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how-to guide
PROCESS CAPABILITY:
How to Measure& Improve
Process Capability
v2
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How-To Guides Available
2011 Rolls-Royce plc
The information in this document is the property of Rolls-Royce plc and may not be
copied or communicated to a third party, or used for any purpose other than that for
which it is supplied without the express written consent of Rolls-Royce plc.
This information is given in good faith based upon the latest information available to
Rolls-Royce plc, no warranty or representation is given concerning such information,
which must not be taken as establishing any contractual or other commitment binding
upon Rolls-Royce plc or any of its subsidiary or associated companies.
How-To Guides Available
how-to guide
MEASUREMENT
SYSTEM ANALYSIS:
v2
How to ensure measurement systems
provide good quality data
Produced by Smallpeice Enterprises Ltd
www.smallpeice.com
how-to guide
KEEPING PROCESSES
IN CONTROL:
How to Construct &
Use SPC Charts
v5
Statistical Process
Control
Measurement
System Analysis
Process
Capability
how-to guide
PROCESS CAPABILITY
v2
How to continuously improve the
capability of a process
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Introduction to the Rolls-Royce Improvement Journey
The focus on quality in Rolls-Royce is not new. It is one of the companys keyvalues, part of the brand and what Rolls-Royce is known for by our customers. In
todays market, having a reputation for quality is more important than ever. That
said, quality is not static, but something we need to work to achieve every day, in
everything we do.
The Improvement Journey to Process Excellence is the framework which helps us
meet our business and quality goals, and this How To Guide will help everyone to
understand and apply a fundamental technique within the Rolls-Royce continuous
improvement toolkit. To sustain progress and create a culture of continuous
improvement, it is vital that these How To principles are ingrained in the way
everything is done at Rolls-Royce. Whether you work in a manufacturing or
transactional environment, these principles apply in all parts of the business and
need to be understood and adopted by everyone.
Overview of the Improvement Journey Steps
The Improvement Journey is a proven, benchmarked description of the 4 stages to
reaching and achieving Process Excellence: Process Basics, Process Control,Process Flow and Capable Processes.
Once the basics are in place and controlled, the use of all steps together will
remove waste and reduce variation, ultimately helping to speed up company
improvements.
Setting the Scene:
The Improvement Context for Process Capability
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Leadership & People
Workplace Organisation
HS&E
Standard Processes
Process Compliance
Performance Mgt - Output
Visual Management
Asset Care
Visit www.infocentre.rolls-royce.com/process_excellence for detailed explanations
and further information on each of the Process Basics steps.
Step 2: Process Control
Process Control builds upon the foundation of Process Basics. The objective of
process control is to allow us to take control of our processes. A process that is in
control is one that is stable and predictable. We can predict within certain limits the
outputs we are going to get. It is not possible to improve the flow or capability of a
process until the process is under control. Therefore checking process control has
been achieved is an important pre-requisite to measuring and improving Process
Capability.
To help company leaders and employees understand where their respective
businesses are on the Improvement Journey a global assessment tool has been
formulated. The overall results of the assessment (against a number of key
building blocks) provide a percentage score for each element of the model.
Central to everything are the people in the organisation and the way we behave.
Journey to Process Excellence principles should become our company DNA the
way we think, our way of life, if we are to sustain our progress and create a
Continuous Improvement culture. Already millions of pounds are being saved
across the business through the application of these principles.
A Structured Approach to Improvement
The Process Capability techniques which are introduced in this How To Guide
should not be applied in isolation without the foundation elements of the
Improvement Journey already being in place.
Step 1: Checking the Process Basics
The first part of the Improvement Journey is to ensure that we have our Process
Basics in place. Process Basics provides the business with a suite of practical
tools to simplify and standardise our workplace. The 8 Process Basics steps can
be applied rapidly in all parts of our business and will create considerable
improvements in quality and performance (and therefore bottom line
improvements):
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Step 3: Process Flow
Process Flow builds on the foundations of the Process Basics and Process
Control. Process Flow is concerned with identifying and eliminating waste in order
to simultaneously improve on time delivery performance and make processes
more efficient. On its own however Process Flow is not enough, the process mustalso be capable. Lack of Process Capability is sometimes the root cause of issues
with the process flow. Process Capability must therefore be measured and
understood at the same time as designing processes for flow.
