% of process tolerance; a measurement close to normal limits of operation may result in adjustment and further measurement to bring the process on target.

Example 2: a process with a tendency towards upward drift may have a zone in the lower region of the specification band that provides a standard for process acceptance of the first item. Continued conformity as the process drifts naturally through use is provided by a tool life/usage control. The zone has been determined through a previous tool wear study. If the measurement is outside this zone, the operator refers to a process guidance document (referenced in the Control Plan) to determine appropriate action (e.g., tool replacement, or adjustment to the tool life/usage standard).

A first piece check strategy may extend to multiple parts – depending on process risk and behavior. For example a very large batch of parts, a rapidly cycling process or high cost parts may require inspection of the first five parts (Pre-Control may be beneficial (see 2.4))

It is good practice to require formal record keeping for approval of first piece checks (e.g., a signature, and/or countersignature/ inspection report).

NOTE: The method should be used in conjunction with other methods to make the control strategy robust to variations that may occur as production continues.




NOTE: First Piece Check should not be confused with First Article Inspection (FAI). For further information in FAI, refer to AS9102.

2.9. Test Piece Evaluation

Some characteristics and properties that are created or changed through processing may not be directly measurable other than through destructive or damaging testing. Use of test pieces processed alongside the product may help to determine the result of the process and also its stability. These test pieces are tested following processing to validate the products of the process and/or confirm the effectiveness of the other process controls.

Such processes should be highly controlled through process parameter controls and monitoring and may be categorized as ‘fixed processes’ or ‘special processes’ often with regulatory control requirements.

A test piece/coupon should be to a defined standard (thus minimizing the variation in the test material itself).

In some instances a test piece may be operated within a first piece check to qualify the process setup prior to the full production run (see 2.8).

Examples of processes that use representative test pieces include the following:

• Heat treatment operations

• Surface treatment operations such as shot peening

Examples of evaluation of test pieces include:

• Mechanical property testing using test bars

• Surface contamination coupons in heat treat or thermal processes

• Coupons determining material removal rates in etch and electro-polish processes

• Cast coupons determining chemical analysis of parts from melts

• A forging that has extra material outside the finished part envelope that will be removed for testing

Once a result has been obtained from a test piece the result can be analyzed with a variety of process control tools such as control charts (variable and attribute) and run charts.

Acceptance of process results by the use of test specimens or coupons is typically approved and agreed to by the customer.

NOTE: There may be regulatory, customer, product specifications, and other requirements that address the extent to which test piece evaluation, or requirements are permissible and established as part of process qualification. Equivalence between test piece and physical product should be understood.




3. PROCESS CAPABILITY INDICES

Process Capability is the ability of a process/product to consistently meet a specification or customer requirement.

Various indices are computed to assess the Process Capability of a given product characteristic.

The definition and calculation of these is often misunderstood and thus misinterpreted. The methods described within this section are based on recognized industry methods. Software tools such as Minitab calculate capability in line with these methods and additionally cater for some specific scenarios that exist such as batch processing where information may be sought about the capability both within and between batches of production.

Process Capability can be assessed for Variable and Attribute data.

3.1. Fundamentals for Variable data

At the heart of capability for variable data, is the need to manage process variation and location to align with customer specification to ensure that requirements can be continually met.

Variability of the process is calculated through statistical methods; these methods aim to anticipate the total process variation rather than just the range seen in the data collected for the capability study. A process spread of 6 standard deviations is used to represent this spread. This 6 standard deviation range theoretically covers 99.73% of the area under a normal distribution curve. Data is assumed to be normally distributed (symmetrical, bell shaped).

Many processes have a tendency – even naturally – to periodic drift or shift. Therefore borderline capability is not desirable for either supplier or customer. A capability of 1.33 is often seen as a minimum to assure continued conformance while allowing for minor process drift. However depending on the process, a higher level of capability may be required. Products with large numbers of characteristics that cannot be controlled independently may require some additional margin for small drifts that may occur through production.

For any capability calculation to be reliable, it is important that the process be in a state of statistical control thus behaving in a predictable manner - otherwise any perceived goodness may be short-lived. It is possible for a process with a ‘good’ capability index to be producing non-conforming product if a state of control is not reached. Process stability is therefore a prerequisite to capability calculation.

Capability indices, Cp, and Pp

Cp and Pp indices are simply a ratio of specification width to process variation thus calculating the ‘potential of the process if centered’. The indices increase if variation is reduced. A Cp or Pp of exactly 1.0 indicates that 6 standard-deviations of process variation match the width of the specification. Such a process if centralized within the specification would be intolerant to even minor drift over time. Not an ideal situation.




Figure 3.1-1 – PROCESS CAPABILITY INDEX Cp/Pp

The process shown in Figure 3.1-1 has a Cp or Pp>1. The process is less variable than allowed by the specification.

Cp and Pp use different methods for estimating process variability. Cp uses ranges of the data within subgroups (or difference between individual values) to estimate the process variation. A statistical constant d2 is used to adjust for the subgroup size. This method estimates the standard deviation of the process rather than calculating by the more involved ‘root sum of squares’ method (which is used to calculate Pp).

The average range over d2 method generates the estimate denoted by sigma hat (Eq. 1).

(Eq. 1)

The root sum of squares method generates the standard deviation denoted by s (see Eq. 2).

𝑠𝑠 = �∑ (𝑥𝑥𝑖𝑖 − �̅�𝑥)2𝑛𝑛𝑖𝑖=1𝑛𝑛 − 1

(Eq. 2)

LSL USL

Tolerance = USL - LSL

6σ




Cp is typically used to assess short term (within subgroup) capability whereas Pp is used to assess longer term (overall) capability.

These are incorporated into the formulae (Eq. 3 and Eq. 4) as follows:

(Eq. 3)

(Eq. 4)

For a stable continuous process behaving in a random manner, Cp, and Pp calculations can be expected to deliver similar values.

Capability indices Cpk & Ppk

In order to estimate the likely performance - against a specification - of the process Cpk and Ppk indices are used. These indices are similar ratios to Cp and Pp but additionally take into account the process location.

Cpl & Cpu, and Ppl & Ppu measure capability against each of the specification limits. The ‘l’ and ‘u’ indices will be equal only if the process is centered. The Cpk or Ppk is the smaller of the upper and lower values.

The ‘l’ and ‘u’ indices can be used to determine how the process is located relative to specifications, however a visual assessment of the capability histogram is usually preferred to understand this situation.

The formulae for these indices is shown (Eq. 5 to Eq. 10)




(Eq. 5)

(Eq. 8)

(Eq. 6)

(Eq. 9)

(Eq. 7)

Eq. 10)

Figure 3.1-2 – ELEMENTS OF PROCESS CAPABILITY INDEX (Cpk/Ppk)

The process shown in Figure 3.1-2 has a Cp of approximately 1.0 but due to being too close to the upper specification limit (with the tail of the distribution outside it) the Cpk is <1 If the process average is outside the specification, the Cpk will be negative.

NOTE: It will not be possible to calculate Cp or Pp indices for processes with unilateral (single sided) tolerances as the tolerance width cannot be defined. However Cpk and Ppk can be calculated from the Cpl/Ppl or Cpu/Ppu (whichever can be calculated).

LSL USL

Distance to LSL Distance to USL

3σ 3σ




Table 3.1 provides guidance on approximate expected performance levels at various levels of Process Capability. The performance rates assume a process perfectly centered between two specification limits. This table assumes a normal distribution.

