STATISTICAL PROCESS CONTROL

� Statistics is defined as the science that deals with the

� Collection,

� Tabulation,

� Analysis,

� Interpretation,

� Presentation of

quantitative data.

� SPC is one of the best technical tool for improving product and

service quality.

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� SPC is a control system which uses statistical techniques for

knowing, all the time, changes in the process.

� It is an effective method

� Helps in preventing defects

� Helps continuous quality improvement.

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� Statistical Process Control

Statistical:

� Statistics are tools used to make predictions on performance.

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� Statistical Process Control

� Process:

� The process involves

� people,

� machines,

� materials,

� methods,

� management

� and environment

working together to produce an output, such as an end product.

PROCESSPeople

EquipmentMethod

EnvironmentMaterialsProcedures

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The Process

People Machines Material

Management Methods Environment

Output

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Statistical Process Control

� Control:

� Controlling a process is

� guiding it

� comparing actual performance against a target.

� Then identifying when and what corrective

action is necessary to achieve the target.

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� S.P.C. is statistical analysis of

� the predictability

� and capacity of a process

� to give a uniform product.

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The Aim of S.P.C. - Detection Strategy

� This focuses on identification of problems after production, by

100% inspection or by customer complaints.

� It is a historically-based strategy.

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Detection Drawbacks:

� Production is already made.

� Customer dissatisfaction.

� Inflated costs - rework; inspection.

� Repetitive problems.

� Neglected improvements.

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The Aim of S.P.C - Prevention Strategy

� Prevention:

� This focuses on in-process production and identification of

problems through analysis of process capability.

� It is a future-orientated strategy.

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Prevention Benefits:

� Improved design and process capability.

� Improved manufacturing quality.

� Improved organisation.

� Continuous Improvement.

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� S.P.C. as a Prevention Tool

� The S.P.C. has to be looked at as a stage towards completely

preventing defects.

� With stable processes, the cost of inspection and defects are

significantly reduced.

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The Benefits of S.P.C.

� Assesses the design intent.

� Achieves a lower cost by providing an early warning

system.

� Monitors performance, preventing defects.

� Provides a common language for discussing process

performance.

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� Process Variations

Process Element Variable Examples

Machine………………………….Speed, operating temperature,

feed rate

Tools………………………………..Shape, wear rate

Fixtures…………………………..Dimensional accuracy

Materials…………………………Composition, dimensions

Operator…………………………Choice of set-up, fatigue

Maintenance…………………Lubrication, calibration

Environment…………………Humidity, temperature

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Process Variations

� No industrial process or machine is able to produce consecutive

items which are identical in appearance, length, weight,

thickness etc.

� The differences may be large or very small, but they are always

there.

� The differences are known as ‘variation’.

� This is the reason why ‘tolerances’ are used.

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Designed Size

10 11 12 13 14 15 16 17 18 19 20

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Natural Variation

14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5

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Process Variability Variations due to:

Natural Causes:• Temperature variation

• Material variation

• Customer differences

• Operator performance

Special Causes:• Machine is breaking

• Untrained operative

• Machine movement

• Process has changed

Must be monitored Early and visible

warning required

Stability

� Common causes are the many sources of variation that are

always present.

� A process operates within ‘normal variation’ when each element

varies in a random manner, within expected limits, such that the

variation cannot be blamed on one element.

� When a process is operating with common causes of variation it

is said to be stable.

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Process Control

� The process can only be termed ‘under control’ if it gives

predictable results.

� Its variability is stable over a long period of time.

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Statistical Process Control Steps

6-22

Produce GoodProvide Service

Stop Process

Yes

No

Assign.Causes?Take Sample

Inspect Sample

Find Out WhyCreate

Control Chart

Start

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� Control Chart Decision Tree

� Determine Sample size (n)

� Variable or Attribute Data

� Variable is measured on a continuous scale

� Attribute is occurrences in n observations

� Determine if sample size is constant or changing

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Start

X bar , R

X bar, S

IX, Moving

Range

p (fraction defective)

or

n p (number def. Per sample

c (defects per

sample or

u defects per unitu

Control Chart Decision Tree

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What does it look like?

o Adding the element of time will help clarify your

understanding of the causes of variation in the processes.

o A run chart is a line graph of data points organized in time

sequence and centered on the median data value.

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Individual X charts

How is it done?

� The data must have a normal distribution (bell curve).

� Have 20 or more data points. Fifteen is the absolute minimum.

� List the data points in time order. Determine the range between each of the consecutive data points.

� Find the mean or average of the data point values.

� Calculate the control limits (three standard deviations)

� Set up the scales for your control chart.