Step 4: Process Capability
Process Capability is concerned with measuring and improving the quality
performance of our processes. The ultimate vision for Process Capability is for all
processes to achieve zero defects. The first step to Process Capability is to be
able to measure and analyse current capability performance. That is the focus of
this guide. Process Basics and Process Control are pre-requisites to measuring
and improving Process Capability.
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INTRODUCTION
1.1: The need for Process Capability analysis
1.2: What is Process Capability?
1.3 Process Capability metrics1.4: Understanding and Interpreting measures of potential Process
Capability (Cp & Pp)
1.5: Understanding and Interpreting measures of actual Process Capability
(Cpk and Ppk)
1.6: Interpretation of the metrics: when is the process capable?
CONDUCTING A PROCESS CAPABILITY ANALYSIS
Step 1: Pre-Study Requirements for Process Capability
Ensuring the basics are in place
Checking the process stability
Setting specification limits
Step 2: Collect and Structure the Data
Step 3: Determining the Correct Capability Analysis to Use
Determining the data type Determining the probability distribution
Step 4: Carry out the Capability Analysis
For Continuous Data Normal
For Continuous Data Non Normal
For Attribute Data Binomial
Step 5: Improving the Process
Compare actual capability to desired capability
Make a decision concerning process changes
Report results of study with recommendations
Step 6: Maintaining Process Capability
CONTENTS
how-to guide
MEASUREMENT
SYSTEM ANALYSIS:
v2
Howto ensure measurement systems
provide good quality data
how-to guide
KEEPING PROCESSES
IN CONTROL:
How to Construct &
Use SPC Charts
v5
PRE-REQUISITES TO READING THIS GUIDE
Before reading this guide you should first have read the
How-To Guides for SPC and MSA. This guide assumes
that you are familiar with the terminology and tools
covered by these earlier guides in the series
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APPENDICES
Appendix 1: Entering Data into Minitab
For continuous data
For binomial data
Appendix 2: Checking the Normality Assumption
Anderson-Darling in Minitab
The normal distribution
Appendix 3: Process Capability Analysis for Normal Data in Minitab
Appendix 4: Distribution Fitting for Non-Normal Data in Minitab
Appendix 5: Process Capability Analysis for Non Normal Data in
Minitab
Appendix 6: Process Capability Analysis for Binomial Data in Minitab
Appendix 7: Basic Statistics for Process Capability Analysis
Estimating process parameters
Appendix 8: Formulae Explained
Short term:
Calculating Cp & Cpk
Long term:
Calculating Pp & Ppk
CONTENTS
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HOW TO USE THIS GUIDE
SEEK
GUIDANCE
F.A.Q
SIGNPOST
The technical
explanation of the
core terminology
The approved
Rolls-Royce answers
to main queries asked
by usersIndicating where you
must seek help from
practitioner experts
such as Black or
Green Belts
Tips on the commonly
observed pitfalls - &
how to avoid them
Where you can find
additional
information, and the
next phase of the
improvement journey
The separate
Workbook which you
must use in parallel
with your learning
This How To Guide is designed as a complete training package that you
can work through individually at your own pace (or in small teams as part of
a facilitated training exercise).
By carefully reading the text, and practising the tools in the associated
Workbook, you will become competent and confident in using theseprocess capability tools in your work area.
The How To Guide is designed to be applicable for use primarily by
Manufacturing Engineers, Design Engineers and Lean Sigma Practitioners
from any area of the business. For this reason, the technical explanations
are based on general business application examples to ensure everyone
can relate to them. Throughout the guide, there are case study examples
which show how the theory is applied at the different stages of the process
control sequence.