CPK %YIELD REJECT RATE (Parts Per Million)

0.5 86.64 133614 0.67 95.45 45500 0.83 98.75 12418 1.00 99.73 2700 1.16 99.95 465 1.33 99.994 63 1.50 99.9993 6.8 1.67 99.99994 0.6 1.83 99.999996 0.04 2.00 99.9999998 0.002

TABLE 3.1 – EXPECTED PERFORMANCE FOR Cpk

For the Cpk and Ppk calculations in this section, the process is assumed normally distributed. If the data are non- normal (skewed for example) alternative methods can be used (see Section 4 – Guidance for Non-Normal Data)

NOTE: The descriptions in this section are fundamentals. Some additional methods for specific situations are described in Section 6 – Scenarios requiring specific analysis methods.

Some characteristics may benefit from being ‘targeted’ to a particular nominal value. These are usually characteristics that influence performance of the product, that have a loss associated with deviation from target even within the specification. These characteristics may have additional requirements communicated by the customer. For these types of characteristics it is important to examine the location of the process relative to this target. It should be noted that due to the calculation methods, high Cpk/Ppk indices do not necessarily imply the process is on target as their calculations use the distance of the process mean to the specification limits. The nominal location is not considered in the calculation.

A target based process capability index (Cpm) may be used in these situations. Cpm is not covered in this standard but is described in statistical texts and provided in statistical software applications.

3.2. Process Stability in Practice

Whilst a state of perfect statistical control is desirable, it is uncommon for manufacturing processes to maintain complete statistical control over long periods. Failure of tests for special causes can occur despite the process being reasonably stable. The important thing is that the capability metric does allow reliable prediction of future performance.

Therefore some process capability analysis on processes which contain minor out of control points may be necessary on occasions where out of control conditions are not considered to be of practical significance (looks at whether the difference is large enough to be of value in a practical sense).

Examples include rare instances of out of control conditions and instances where control limits are broken by negligible amounts.

Processes with points well beyond the control limits (such as beyond 4 sigma), should not be considered stable for capability calculations.

To mitigate the effect an out of control process can have on the capability calculation it is recommended to calculate Ppk, since it includes all sources of variation and thus be a more reliable statistic than Cpk.

In situations such as these, the advice of a process control specialist should be obtained.




In figure 3.2-1 there are several points beyond the control limits but looking at the capability histogram the control limits are far from the spec limits, so using practical considerations the process control specialist could consider it stable and recommend use of Ppk.

Figure 3.2-1 – High capability – practically stable




In figure 3.3-2 there are two points shown slightly beyond the control limits. The process control specialist could consider it stable and recommend use of Ppk. In the capability histogram the red “overall” curve is a better fit than the black “within” curve, considering the most important region to the right (closest to the spec limit), demonstrating the value of using Ppk over Cpk.

Figure 3.2-2 – Use of Ppk




In figure 3.2-3 there are points that are well beyond the control limits, so this process cannot be considered stable and the capability values displayed are not a good prediction of future performance.

Figure 3.2-3 – Points well outside control limits

3.3. Process Capability for Attribute Data

Process and product attribute data differs from variable data in that measurement is not done on a continuous scale (as is usually the case for geometric requirements). For attribute data the use of indices such as Cpk or Ppk do not make sense. However the stability of the process can be demonstrated by control charts specific to attribute data, and the performance against standard can be quantified in a number of ways.

It is important that the process is stable (in a state of statistical control). This is done using the appropriate attribute control chart.

It is also important when measuring performance that the rate or proportion of defects has reached a level where it has stabilized and is accurate. This is done by plotting the cumulative defective proportion. As more data is collected the cumulative proportion should stabilize (flatten out) indicating enough data has been collected for the capability assessment to be reliable.

The specific type of capability analysis will depend on the nature of the data:

• When examining performance, where the measure is proportion defective, the data is expected to follow a binomial distribution. A binomial capability study is appropriate using a P or nP chart to assess the capability.

• If the data is measuring the number of defects per item (or group of items) the data is expected to follow a Poisson distribution. A Poisson capability study is appropriate using a C or U chart to assess the capability.




Figure 3.2-1 – BINOMIAL CAPABILITY STUDY

Figure 3.2-1 shows a Binomial Capability Study. The proportion defective from 35 batches of parts. The proportion defective is stable and is running at 1.19%.

Figure 3.2-2 – POISSON CAPABILITY STUDY

Figure 3.2-2 shows a Poisson Capability Study. The capability is expressed as Defects Per Unit (DPU). The capability is 1.74 DPU (represented by ῡ on the U chart shown).

NOTE: For the analysis to be effective there are some underlying assumptions with regard to the distribution of defectives and defects within the sample. These assumptions are covered in various SPC texts. In summary of these, the user should ensure defectives are random and independent (not occurring in clusters). And defects or defectives within a sample subgroup are not so infrequent as to make the analysis of stability meaningless. If this cannot be

34312825221 91 61 31 0741

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UCL=0.05391

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Upper CI: 2.4220

%Defective: 1 .1 9Lower CI: 0.77Upper CI: 1 .75Target: 0.00PPM Def: 1 1 905Lower CI: 771 9Upper CI: 1 7524Process Z: 2.2602Lower CI: 2.1 078

(95.0% confidence)Summary Stats

Sample

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Binomial Process Capability Report for DefectivesP Chart

Cumulative %Defective

Binomial Plot

Histogram

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Mean Def: 1 .7429Lower CI: 1 .3331Upper CI: 2.2388Mean DPU: 1 .7429Lower CI: 1 .3331Upper CI: 2.2388Min DPU: 0.0000Max DPU: 5.0000Targ DPU: 0.0000

(95.0% confidence)Summary Stats

Sample

DPU

420

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Expe

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Def

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543210

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Poisson Process Capability Report for DefectsU Chart

Cumulative DPU

Poisson Plot

Histogram




avoided then other approaches can be used for rare events (see 2.6: Note on Rare Events). Subgroup size is an important consideration to ensure the assumptions are met.




4. GUIDANCE FOR NON-NORMAL DATA

The capability methods discussed for variables data (in section 3.1) are based on an assumption that the underlying data distribution is Normal (i.e., follows a Normal Distribution Curve).

Where data fails to meet this assumption, capability indices can lead to wrong conclusions. For example a predicted defect rate may be inaccurate, or a Cpk/Ppk level may be judged to be adequate when it shouldn’t be. In extreme cases a seemingly adequate Cpk may produce a large proportion of defects. Figure 4-1 shows data following a non-normal distribution. There is a discrepancy between the observed level of non-conformance (4%) and that expected based on an analysis that assumes normality (0.63%).This may lead to incorrect estimates for cost of poor quality, factory flow, capacity and lead time, and related planning.

Figure 4-1 – A NON-NORMAL DISTRIBUTION

Causes of non-normality include:

• A natural skew caused by a boundary condition that cannot be exceeded (e.g., flatness, roundness, runout)

• Data are calculated from two (or more) components of variation (e.g., the true position of a hole derived from x and y coordinates)

• A cyclic process behaviour

• A process with a natural tendency to drift

• Selective or biased measurements

• Process instability – lack of control

• Lack of resolution in measurement systems or rounding

• Reworking non-conformances prior to measurement

• Human factors (e.g., purposely stopping at a maximum limit when machining down to a size)

• 2 distributions being present within the data (i.e., bi-modal).