� Draw a solid line representing the data mean.

� Draw the upper and lower control limits.

� Plot the data points in time sequence.

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Control Charts� Next, look at the upper and lower

control limits. If your process is in

control, 99.73% of all the data

points will be inside those lines.

� The upper and lower control limits

represent three standard deviations

on either side of the mean.

� Divide the distance between the

centerline and the upper control

limit into three equal zones

representing three standard

deviations. 8/11/201527

� Search for trends:

� Two out of three consecutive points

are in zone “C”

� Four out of five consecutive points

on the same side of the center line

are on zone “B” or “C”

� Only one of 10 consecutive points

is in zone “A”

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�Basic Control Chartsinterpretation rules:

� Specials are any points abovethe UCL or below the LCL

� A Run violation is seven ormore consecutive points aboveor below the center (20-25 plotpoints)

� A trend violation is any upwardor downward movement offive or more consecutive pointsor drifts of seven or morepoints (10-20 plot points)

� A 1-in-20 violation is morethan one point in twentyconsecutive points close to thecenter line

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� Attribute Control charts :

To monitor Attribute data (Characteristics that are measured as

either "acceptable" or "not acceptable", thus have only discrete,

binary, or integer values).

� Variable Control charts :

To monitor the Variable data (Characteristics that are measured

on a continuous scale).

� Control charts for Variables

� X-bar chart

� It is used to monitor change in mean of a process.

� Variation in the average of the samples.

� R-chart

it shows the consistencyof the process.

Control charts

� Control charts for Attributes

� P-chart

� C-Chart

� np-Chart

� U-Chart

CONTROL CHARTS FOR VARIABLES

� Sources Of Variation

� Types Of Variation

� Types Of Variable Control Charts

� Control Chart Patterns

� Control Chart And Warning Control Limit

� Basic Equations And Example

� Consequences Of Misinterpreting Control Charts

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�Control chart is a graph that displays data taken over time andvariations of this data.

�Control charts, also known as Shewhart charts or process-behavior charts

�One of the axioms or truism of manufacturing is that no twoobjects are ever made exactly alike.

�When variations are very small, it may appear that items areidentical; but precision instruments will show difference.

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SOURCES OF VARIATION

Mainly there are four sources of variations. They are,

�Processes

�Materials

�Operators

�Miscellaneous factors

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TYPES OF VARIATIONS

There are two kinds of variations. They are,

1. Assignable (or special) causes of variations and

2. Chance (or random or common) causes of variations.

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1. Assignable causes of variations

�Assignable causes of variations are larger in magnitude andcan be easily traced and detected.

� The prime objective of control chart is detecting assignablecauses of variation by analyzing data(length, dia.. Etc.)

�Actions on the part of both management and workers willreduce the occurrence of assignable causes.

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REASONS FOR ASSIGNABLE CAUSES OF VARIATION

� Difference among machines.

� Difference among materials.

� Difference among process.

� Difference in each of these factors overtime.

� Difference in their relationship to one another. 8/11/201539

2. CHANCE (OR RANDOM OR COMMON) CAUSES OF VARIATIONS

� Chances causes of variations are inevitable in any process.

� These are difficult to trace and control even under best conditions of

production.

� All occur at random and cannot be avoided.

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REASONS FOR CHANCE CAUSES OF VARIATION

� Human variability from one operation cycle to the next

� Minor variations in raw materials

� Fluctuations in working conditions.

� Lack of adequate supervision skills.

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TYPES OF VARIABLE CONTROL CHARTS

�X Bar or average chart

� R or Range chart

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CONTROL CHART PATTERNS

1. Natural Patterns

� In natural pattern no points fall outside the control limits.

� The majority of points are near the center line.

2. Sudden shifts in Level

� Many changes can bring about a sudden change( or jump) in

pattern on an X bar and R charts

� Changes in process settings like temperature, depth of cut,

new operators, etc. 8/11/201543

CONTROL CHART PATTERNS CONT..

3. Graduation shifts in the Level

� Gradual shifts in the level occurs when a process parameter changesgradually over a period of time.

� Such gradual shift in X bar chart may occur because the incoming quality ofraw materials changed over time, change in style of supervision etc.

� Such shift in R chart may occur because of new operator, decrease inworker skill due to fatigue etc.

4. Tending Pattern

� Trend pattern represents changes that steadily increase or decrease.

� Trend pattern in X bar chart may occur because of tool wear, die wear etc8/11/201544

CONTROL CHART PATTERNS CONT..

� Trending pattern in R chart may occur because of Gradual improvement in operator still resulting from on-the-job training.

� Decrease in operator skill due to fatigue.