Before you start, make sure you also have the Workbook available. It isessential that you work through this in parallel with the How To Guide, and
that you complete the practise questions, plus case study exercise before
you start to use Process Capability techniques in the business.
WORKBOOK
EXERCISE
Icons are used throughout to highlight key elements, and to
signpost supplementary information where appropriate.
Indicates a key
learning point
KEY POINT
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Step 1
Pre-Study Requirements
Step 2
Determining the correct
metric/analysis to use
Step 3
Collect the data
Step 4
Type of Study
Normal Capability
AnalysisBinomial Capability
Analysis
Appendix 1:Checking the normality
assumption
Appendix 2:Entering the data in
Minitab
Step 5
Improving the process
Step 6
Maintaining the improvement
1
2
3
4
5
6
GUIDE STRUCTURE
The flowchart below illustrates the structure of this Guide. The Guide provides step by
step instructions for conducting and interpreting the Process Capability Analysis. Steps
1, 2, 3, 5 & 6 below are common for all types of capability study. Step 4 differs
depending on the type of the study (see step 2 for full guidelines on how to select the
appropriate type of study).
Supplementary information on how to carry out the analysis using Minitab statistical
software is provided in the appendices as outlined below. Additional optional material
is also provided in Appendix 7 & 8 explaining the underlying statistics and equations
used for each analysis method.
Non-Normal
Capability Analysis
Appendix 3 Appendix 4 & 5 Appendix 6
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1.1: The Need for Process Capability AnalysisAt Rolls-Royce we manage thousands of processes everyday. Each one of
our processes has a customer or customers (either internal or external) who
receive the outputs from each process. Our process outputs may be a
physical part or assembly, a design, information or a service. In all cases we
need to know how good each process is at delivering its output to our
customers . This information enables us to effectively manage and improve
process performance and to keep our customers happy.
Without reliable measures of how good our processes are we do not have
the information that we need to manage and improve our processes or
understand our priorities! We must therefore develop methods to quantify
and measure how good our processes are at satisfying our customers. We
must also have a mechanism to allow us to compare the performance of
different processes using common measures.
Process Capability analysis provides us with a common set of comparable
measures for measuring how good our processes are at satisfying ourcustomer requirements.
Capability analysis can help answer the following questions :
Is my process meeting customer specifications?
How will the process perform in the future?
Are improvements needed in the process?
Have we sustained these improvements, or has the process regressed
to its previous unimproved state?
Section 1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
In this section:
1.1: The need for Process Capability Analysis
1.2: What is Process Capability?1.3 Process Capability Metrics
1.4: Understanding and Interpreting measures of Potential Capability and Performance
(Cp & Pp)
1.5: Understanding and Interpreting measures of Process Capability (Cpk ) and
Performance Capability (Ppk)
1.6: Interpretation of the metrics: when is the process capable?
1
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1.2: What is Process Capability?
Process capability is broadly defined as the ability of a process to satisfy
customer expectations. Some processes do a good job of meeting customer
requirements and therefore are considered capable, whilst others do not
and are designated not capable.
The concept of measuring and reporting how good our processes are is of
course not new. Many processes already have measures in place to assess
their ability to meet specification. The most common approach to measuring
process capability is simply to measure the percentage pass or fail rate
for the process.
Percentage pass (or fail) is probably the most widely used and well
understood method of summarising process performance. However what is
often less well understood is that simply counting the number of units that
pass or fail inspection or test is not the best or the most powerful method of
calculating process capability.
Process capability is the ability to produce products or provide services
that meet specifications defined by the customer's needs.
Capability analysis reveals how well each of our processes meets these
specifications, and provides insight into how to improve the process and
sustain your improvements.
Introduction 2
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To understand this consider the two data sets below:
These two histograms each visualise the weight of a cake in grams
(represented by the grey bars) in relation to the customer requirement that
the weight must fall between (198g 202g represented by the two lines).
In both cases we see that 100% of the cakes produced in these samples
fall between the minimum and maximum weight requirements. Both
processes can therefore claim, using % count as the measure, that their
process capability is 100% good.