• Biasing the sample of data (e.g., selectively removing parts of certain dimensions)

0.240.1 80.1 20.060.00-0.06

Pp *PPL *PPU 0.83Ppk 0.83Cpm *

Cp *CPL *CPU 0.90Cpk 0.90

Potential (Within) Capability

Overall Capability

% < LB 0.00 * *% > USL 4.00 0.63 0.33% Total 4.00 0.63 0.33

Observed Expected Overall Expected WithinPerformance

LB USL

Process Capability Report for Flatness




5549433731251 91 371

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Indi

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UCL=0.839

LCL=-0.722

5549433731251 91 371

1 .00

0.75

0.50

0.25

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Observation

Mov

ing

Rang

e

__MR=0.293

UCL=0.959

LCL=0

I-MR Chart

0.60.40.20.0-0.2-0.4

Pp 1 .00PPL 1 .12PPU 0.89Ppk 0.89Cpm *

Cp 0.64CPL 0.72CPU 0.57Cpk 0.57


Overall Capability

% < LSL 0.00 0.04 1 .59% > USL 0.00 0.39 4.48% Total 0.00 0.43 6.07


LSL USLOverallWithin

Process Capability Report

5549433731251 91 371

0.30

0.1 5

0.00

-0.1 5

-0.30

Observation

Indi

vidu

al V

alue

_X=-0.0203

UCL=0.1796

LCL=-0.2202

5549433731251 91 371

0.4

0.3

0.2

0.1

0.0

Observation

Mov

ing

Ran

ge

__MR=0.0752

UCL=0.2456

LCL=0

1

11

1

11

1111

11

1

11

1

1

11

1

I-MR Chart

Pp 0.57PPL 0.53PPU 0.61Ppk 0.53Cpm *

Cp 1 .50CPL 1 .40CPU 1 .60Cpk 1 .40


Overall Capability

% < LSL 0.00 5.46 0.00% > USL 3.33 3.33 0.00% Total 3.33 8.79 0.00



Process Capability Report

Some of these should be addressed by investigating the process, measurement system or data sampling issue. However some of these causes are genuine and unavoidable and the analyst will need to find ways of using alternative methods to assess control and capability. Further guidance follows.

Figures 4-2 & 4-3 show the effect on capability analysis caused by a bi-modal process. In this case one with oscillation present between data points. There is a discrepancy between the expected overall and within subgroup capability. Here the total non-conformance estimate may be overly pessimistic. It should be noted that this obvious pattern of behaviour should ideally be recognized in the analysis of the process stability.

Figures 4-2 & 4-3 – A BIMODAL PROCESS DUE TO OSCILLATION

Figures 4-4 & 4-5 show the effect on a capability analysis due to step changes in the process. This should ideally be recognised during a stability assessment. Note that the Cpk index is a misleading 1.4 despite the process generating defects. Because the process is out of statistical control, the value of Cpk is not reliable.

Figures 4-4 & 4-5 – A BIMODAL PROCESS DUE TO STEP CHANGES




Table 4-1 - Describes some of the actions that can be taken in some of the scenarios described in this section.

Table 4-1 – GUIDANCE FOR NON-NORMAL PROCESSES

Scenario Guidance

The process is out of statistical control with no pattern to the data or to the signals of special cause

Capability analysis cannot adequately describe or predict future process behaviour.

Conduct improvement activity, problem solving, and standardization and use process control charts to confirm stability has been achieved before undertaking capability analysis. Consider containment to protect customer.

The process has a natural skew that can be explained either due to a natural boundary or the type of characteristic being measured.

Explore the following alternative methods for capability analysis:

Identify an alternative distribution that is the closest fit to the data and conduct a non-normal capability analysis based on that distribution. (see 4.2.1)

Use data transformation methods (see 4.2.2)

The process has a ‘batching effect’ and exhibits a variation due to within batch variability and a step change due to variation from batch to batch.

Confirm the cause of this behaviour and confirm it is a natural and unavoidable consequence.

If the batch averages are stable (when viewed on an I-MR control chart) a Between/Within capability analysis may be possible (discussed in 6.1). This type of analysis considers both sources of variation to make more accurate prediction of conformity level. Data should be taken from a number of batches to ensure the process location is of adequate precision.

Bimodal data due to oscillation or due to differences in tooling, machines, etc.

Understand the cause of the bimodal process behaviour and attempt to limit it. (e.g., two machines may be aligned differently – calibration may rectify this).

In the event that eliminating the source is not possible, the data may be analyzed by population group to assess capability (such as each machine analyzed separately).

Note: For certain characteristics variations of this nature can affect product performance. The customer may be consulted to confirm that any such behaviour is not detrimental to the function of the product.




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Assessing Normality

Assessing a process distribution is easily performed using computer software applications. The examples used within this standard are created with a software application called Minitab.

A normal probability plot (for example Figure 4-6) helps if the data is a good fit to the selected distribution. The data is plotted against a line of best-fit and its confidence interval and an assessment made. If the data deviates significantly from the interval then the population is judged to be non-normal. If nearly all the data lies within the confidence interval a capability analysis using the selected distribution would be appropriate.

In addition to the visual assessment, statistical software applications include statistical tests such as the Anderson Darling which assesses normality and generates statistics such as a ‘p-value’. The p-value, in this case, is the probability of getting a result that is more extreme than the ones in your sample, if the distribution is actually normal. It is commonplace to reject normality if the p-value is less than 0.05 (this threshold allows a 5% chance of accepting non-normality incorrectly – an error known as alpha risk).

Figures 4-6 to Figure 4-11 show some possible outcomes of this analysis.

Figures 4-6 & 4-7 – NORMALITY ASSESSMENT (PROCESS APPROXIMATELY NORMAL).

A process following an approximately normal distribution is shown in Figure F7. When plotted on a probability plot (Figure 4-6) most data points fall within the confidence interval. P-Value 0.228 indicates support for normality since it’s greater than .05

Figures 4-8 & 4-9 – NORMALITY ASSESSMENT (NON-NORMAL PROCESS)




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A non-normal distribution is shown in Figure 4-9. When plotted on a normal probability plot (Figure 4-8) the data does not follow the line of best fit and the data has a knee and goes beyond the confidence interval. The user would infer from this that the data is non-normal. Additionally the p-value can be seen to be much lower than 0.05. A capability analysis with the assumption of a normal distribution should not be performed. Distribution identification or data transformation methods would be appropriate.

Figure 4-10 & 4-11 – NORMALITY ASSESSMENT (BIMODAL DISTRIBUTION)

A bimodal set of data is shown in Figure 4-11. When plotted on a normal probability plot (Figure 4-10) the data deviates completely from the line of best-fit and two clusters are clearly visible. The user would conclude that the data is non-normal. A capability analysis with the assumption of a normal distribution should not be performed. This type of behaviour should be visible through simpler histogram or control chart analysis, and an approach may be decided upon without the need for further and more complex distribution identification or data transformation.

4.1. Using Control Charts with Non-Normal Data

Control charts such as I-MR are reasonably robust to slight deviations from normality. However in some cases control charts based on non-normal data distributions can lead to limits that do not accurately represent the natural variation of the process. This results typically in control charts with ‘false signals’ of special causes.

Two common strategies of dealing with this situation are as follows:

Use averages (apply central limit theorem).

The distribution of averages is known to tend towards normality as the sample size increases (known as central limit theorem). If the process is such that items can be subgrouped and averages plotted then this may be adequate to avoid the use of more complex methods. An X-Bar and R chart may be used.

Figure 4-12 shows the effect using a uniform distribution. The distribution of averages becomes normally distributed (and less variable) as the sample sizes increases

Figure 4-12 – EFFECT OF TAKING AVERAGES ON A FLAT (UNIFORM) DISTRIBUTION

Data transformation and transformed limits

In certain cases applying a mathematical transformation to each data value (e.g., x²) may result in the distribution changing shape. If the resulting distribution is approximately normal a regular control chart may be used to assess the stability of the process.

However for process monitoring these transformed values may not make sense to the operator. And if the operator is plotting the chart manually, introducing any calculation into the process adds complexity. It would be most desirable for




the operator to plot the actual measurements. For this to work, the control limits will need to be set in advance by initially transforming a set of gathered data to assess stability and establish limits for the transformed data, then define limits that can be used with the actual untransformed data through a reverse transformation. These limits may then be deployed as a ‘blank’ control chart with a set of appropriate limits that the operator then works to.