5. Cyclic Patterns

� Cyclic patterns are characterized by a repetitive periodic behavior in the system.

� Cyclic patterns in X bar chart may occur because of rotation of operators, periodic changes in temperature, humidity etc.

� Cyclic patterns in R chart may occur because of operator fatigue, periodic maintenance of equipment's etc.

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CONTROL CHART PATTERNS CONT..

6. Wild Patterns

� Bunching ( or groups) are clusters of several observations

that are decidedly different from other points of the plot.

� Such behavior is due to use of new vendor for a short period

of time, use of a machine for a brief period of time etc.

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CONTROL CHART AND WARNING LIMITS

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Formula

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Example problem for X bar and R Chart

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� The goliath Tool company produces slip ring bearings which

look like washers. They fit around shaft such as drive shafts in

machinery or motors. In the production process for a

particular slip ring bearing the employees have taken 10

samples (during a 10 day period) of 5 slip ring bearings. The

individual observations are shown below. Prepare the R chart

and X bar chart.

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Sample

No

Observation (slip ring diameters cm)

1 2 3 4 5

1 5.02 5.01 4.94 4.99 4.96

2 5.01 5.03 5.07 4.95 4.96

3 4.99 5 4.93 4.92 4.99

4 5.03 4.91 5.01 4.98 4.89

5 4.95 4.92 5.03 5.05 5.01

6 4.97 5.06 5.06 4.96 5.03

7 5.05 5.01 5.1 4.96 4.99

8 5.09 5.1 5 4.99 5.08

9 5.14 5.1 4.99 5.08 5.09

10 5.01 4.98 5.08 5.07 4.99

CONSEQUENCES OF MISINTERPRETING CONTROL CHARTS

� Blaming people for problems that they cannot control.

� Spending time and money looking for problems that do not exist.

� Spending time and money on unnecessary process adjustments.

� Taking action where no action is warranted.

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�Our goal is to decrease the variation inherent in a

process/material/operator over time.

�As we improve those factors ( mentioned above), the spread of

the data will continue to decrease.

�Quality improves!!

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“Process Capability”

is the ability of a process to make a feature within its tolerance.

� Process Capability

A critical aspect of statistical quality control is evaluating the

ability of a production process to meet or exceed preset

specifications. This is called process capability.

� Product specifications, often called tolerances, are preset

ranges of acceptable quality characteristics, such as product

dimensions.

� For a product to be considered acceptable, its characteristics

must fall within this preset range.

� Otherwise, the product is not acceptable.

� Product specifications, or tolerance limits, are usually

established by design engineers or product design specialists.

� Process capability is the ability of the process to meet the

design specifications for a service or product.

� Nominal value is a target for design specifications.

� Tolerance is an allowance above or below the nominal value.

20 25 30

Upperspecification

Lowerspecification

Nominalvalue

Process is capable

Process distribution

Process is not capable

20 25 30

Upperspecification

Lowerspecification

Nominalvalue

Process distribution

� Process capability is measured by the process capability index

( Cp ) .

� which is computed as the ratio of the specification width to

the width of the process variability

�

R bar Mean of the sample range

d2 is the value taken from statistical table

2d

RX6= widthProcess

Cpk = Minimum ofUpper specification – x

3σ

x – Lower specification

3σ,

= =

Process Capability Index, Cpk, is an index that measures the

potential for a process to generate defective outputs relative to

either upper or lower specifications.

Process Capability Index, Cpk

We take the minimum of the two ratios because it gives the worst-

case situation.

� where the specification width is the difference between the

upper specification limit (USL) and the lower specification limit

(LSL) of the process.

� The process width is computed as 6 standard deviations (6σ)

of the process being monitored.

� A six sigma process is one in which 99.99966% of the products

manufactured are statistically expected to be free of defects

(3.4 defective parts/million) .

� Cp = 1 Process variability just meets specifications.

� Cp <= 1 Process is not capable of meeting

specifications .

� Cp >= 1 Process is capable of meeting specifications

Yes: No:

No:

No:

Yes:

Yes:

potentially capable

if re-centered

potentially capable

if re-centered

too wide

Problem

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� In a capabilty study of a lathe used in turning a shaft to a

diameter of 23.75 +-0.1 mm a sample of 6 consecutive

pieces was taken each day for 8 days . The values of ∑xbar=

190.156

� ∑R =0.54 .Construct the control chart and fnd out the

process capability of the machine

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d2= 2.534

A2=0.48

D3=0

D4=2

2

6Prd

RXocesswidth =

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� ucl = 23.802

� Lcl= 23.7322

� Cp=1.254

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� Problem

� The length of time customers of Statistical Software, Inc.

waited from the time their call was answered until a technical

representative answered their question or solved their

problem is recorded in Table 20-1.