However, as you can see this does not tell the whole story! Process 1 has
much more variation in cake weight than process 2. We can see therefore
(assuming both processes are in control) that there is a much higher
likelihood of process 1 making a defective cake than process 2. Process 2
is visibly more capable than process 2 but how can we put this into
numbers?
.
Introduction3
1.2: What is Process Capability (continued)
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Introduction 4
1.3: Process Capability Metrics
When assessing process capability we need to use more than one metric
to describe the process.
A good way to understand the need for multiple metrics is to consider the
different ways in which a process can fail to meet a customer requirements.
There are three different scenarios which result in a process being not
capable which we will illustrate here by returning to the cake weight
example:
1) The process variation is too large
Here the amount of variation (the spread) in cake weight is wider than
the acceptable tolerance limit of 198 202g which means that the
process is not capable of delivering 100% of the cakes within customer
requirements.
2) The process average is not properly centred
Here the amount of variation (the spread) of the cake weight is smaller
than the acceptable tolerance limit however the average weight of theprocess is above the target weight of 200g. This means that the
process is likely to produce a cake which is too heavy and is therefore
not capable of delivering 100% of the cakes within customer
requirements despite having a relatively small process spread.
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1.3: Process Capability Metrics (continued)
3) The process average is not properly centred and the process
variation is too large
Here you can see that the process spread is too wide andthe process
average is above the centre weight of 200g. This means that the
process is not capable for more than one reason.
Over time different capability metrics have been developed to cover each of
the above scenarios.
In this guide we will cover how to calculate and interpret metrics for two of
the above scenarios:
- Metrics which consider only process variation (commonly known as
potential capability metrics)
- Metrics which consider both process variation and centring of the
average (commonly known as actual capability metrics)
In addition, for both potential and actual capability metrics, we will also
differentiate between what is known as short term and long term processcapability. This will be fully explained later in this guide but in general terms
this relates to the way that the process variation is estimated as explained
on the next page.
5 Introduction
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Introduction 6
Day 1 Day 2 Day 3 CombinedVariation
Sho
rtterm
Shortterm
Short
term
LongT
erm
1.3: Process Capability Metrics (continued)
Understanding Short Term & Long Term Variation
Process Capability can be calculated using either Short Term or Long
Term metrics. The difference between the two relates to the way in whichthe process spread (variability) is calculated.
Short term variation relates to variation that happens in the short term. For
example within the period of one day, one shift or one machine batch run.
We must be careful when using short term data as it will not reflect all of the
variation that exists in a process as the process shifts and drifts over time.
This is illustrated in the diagram below:
In this illustration we can see how a process may change slightly from one
time period to the next. These changes could be due to variation in the
machines, methods, materials, operators or environmental conditions over
time and are to be expected. If all of the data is combined then the longer
term view gives the complete variation in the process. This is known as long
term variation and takes into account the overall process variation.
Short Term Variation is the variation seen in the short term only
Short Term Process Capability is calculated using the spread seen
solely from short term variation
Long Term Variation is the variation of the overall process population
Long Term Process Capability (commonly known as Process
Performance) is calculated using the spread seen from long term
variation
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7 Introduction
1.3: Process Capability Metrics (continued)
In summary then, we will look at capability metrics for both potential
capability and actual capability and for each will also consider where
appropriate both short term and long term capability metrics.
The metrics which Rolls-Royce uses (following common standards used
within most manufacturing companies) are as follows:
*Note: Cp & Cpk are only used for Normally Distributed Data
The correct choice of metric will depend on how the data has been
collected, the data type and distribution and on which aspects of the
process capability you are interested in.
We will now provide an introduction to understanding and interpreting each
of the above metrics. Full details of how to select and calculate each metric
will be provided in section 2.
Capability
(Short Term)
Performance
(Long Term)
Potential Cp Pp
Actual Cpk Ppk
KEY POINT
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Introduction 8
1.4 Understanding and Interpreting Measures of Potential
Capability
Defining Potential Capability
In section 1.3 we learned that Cp and Pp are capability metrics which
consideronlyprocess variation and that these measures are commonly
known as potential capability metrics.