NOTE: Alternatively in some situations a simpler method such as Pre-Control may be useful.

The user should consider the benefits of using transformations against the potential for confusion brought about by complexity. Alternative methods may be used if more practical. For more information Statistical Process Control (SPC) - AIAG ISBN 1605341088 may be referred to.

Figure 4-13 shows a non-normal (heavily skewed) process using a regular I-MR Control chart. In this example the lower limit <0 and the upper control limit does not take into account the skewed distribution. This chart would trigger some inappropriate reaction to ‘special cause’ signals.

Figure 4-13 – A NON-NORMAL (SKEWED) PROCESS USING AN I-MR Control chart.

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Figure 4-14 shows a control chart for the process shown in Figure 4-13 but with the data transformed; in this case by raising each data point to the power 0.5, i.e., taking the square root. The transformation parameter (in this case 0.5) is known as Lambda λ. Software can be used to derive the optimal lambda value or other transformation. The process can be seen to be stable – however the data and the Y scale on the chart makes little or no sense to the user.

Figure 4-14 – A CONTROL CHART USING TRANSFORMED DATA

Figure 4-15 shows a control chart using the original measured values. The control limits are derived from the limits based on the transformed data from Figure F14. The upper control limit (UCL) is calculated by reversing the transformation. In this case squaring the limit from the transformed chart (UCL = 0.55982 = 0.3134). The operator may now continue to plot the measured values against this limit and react appropriately to special causes.

Figure 4-15 – A CONTROL CHART OF NON-NORMAL DATA WITH APPROPRIATE LIMITS.

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Control Chart of Flatness (with transformed control limits)




NOTE: A number of transformation functions may be possible. Statistical computer software can identify the optimal transformation to be applied. The examples in this document use Minitab software.

4.2. Capability Analysis for Non-Normal data

A number of methods exist for analysis of non-normal data for capability purposes. Two are described in brief for awareness. For further information a specialist should be consulted.

When these analyses are performed it should be declared in any reports to ensure analysis transparency.

Method 1 – Identify a distribution that fits the data being analyzed.

This method involves using probability plots for a range of possible distributions and finding the distribution with the best fit. The capability will then be calculated using this distribution. The interpretation of probability plots is essentially the same for other distributions as the methods used for assessing normality.

In the example shown in Figure 4-16 the data is not normal but seems to fit three other distributions available. In this example the user continues with a Weibull distribution capability analysis shown in Figure 4-17. Either of the other 2 distributions shown on the chart appear suitable alternatives as the data aligns with their confidence intervals. The user may seek further guidance on distribution selection. Some distributions are known to fit certain scenarios well, as described in Implementing Six Sigma – Breyfogle 2003. ISBN 0-471-26572-1

For practicality this method requires the use of analytical software.

Figure 4-16 – DISTRIBUTION IDENTIFICATION USING MINITAB SOFTWARE

WeibullAD = 0.305 P-Value > 0.250

GammaAD = 0.286 P-Value > 0.250

Goodness of Fit Test

NormalAD = 4.31 1 P-Value < 0.005

ExponentialAD = 0.378 P-Value = 0.682

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Figure 4-17 - PROCESS CAPABILITY ANALYSIS USING A WEIBULL DISTRIBUTION

Method 2 – Apply a transformation then calculate using normal capability methods

If a transformation can be found that fits a normal distribution then methods based on the normal distribution as described in Section 3 can be used.

In the example shown in Figure 4-18 software has been used to perform a Box-Cox transformation on the data. The transformation performed is to raise the data values to power of lambda where λ = 0.26. The transformed data has been checked against a probability plot to ensure it is approximately normal, and then a capability analysis has been performed.

Figure 4-18 – PROBABILITY PLOT OF ORIGINAL DATA (LEFT) AND TRANSFORMED DATA (RIGHT)

0.280.240.200.160.120.080.040.00

LB 0Target *USL 0.3Sample Mean 0.0577495Sample N 100Shape 0.970913Scale 0.0570221

Process DataPp *PPL *PPU 0.73Ppk 0.73

Overall Capability

PPM < LB 0.00PPM > USL 0.00PPM Total 0.00

Observed Performance

PPM < LB *PPM > USL 6650.45PPM Total 6650.45

Exp. Overall Performance

LB USL

Process Capability Report for FlatnessCalculations Based on Weibull Distribution Model

Goodness of Fit Test

NormalAD = 4.31 1 P-Value < 0.005

Box-Cox TransformationAD = 0.383 P-Value = 0.391

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Probability Plot for FlatnessNormal - 95% CI Normal - 95% CI




Figure 4-19 – CAPABILITY ANALYSIS OF TRANSFORMED DATA. THE CAPABILITY IS NOT IDEAL.

Problems caused by Zero values

Zero values can present some problems when conducting certain transformations and alternative distribution analysis (Weibull for example). In this case a ‘data shift’ may be performed. A method known as ‘McAdam’s Zero Shift’ involves adjusting all zero values upwards by 20% of the data resolution.(i.e., if the measurement resolution is 0.0001” substitute all zero values with 0.00002”). The analysis should record that this adjustment has been performed.

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USL* 0.731 424Sample Mean* 0.42862StDev(Overall)* 0.1 30041StDev(Within)* 0.1 34083

LB 0Target *USL 0.3Sample Mean 0.0577495Sample N 1 00StDev(Overall) 0.057041 4StDev(Within) 0.0524398

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Process Data

Pp *PPL *PPU 0.78Ppk 0.78Cpm *

Cp *CPL *CPU 0.75Cpk 0.75


Overall Capability

% < LB 0.00 * *% > USL 0.00 0.99 1 .20% Total 0.00 0.99 1 .20

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Observed Expected Overall* Expected Within*Performance

transformed dataLB* USL*

OverallWithin

Process Capability Report for FlatnessUsing Box-Cox Transformation With λ = 0.26




5. COMMON SOURCES OF VARIATION

Figure 5-1, describes some of the common causes of variation for manufacturing processes. It is not an exhaustive list but may offer some areas of focus when considering a control strategy.

Figure 5-1 – COMMON SOURCES OF VARIATION




6. SCENARIOS REQUIRING SPECIFIC ANALYSIS METHODS

The following section discusses a few situations that are perceived a challenge in certain manufacturing environments. It does not provide an exhaustive list but offers some ideas that may also be transferrable. The examples attempt to improve effectiveness of efficiency of the analysis.

6.1. Assessing Control and Capability of Multiple Variable Features

When dealing with products with groups of characteristics (e.g., patterns of holes) assessing control and capability of each characteristic separately can be both time consuming and runs the risk of missing important aspects of control of the process/product.

The following methods can be used in these situations. They could be modified according to the specific situation. Table 6-1 summarizes the methods and their uses.

Table 6-1 – CONTROLLING MULTIPLE VARIABLES USING AVERAGE AND RANGE CHARTS

Scenario When to use Control type (which chart) Use in monitoring

When multiple identical features are to be controlled (for example a large pattern of holes on a casing)

Appropriate:

This method may be employed when it can be shown that there is a logical rationale for the features to be grouped.

Not Appropriate:

When the features are grouped from a definition perspective, but not from a manufacturing one. For example features produced at different operations.