� Develop a control chart.

� Does it appear that there is any time when there is too much

variation in the operation?

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ATTRIBUTE CONTROL CHARTS

Attribute charts

� Many quality characteristics cannot be convenientlyrepresented numerically.

� In such cases, each item inspected is classified aseither conforming or nonconforming to thespecifications on that quality characteristic.

� Quality characteristics of this type are calledattributes.

� Examples are nonfunctional semiconductor chips,warped connecting rods, etc,.

Control Charts for Attributes Data

� p charts: proportion of units nonconforming

� np charts: number of units nonconforming

� c charts: count of nonconformities.

� u charts: count of nonconformities per unit.

Type of Attribute Charts

p charts

� This chart shows the fraction of nonconforming ordefective product produced by a manufacturingprocess.

� It is also called the control chart for fractionnonconforming.

np charts

� This chart shows the number of nonconforming.Almost the same as the p chart.

c charts

� This shows the number of defects or nonconformitiesproduced by a manufacturing process.

u charts

� This chart shows the nonconformities per unit produced bya manufacturing process.

p charts• In this chart, we plot the percent of defectives (per

batch, per day, per machine, etc.).

• However, the control limits in this chart are not based on

the distribution of rate events but rather on the

binomial distribution (of proportions).

Formula� Fraction nonconforming:

p = No of defects/n

� where p = proportion or fraction non conformities in the

sample or subgroup,

� n = number in the sample or subgroup,

P chart

n

pppUCL

)1(3

−+=

n

pppLCL

)1(3

−−=

inspected no total

defectives of No=p

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Sample

Nof pieces

inspected

No of defects

identified

1 300 25

2 300 30

3 300 35

4 300 40

5 300 45

6 300 35

7 300 40

8 300 30

9 300 20

10 300 50

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Sample no Sample sizeNo of defective

pieces

1 90 9

2 65 7

3 85 3

4 70 2

5 80 9

6 80 5

7 70 3

8 95 9

9 90 6

10 75 7

Example

P chart

np Chart

� When the subgroup size is constant, the chart constructed

for the actual no. of defectives rather than the fraction

defectives is called np-chart.

� Advantages

� np-chart is easier for operating personnel to understand.

� Inspection results are posted directly to chart without any

calculations.

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� A manufacturer uses a injection moulding to produce a plastic

insulation barrier. He inspects 100 barriers daily picked

randomly from the production and determines the no. of

defects by visual inspection. He wishes to use the data

accumulated during a 10 day period to construct an attribute

chart. The results of inspection are shown below.

(a) Plot np-chart and offer your comments

(b) What control limits would you recommend for the future

period.

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c Chart

ccUCL 3+=ccLCL 3−=

•The procedures for c chart are the same as those for the p

chart.

•If count of nonconformities, co, is unknown, it must be found bycollecting data, calculating UCL & LCL.

samples of no Total

samples allin defects of No=C

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Applications of C and U chart

� Number of surface defects in a galvanized sheet.

� Number of imperfections in a certain area of cloth.

� Number of defective units in an air craft unit.

� Number of mistakes per unit.

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� The following data refers to the no. of missing rivets on an

aircraft body noticed during preventive maintenance schedule.

(a) Compute the control limits for a suitable control chart.

(b) Plot the data and offer your comments.

(c) What value of C would you recommend for the future period

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u Chart

� The u chart is mathematically equivalent to the c chart.

n

cu = ∑

∑=

n

cu

n

uuUCL 3+=

n

uuLCL 3−=

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Listed below are the cloths produced on a daily basis in a small

textile mill and the corresponding number of imperfections

found in their bales is as follows.

(a) Use the data to estimate U .

(b) Determine the control limits and plot the data.

(c) What value of U1 would you recommend for the future period

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� Determine the control limits for the following data using

suitable control chart. Plot the data and offer your

comments.

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Castings

No of Defects

1 2

2 4

3 1

4 5

5 5

6 6

7 3

8 4

9 0

10 7

Nonconformity Classification

� Critical nonconformities

� Indicate hazardous or unsafe conditions.

� Major nonconformities

� Failure

� Minor nonconformities

Advantages of attribute control charts

� Allowing for quick summaries, that is, the engineer may simply

classify products as acceptable or unacceptable, based on

various quality criteria.

� Thus, attribute charts sometimes bypass the need for

expensive, precise devices and time-consuming measurement

procedures.

� More easily understood by managers unfamiliar with quality

control procedures.