When the variation within the group of features on a part is roughly similar to the variation between parts an Xbar-R chart may be used. This chart will plot the average of the characteristics on the Xbar chart, and the range within the feature group on the R chart. An example is discussed in 6.1.1

When the variation within the group of features on a part is less than the variation between parts an Xbar-R chart will lead to false signals on the Xbar chart. In this case an I-MR-R/S (also known as a 3 way control chart) can be used. This chart plots the average of the characteristics on the Xbar chart, the moving range between the averages on the MR chart, and the range within on the R chart. An example is discussed in 6.1.2

NOTE: In many cases the Xbar-R chart will not work in practice because the assumption that the variation within and between subgroups is not met. A stable process may appear out of control. Due to the theory that variation in averages decreases as sample sizes increase the Xbar-R chart becomes less useful as the number of characteristics becomes high. In these cases a 3-way control chart is useful.

The Xbar chart shows the trend of averages and special causes relating to them. Signals on this chart should be investigated from a perspective of “a source of variation between averages contributing to the total variation.” For example a setup related issue or machine alignment.

The R chart plots the variation within the groups. Signals on this chart should be investigated from the perspective of “a cause affecting the variation within the group”. For example distortion on a large casing or a misalignment of a pattern of holes where position of the holes is being monitored (and this misalignment causes a systematic pattern such a ‘sine wave’ to be introduced. Also a single outlying characteristic or a shift in characteristics mid-way through the production cycle (for example caused by a tool damaged mid cycle).

The MR chart shows the trend between parts and signals unusually large fluctuations between parts and emerging trends caused by increasing (or decreasing) overall variation. Signals on this chart do no not necessarily result in signals on the Xbar or R charts but may do in certain circumstances.




Examples of analysis

SCENARIO 1 – THE VARIATION WITHIN THE GROUP IS REPRESENTATIVE OF THE OVERALL VARIATION

A product with 20 identical characteristics is analyzed (Figure 6-1) and found to have a level of variation within each part that represents the overall variation fairly well (i.e., the process location does not appear to shift significantly between parts). In this case the control limits on an Xbar-R chart (Figure 6-2) with subgroup size set to 20 (i.e., the number of identical features in the group) provide a good approximation of the natural process variation.

Figure 6-1 – VARIATION WITHIN AND OVERALL IS SIMILAR

Figure 6-2 – XBAR-R CHART PRODUCED FROM DATA FROM Figure 6-1.

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Time Series Plot of Pattern of 20 holes (over 15 parts)

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Xbar-R Chart of Pattern of 20 holes (over 15 parts)




SCENARIO 2 – THE VARIATION WITHIN THE GROUP IS NOT REPRESENTATIVE OF THE OVERALL VARIATION

A second product with 20 identical characteristics is analyzed (Figure 6-3) and found to have a level of variation within each part which does not represent the overall variation well (i.e., the process location appear to shift between parts by a greater amount than the change from feature to feature within the part). In this case the control limits on an Xbar-R chart (Figure 6-4) become too narrow to represent the natural variation between parts and in this case all the points on the Xbar chart fall outside the limits. This is due to the limits on the Xbar chart being derived from the range within the subgroup (in this case set at 20 to demonstrate the effect). This chart will be of no use in practice.

An I-MR chart also is of little use (Figure 6-5) due to limits being based typically on short term ‘point to point variation.

A three way style control chart shown (Figure 6-6) is more useful. The R chart allows the user to examine the variation within the part. The MR chart shows the state of control between part averages that allows the user to detect any unusual shifts and the Xbar chart allows the user to see when the process goes outside its normal range, or drifts over time.

Figure 6-3 – PATTERN OF 20 HOLES

In Figure 6-3 the variation within the group of features can be seen to be less than the variation from part to part. This is natural behaviour in this context as setup variation is not present within part but causes variation from part to part. Using control charts that calculate their control limits based on variation within the group can lead to incorrect limits. As shown in the charts Figure 6-4 and 6-5.

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Time Series Plot of Pattern of 20 holes (over 15 parts)




Figure 6-4 – X BAR AND R CHART OF PATTERN OF 20 HOLES

In Figure 6-4 the data are plotted on an Xbar-R chart. The resulting limits are much narrower than is appropriate. The process is varying normally (but with different levels of ‘within’ and ‘between’ variation). In this situation an Xbar-R chart is not useful.

Figure 6-5 – I-MR CHART OF PATTERN OF 20 HOLES

In Figure 6-5 an I-MR chart illustrates the issue of using such a chart when the ‘within’ and ‘between’ variation is different. The chart is giving many false signals due to the limits not being representative of the natural process variation.

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Figure 6-6 – A 3 WAY CONTROL CHART OF PATTERN OF 20 HOLES

In Figure 6-6 where the pattern of 20 holes is plotted on a 3-way control chart, the process can be seen to be stable. The average values show only random behaviour on the I chart, as does the moving range chart (between parts) and the S chart (within parts).

Capability Assessment for multiple identical feature groups

Capability assessment for this scenario may present some added complications beyond the generic method described in Section 3.

Often in situations where multiple identical features are being analyzed, the variation within the feature group is not representative of the overall process variation due to other sources of variation (setups, tool changes, material variation). In these situations the ‘short term’ estimate for capability provided by typical Cpk calculations provides an overly optimistic view of the capability that cannot be relied upon.

Figure 6-7 shows this effect using the data discussed in the previous section on Figure 6-3. The capability indices Cp and Cpk are not representative of process performance. The Pp and Ppk indices appear to be a better representation. Performance is estimated at 54 parts per million defectives.

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I-MR-R/S (Between/Within) Chart of pattern of 20 holes (over 15 parts)




Figure 6-7 – CAPABILITY ANALYSIS FOR PATTERN OF 20 HOLES

In many situations an assessment of Ppk will provide adequate information on the overall process capability. This is due to the fact that the method of calculation recognizes the variance from the average for each data point, whereas the Cpk method only looks at variation within the subgroups.

Occasionally a scenario may present itself that warrants a more complex assessment to take into account both ‘within’ and ‘between’ variation. This may be most relevant in cases of borderline capability.

The method for calculating capability in this scenario involves calculation of the ‘within’ group variability and the ‘between’ group variability and taking the square root of the sum of the variances to achieve a total variability known as ‘between/within’ (the concept is illustrated in Eq. 11) . This is then used as the variation component in a regular Cpk calculation. This type of analysis is shown in Figure 6-8.

σB / W = SQRT (σ2Between + σ2Within)

(Eq. 11)

Pp 1 .43PPL 1 .56PPU 1 .29Ppk 1 .29Cpm *

Cp 4.01CPL 4.39CPU 3.63Cpk 3.63


Overall Capability

PPM < LSL 0.00 1 .41 0.00PPM > USL 0.00 52.45 0.00PPM Total 0.00 53.86 0.00



Process Capability Report for Pattern of 20 holes (over 1 5 parts)




Figure 6-8 – A BETWEEN/WITHIN CAPABILITY ANALYSIS

Using the data from the previous scenario (from Figure 6-7), a Between/Within capability analysis produces a Cpk of 1.21 which is more representative of process performance. The expected PPM defective is estimated at 156 as opposed to 54 produced by Ppk analysis using a regular method of calculation.

From a practical perspective, where capability is clearly at a high level, a regular Ppk calculation will usually suffice however for borderline situations the method that considers between and within capability is advisable.

Statistical software such as Minitab is capable of running ‘Between/Within’ capability analysis.

A more comprehensive guide on capability methods can be found in Implementing Six Sigma – Breyfogle 2003. ISBN 0-471-26572-1.

Pp 1 .43PPL 1 .56PPU 1 .29Ppk 1 .29Cpm *

Cp 1 .33CPL 1 .46CPU 1 .21Cpk 1 .21

B/W Capability

Overall Capability

PPM < LSL 0.00 1 .41 6.35PPM > USL 0.00 52.45 149.90PPM Total 0.00 53.86 156.25

Observed Expected Overall Expected B/WPerformance

LSL USLOverallB/W

Between/Within Capability Report for Pattern of 20 holes (over 1 5 parts)




6.2. Assessing Control and Capability of Variable Data by Process or Part Family

Process based studies may be acceptable to allow qualification by similarity to be undertaken, e.g., similar parts, geometries, tolerances, and design characteristics. The supplier should liaise with their purchaser to confirm suitability for this approach.

Table 6-2 – PART FAMILY APPROACH

SCENARIO – HOUSING BUSHING TARGET I-MR CHART

For manufacturers practicing cellular manufacturing of part families, Target I-MR Charts can be more efficient than operating separate product specific charts. Rather than implement control charts for each distinct part number, a supplier may choose to combine similarly made part numbers on the same chart. The basic assumptions of this method are that these similar products share common processing methods and exhibit similar process behaviour and variation. Tolerances & materials will likely be similar as differences may give rise to differing levels of capability. What follows is an illustrated example.

An aerospace manufacturer produces a variety of machined products for several aerospace engine customers. The company recently reorganized its operations into cells making common products formulated into part families. The part families are a collection of specific products with common material specifications, characteristic tolerances as well as sharing similar process operations. One family is the Housing Bushing family. The bushings are made out of brass and press fitted into customer housings. The supplier selects a control chart as the control method for the outside diameter of the parts.

The original process control approach utilized an I-MR Control Chart for each specific part number. With smaller lot sizes being manufactured to reduce inventories, the manufacturer decides to utilize the Target I-MR Chart for the part family. Table 6-3 shows a list of diameter characteristics in a part family manufactured in a cell:

Scenario When to use Control type (which chart) Use in monitoring

When a characteristic exists on a range of products and is considered not product specific

Potentially a low volume environment where a statement of capability is not feasible from the sample sizes available.

Appropriate:

This method may be employed when it can be shown there is a logical rationale for the process or part family approach.

When the geometry and tolerances are similar across the products.

Not Appropriate:

When the features have widely differing tolerances and geometry.

Parts with obvious differences in process of manufacture.

Where geometric requirements are identical, the actual measured values may be used.

Where nominal values differ the ‘deviation from nominal’ for each characteristic may be used.

Generally speaking the selection of control chart is then no different from the guidance within other sections of this standard.

For individual values, use what is called the “Target IX-MR Chart” (see scenario in 6.2.1). For subgroup averages (n= 3, 4, 5, or 6) use what is called a “Target Xbar-R Chart”.

Prior to accepting the use of the control chart, confirmation should be made that the standardized data are all (within reason) from a single distribution. If not, the limits on the control chart may give rise to false signals. This assessment may be done with analysis of variance (ANOVA) techniques or in certain cases simple graphical analysis.




PART IDENTIFIER

PART NUMBER

FEATURE FEATURE SIZE NOMINAL DIMENSION

A 890150-1 Outside Diameter .250 +/- .005 .250 inch

B 890160-1 Outside Diameter .500 +/- .004 .500 inch

C 890170-1 Outside Diameter .975 +/- .005 .975 inch

Table 6-3 – DIAMETER CHARACTERISTICS FOR PROCESS CONTROL EXAMPLE

Methodology

The Target I-MR Chart, Figure 6-9 (showing both Individuals and Moving Ranges) illustrates the initial 20 piece production run executed during the week. The number of consecutive parts made for each part number is lower than would be required for individual control charts per part number (e.g., 3, 4, 5 etc.). This is due to the quick-change set-up methods employed by the manufacturer enabling production of individual items as opposed to batches of parts.

The data plotted on the I chart are the deviations from the nominal value for the part being measured.

The values plotted on the MR chart are the absolute differences between consecutive deviations (from the I chart). This means there are no negative values on this chart.

This type of chart is a variation of the standard Individuals & Moving Range (I-MR) Chart (see 2.2).

For each part produced, the deviation from the nominal value for that part number is calculated and plotted (on the I chart). Next the moving ranges between each point on the Individuals chart are calculated. These values are plotted on the moving range chart (MR).

An example of data calculation is illustrated in Figure 6-9 (row 1 to 4).

The control limits are then calculated in the same way as a regular I-MR Chart.

Thus all actual values that are measured are “normalized” by their nominal values. This allows different part numbers with different feature nominals to be combined on the same chart.




Figure 6-9 – TARGET I-MR CHART FOR THE BUSHING PROCESS EXAMPLE

It can be seen on the Target I-MR Chart in Figure 6-9 that the bushing process is in a state of statistical control. This assures the manufacturer that the process is stable. All three part numbers exhibit a similar level of variation (precision) and process location (average).

The calculations for the Target I-MR Chart control limits, Moving Range control limits, and Process Capability Indexes Cp & Cpk are illustrated in Figure 6-10.

NOTE: The chart uses standard I-MR control limit calculations. Care should be taken for the calculation of Cpk. For capability of the ‘normalized’ values to make sense the tolerances should also be normalized (i.e., expressed as deviation from nominal). For example the lower specification limit for Part A would be -0.005 not 0.245 and the upper specification limit 0.005 not 0.255.

Chart No.: 1 of 1

PART:DATE/TIME:

VALUE:

MOVING RANGE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

VALU

E -N

OM

INAL

MO

VIN

G R

ANG

E

(X)

(MR)

NOMINAL:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

PART A:PART NUMBER: ______________DESCRIPTION: _______________USL: __________ LSL: ________NOMINAL: ___________________

PART B:PART NUMBER: ______________DESCRIPTION: _______________USL: __________ LSL: ________NOMINAL: ___________________

PART C:PART NUMBER: ______________DESCRIPTION: _______________USL: __________ LSL: ________NOMINAL: ___________________

PART D:PART NUMBER: ________________DESCRIPTION: _________________USL: __________ LSL: __________NOMINAL: _____________________

NOTES:

0

890150-1BUSHING

.255 .245.250 INCH

890160-1BUSHING

.504 .496.500 INCH

890170-1BUSHING

.980 .970.975 INCH

A A A A A A B B B C CB B B B B C C C C

.252 .249 .250 .501 .498 .500 .502 .497 .976 .977 .974 .974 .250 .250 .249 .502 .500 .498 .975 .974

.250 .250 .250 .500 .500 .500 .500 .500 .975 .975 .975 .975 .250 .250 .250 .500 .500 .500 .975 .975

.002 -.001 0 .001 -.002 0 .002 -.003 .001 .002 -.001 -.001 0 0 -.001__ .003 .001 .001 .003 .002 .002 .005 .004 .001 .003 0 .001 0 .001

+.002

+.004

+.006

-.006

-.004

-.002

0

.002

.004

.006

.008

VALUE-NOMINAL

1234

(ROW 1 - ROW 2) .002.003

0.002

-.002.002

0.002

-.001.001

UCLr

LCLx

UCLx




Figure 6-10 – CALCULATED STATISTICS FOR THE BUSHING PROCESS EXAMPLE

Interpretation of Results

In Figure 6-9 the process appears to be in a state of statistical control due to the absence of patterns that indicate special causes of variation. The supplier concludes that the three different part numbers are ‘in family’ and that grouping on the same chart is valid. However the process capability shown in Figure 6-10 shows need for improvement. The tightest tolerance part, which is Part B, has a Cp = 0.78 and a Cpk = 0.76 while parts A and C, that share the same tolerance band, have a Cp = 0.98 and Cpk = 0.96. Given the goal of having a process Cpk of minimum 1.33, and the fact the overall process is stable and centered, an investigation will be required on the common cause sources of variation to see what can be changed to improve the overall process capability.

NOTE: Prior to calculating control limits and process capability indexes it is good practice - because the data displayed are individual values - to perform a normality test. This is easily done using statistical software. Figure 6-11 shows the Probability Plot illustrating that the data can be judged to be a normal distribution (p-value 0.114 is greater than the 0.05 threshold typically used – assuming a 5% alpha risk is acceptable).

Worksheet for Target IX-MR ChartNote Comments

k = Number of Subgroups =

R CHART X CHART

CENTRALLINE

UPPERCONTROLLIMIT

LOWERCONTROLLIMIT

R = Total of MR valuesk - 1 X = Total of Row 3 values

No. of subgroups

UCL = D x R4

R = .037/19 = .0019 X = -.002/20 = -.0001

UCL = 3.27*.0019 = .0062R

LCL = 0R

UCL = X + 3X

UCL = -.0001 + 3(.0017)X

LCL = X - 3X

LCL = -.0001 - 3(.0017)X

CONTROL CHART FACTORS FOR n = 2:

D = 3.27, d = 1.1284 2

=Rd 2

= .0019/1.128 = .0017Cp Cpk

ET = Engineering Tolerance = USL - LSL

NT = Natural Tolerance = 6

Cp = ET/NT = (USL-LSL)/6

Cpu = (USL-X)/3 =

Cpl = (X-LSL)/3 =

* Cpk = MIN {Cpu, Cpl}

OR

O

O

O

O

O

O

ET (Part A) = .010” ET (Part C) = .010”

ET (Part B) = .008" ET (Part D) = _____

PROCESS CAPABILITY

Is the process in control? YES __X___ NO _____

Unilateral Tolerance? YES _____ NO __X__

INDEXPART PART A PART B PART C PART D

Cp

CpkCheck one:

Cpl X_Cpu ___

20

UCL = .0050X

LCL = -.0052X

.010/6(.0017) = .98 .008/6(.0017) = .78 .010/6(.0017) = .98

-.0001 - (-.005)3 * .0017

= .96-.0001 - (-.004)

3 * .0017= .76

-.0001 - (-.005)3 * .0017

= .96




Figure 6-11 – NORMAL PROBABILITY PLOT

The capability of the process can be calculated from the deviation from target provided the process is stable. It is wise to analyse both Cpk and Ppk indices in this situation to check that they are similar as seen in Figure 6-12 for the two bushings that share the +/- 0.005” tolerance.

Figure 6-12 – PROCESS CAPABILITY ANALYSIS

0.0040.0030.0020.0010.000-0.001-0.002-0.003-0.004

99

95

90

80706050403020

10

5

1

Delta

Perc

ent

Mean -0.0001StDev 0.001447N 20AD 0.584P-Value 0.114

Probability Plot of DeltaNormal

0.0040.0020.000-0.002-0.004

LSL USL

LSL -0.005Target *USL 0.005Sample Mean -0.0001Sample N 20StDev (Within) 0.00172639StDev (O v erall) 0.00144732

Process Data

C p 0.97C PL 0.95C PU 0.98C pk 0.95

Pp 1.15PPL 1.13PPU 1.17Ppk 1.13C pm *

O v erall C apability

Potential (Within) C apability

% < LSL 0.00% > USL 0.00% Total 0.00

O bserv ed Performance% < LSL 0.23% > USL 0.16% Total 0.38

Exp. Within Performance% < LSL 0.04% > USL 0.02% Total 0.06

Exp. O v erall Performance

WithinOverall

Process Capability of Delta




7. COMPUTER BASED SYSTEMS AND SOFTWARE

Many of the methods used in this standard can be implemented using traditional ‘pencil and paper’ solutions. Control charting is a relatively simple task requiring nothing more complex than calculation of averages and basic multiplication and division.

Control charts can be manually created and plotted and many suggest this lends a level of understanding and engagement to the deployment.

However there are drawbacks as the use of these tools becomes more mature and demand increases:

• The need to manually plot and annotate the chart

• Failed tests for special cause are not automatically highlighted

• The risk of errors being made both in data capture and computation

• The cost of administration keeping the manual charts up to date and replenished when complete

• The limit to the time available for analysis, more so with complex product with multiple characteristics

• The lack of timely access to historical information.

SPC systems make the task much easier and have the following advantages:

• Direct linkage to gauging for data input (either via interfaces such as RS232 standard interface or wireless technologies)

• Direct analysis to computer controlled devices such as CMM’s.

• More advanced capability analysis methods (feature groups, and non-normal process capability analysis)

• More accurate predictions (projected defect rates for example)

• Easier use of data for process simulation.

Systems tend to fall into categories of data collection and process monitoring (real time) and off line analytics. Additionally tools are available that provide configurable management information dashboards containing Yield, Overall Equipment Effectiveness (OEE) and other performance trends, Pareto, and other defect analysis in real time.

Systems may be provided by metrology vendors to provide functionality to their systems or as standalone. The benefits of equipment manufacturers’ proprietary systems include the ability to simply interface with their offerings whilst the benefits of offerings by independents tend to be flexibility; the ease of configuration to multiple data formats from different equipment vendors.

Generally speaking a computer based solution tends to be more robust than a paper based one.




8. METHODS AND FORMULAE

The statistical formulae provided in Tables 8-1 and 8-2 can be used for calculating the center lines and control limits on commonly used control charts. Other methods may be used depending on the application.

Table 8-3 provides formulae for Process Capability.

TABLE 8-1 – STATISTICAL FORMULAE FOR VARIABLES CONTROL CHARTS I-MR Chart

Centre line : Individuals Chart

(Eq. 8.1)

Centre line : Moving Range Chart

Note: N is the number of moving range values (Eq. 8.2)

Upper Control Limit (Individuals chart)

(Eq. 8.3)

Lower Control Limit (Individuals chart)

(Eq. 8.4)

Upper Control Limit (Moving Range Chart)

(Eq. 8.5)

Lower Control Limit (Moving Range Chart)

(Eq. 8.6)

Only used if the range is calculated over a number of data points. This will default to 0 for moving range between consecutive data points.

Xbar and R chart

Centre line : Xbar Chart

(Eq. 8.7)




Centre line : Range Chart

Note: N is the number of range values (Eq. 8.8)

Upper Control Limit (Xbar chart)

(Eq. 8.9)

Lower Control Limit (Xbar chart)

(Eq. 8.10)

Upper Control Limit (Range Chart)

(Eq. 8.11)

Lower Control Limit (Range Chart)

(Eq. 8.12)

Xbar and MR-R/S

Centre Line (Xbar chart)

(Eq. 8.13)

Centre line (MR chart)

Note: N is the number of moving range values (Eq. 8.14)

Centre line (R chart)

Note: N is the number of range values (Eq. 8.15)

Upper control limit (Xbar chart)

(Eq. 8.16)




Lower control limit (Xbar chart)

(Eq. 8.17)

Upper control limit (MR chart)

(Eq. 8.18)

Lower control limits (MR chart)

(Eq. 8.19)

Upper control limit (R chart)

(Eq. 8.20)

Lower control limit (R chart)

(Eq. 8.21)

TABLE 8-2 – STATISTICAL FORMULAE FOR ATTRIBUTE CHARTS

P Chart

Centre Line (P chart)

(Eq. 8.22)

Upper control limit

(Eq. 8.23)

Lower control limit

(Eq. 8.24)




nP Chart

Centre line

(Eq. 8.25)

Upper control limit

(Eq. 8.26)

Lower control limit

(Eq. 8.27)

C Chart

Centre line

(Eq. 8.28)

Upper control limit

(Eq. 8.29)

Lower control limit

(Eq. 8.30)

U Chart

Centre line

(Eq. 8.31)

Upper control limit

(Eq. 8.32)




Lower control limit

(Eq. 8.33)

TABLE 8-3 – STATISTICAL FORMULAE FOR PROCESS CAPABILITY

Sigma (standard deviation) for control charts

(Eq. 8.34)

Sample standard deviation

𝑠𝑠 = �∑ (𝑥𝑥𝑖𝑖 − �̅�𝑥)2𝑛𝑛𝑖𝑖=1𝑛𝑛 − 1

(Eq. 8.35)

Cp

(Eq. 8.36)

Cpu

(Eq. 8.37)

Cpl

(Eq. 8.38)

Cpk

(Eq. 8.39)

Pp

(Eq. 8.40)




Ppu

(Eq. 8.41)

Ppl

(Eq. 8.42)

Ppk

(Eq. 8.43)

Table 8-4 is used as reference to determine the relevant value of the statistical constants in the formulae provided

TABLE 8-4 – TABLE OF STATISTICAL CONSTANTS

Subgroup Size A2 A3 d2 D3 D4 B3 B4 2 1.880 2.659 1.128 0 3.267 0 3.267 3 1.023 1.954 1.693 0 2.574 0 2.568 4 0.729 1.628 2.059 0 2.282 0 2.266 5 0.577 1.427 2.326 0 2.114 0 2.089 6 0.483 1.287 2.534 0 2.004 0.030 1.970 7 0.419 1.182 2.704 0.076 1.924 0.118 1.882 8 0.373 1.099 2.847 0.136 1.864 0.185 1.815 9 0.337 1.032 2.970 0.184 1.816 0.239 1.761 10 0.308 0.975 3.078 0.223 1.777 0.284 1.716 11 0.285 0.927 3.173 0.256 1.744 0.321 1.679 12 0.266 0.886 3.258 0.283 1.717 0.354 1.646 13 0.249 0.850 3.336 0.307 1.693 0.382 1.618 14 0.235 0.817 3.407 0.328 1.672 0.406 1.594 15 0.223 0.789 3.472 0.347 1.653 0.428 1.572 16 0.212 0.763 3.532 0.363 1.637 0.448 1.552 17 0.203 0.739 3.588 0.378 1.622 0.466 1.534 18 0.194 0.718 3.640 0.391 1.608 0.482 1.518 19 0.187 0.698 3.689 0.403 1.597 0.497 1.503 20 0.180 0.680 3.735 0.415 1.585 0.510 1.490 21 0.173 0.663 3.778 0.425 1.575 0.523 1.477 22 0.167 0.647 3.819 0.434 1.566 0.534 1.466 23 0.162 0.633 3.858 0.443 1.557 0.545 1.455 24 0.157 0.619 3.895 0.451 1.548 0.555 1.445 25 0.153 0.606 3.931 0.459 1.541 0.565 1.435




9. AS13006 PROCESS CONTROL MATURITY REVIEW

Table – 9-1 contains some questions that can be used to assess the health of process control within a factory. The question set is not exhaustive.

TABLE 9-1 – Process Control Maturity Review

CATEGORY ENABLERS SUGGESTED QUESTIONS

Leadership Management provides the necessary leadership, infrastructure and environment for a robust process control system. Management are able to see and deal with performance trends

Discuss process control with business management Is process control built into the business management system and procedures? Do they champion the focus on process control (adoption of PFMEA, Control Plan)?

Are they making changes to enable better process control (e.g., systems and software solutions both in process and for offline analysis)?

Have they undertaken training themselves to ensure they are conveying correct messages?

Are systems/governance in place to view issues and performance trends (e.g., Right First Time, Process Yield, and Defect Rate) and is there evidence they are acted on?

Control Plan

The Control Plan is complete, comprehensive, and utilized as part of the running of the manufacturing operation. There is linkage to the process risks via the PFMEA.

View the Control Plan Is it in place and does it cover all aspects of the process routing?

Does it relate to the control methods declared in the PFMEA?

Is it focused on process control (as opposed to inspection)?

Is the reaction plan explicit and detailed?

Are the control items traceable to the appropriate technical instruction?

Are all aspects declared in the Control Plan covered adequately in the work instructions and related documentation (for example: The acceptance criteria and the reaction plan)?

Process Work Instructions

Work instructions will contain control activities at a sufficient level of detail to allow consistent application.

View the work instructions relating to specific controls declared within the Control Plan Do they contain all the necessary information required to conduct the process step?

Is there evidence of clarification of the standard method within the work instruction or standard operating procedure?

Do the instructions call out any special items or care points?

Ask the operator how the controls are used Is the process control activity part of a closed loop system where action can be taken in a timely manner?

Can the operator describe why standardized items are of importance?




TABLE 9-1 (continued)


Data Collection System

The data collection is sufficient to maintain process control and capability and is versatile enough to meet future demands.

Go to the operation Is data collected in a way that is sustainable in the longer term?

Is the data collection scalable to other parts and across the facility?

Are there plans to improve the way data is collected? Ask the personnel Can the data be analyzed quickly enough to make timely decisions?

Process Monitoring

The operator is engaged in process control and takes timely action when required

Go to the point of process Is the control at the point of process as opposed to being remote (at a later operation)?

Is the process monitoring being done with measurement systems of adequate quality? Is there MSA to confirm this?

Are the rules of operation available, clear, and concise?

Is there evidence of positive action to special events?

Are visual standards adequate?

Reaction Plan

The actions required when control criteria are not met are clear, understood, and embedded.

Review the Control Plan and supporting documents Is there evidence that any exceptions to process control criteria are actioned appropriately? Does the reaction plan call for any immediate actions to be carried out to determine the cause of the problem (recovery actions) and also when further advice should be sought? Is there a called out method of issue escalation (e.g., for repeated issues)?

Visual Management The operators and management can easily see the status of control. The process can be understood by all.

Go to the shop floor Are controls set up with visual 'status at a glance' philosophy?

Are control charts visible and up to date?

Are care items, foundational control activities, and other checks visible and complied with?

Is there evidence of action to maintain control or react to special cause events?




TABLE 9-1 (continued)


Training & Skills

The necessary process control skills & proficiencies have been provided and are being practiced routinely.

Ask the local leader Do they have a mechanism in place to control the competence and training needs of their workers? Does this include process control?

Looking to the future, are they taking specific actions to develop further? Ask the technical and quality personnel Are they knowledgeable about control principles and methods?

Have they undertaken training courses to develop their knowledge? If so are those training courses available to their peers and leaders?

View evidence of their work. Is a data driven approach evident?

Are they using methods they are using adequate for the types of product/process? For instance high complex processes requiring optimization may benefit from application of Design of Experiments knowledge.

Ask the operator Are training courses available and being used by personnel to support the deployment and operation of process control?

Do they have local support/coaching?

Data Analysis

Process capability data is used to improve product quality

Ask the technical personnel and local leadership Can the capability data be readily retrieved?

Is there evidence that the capability data is being used to prioritize, drive improvement, and validate those improvements (i.e., before/after capability)? Has adequate effort been made to understand the causes of process variation when defining the Control Plan Items, methods, and criteria? For instance Design of Experiments for process screening and optimization of parameters. Where Non-Statistical tools are used, have the acceptance criteria for those controls been based on any scientific study as opposed to being arbitrarily selected?

Foundational Activities

The organization effectively demonstrates foundational process control activities

Is the handling, storage, and packaging of parts well enough defined to avoid risk of damage, including application of 5S principles for workplace organization (i.e., sort, set in order, shine, standardize and sustain)?

Do the process control activities extend to Machines, Fixtures, Tooling, and Raw Materials? Are the standards appropriate to the product tolerances required?

Sub-tier Deployment

AS13006 process control requirements are implemented at sub-tiers.

Are the requirements formally instructed?

Has engagement been adequate to gain full engagement with the spirit and intent of process control (as opposed to putting a 'tick in the box')?




PREPARED BY THE AEROSPACE ENGINE SUPPLIER QUALITY (AESQ) STRATEGY GROUP

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