Potential capability is so called because, by not taking the location of the
process average into account, it reveals what couldhappen ifthe process
is centred. In other words it allows us to understand thepotential
performance of the process ifthe process is centred.
To understand this better lets return to some of the cake weight scenarios
we looked at earlier:
These two processes have an identical process spread. In the example to
the left the process average is perfectly centred between the customer
specification limits whilst in the example to the right the process average
is off centre. Considering onlyprocess spread both processes have the
same potential process capability. The process to the left is perfectly
centred so already performs to its full potential. The process to the right is
off-centre so does not perform to its full potential.
Potential capability metrics consider only process spread whencalculating how good the process is
Potential capability reveals how the process could perform if the
process is centred
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1.4 Understanding and Interpreting Measures of Potential
Capability continued
9 Introduction
Understanding Potential Capability
The potential capability metrics we will use are Cp and Pp. Both are
interpreted in essentially the same way.
In general terms these potential capability metrics are a comparison of
tolerance width against process spread. A simple ratio of
Tolerance/Spread.
To understand this, consider the example below. Here we can see that the
process performance is clearly poor with 100% of the cake weights sitting
beyond the maximum weight. The process potential however is quite good.
You can see clearly that the process spread (approximately 2g) is small in
comparison to the process tolerance (from 198g to 202g which equals a
tolerance band of 4g). In this case the Tolerance/Spread = 2.
For Cp & Pp metrics higher numbers represent better capability than lower
numbers.
This process has the potential, if centred, to perform well although in
reality it has a big performance problem!
A common pitfall is for potential capability measures such as Cp or Pp
to be used incorrectly to describe actual process performance.Remember that it is quite common that the potential and actual
process performance differ. Therefore the use of potential process
capability measures is best restricted to helping understand the
improvement potential of our processes or for rare circumstances when
the position of the process average is not important.
KEY POINT
Spread
Tolerance Width
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Introduction 10
For this example, to understand the potential we can consider how many
times the spread of this process could fit within the tolerance width.
In this case the tolerance width is twice that of the process width giving a
potential process capability metric of 2.
Quite often a process is considered to possess potential capability if its
spread is equal to (or less than) the width of the tolerance. The narrower the
process variation the greater the potential. If the process spread fits less
than one times into the tolerance then the process potential would beconsidered not capable.
The precise methods used for estimating spread of the data and for
calculating these metrics will be covered in section 2.
Spread Spread
Tolerance Width
1.4 Understanding and Interpreting Measures of Potential
Capability continued
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Introduction11
1.5 Understanding and Interpreting Measures of Actual
Capability
Defining Actual Capability
In section 1.3 we learned that Cpk and Ppk are capability metrics whichconsider both process variation andcentring of the average process
variation and that these measures are commonly known as actual
capability metrics.
Actual capability is so called because, by taking into account both process
variation and the location of the process average into account, it reveals the
actual expected performance of the process. To understand this better lets
return to some of the cake weight scenarios:
These two processes have very similar process spreads and so have the
same potential capability. However in the example to the left the process
average is perfectly centred between the customer specification limits
meaning it has a good actual capability. Whilst in the example to the right
the process average is off centre meaning that is does not have a good
actual capability.
Moving the process average does not affect potential process capability but
greatly affects actual capability.
Actual capability metrics considerboth process variation andcentring
of the average process variation
Actual capability measures how well the process output actually
conforms to specification
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1.5 Understanding and Interpreting Measures of Actual
Capability continued
Introduction 12
Understanding Actual Capability
The actual capability metrics we will use are Cpk and Ppk. Both areinterpreted in essentially the same way.
Whilst the Cp and Pp solely considered the process spread in relationship to
the tolerance width, the Cpk and Ppk metrics must also take into account
the position of the process average. To understand this consider the cake
weight scenarios below:
Scenario 1 Scenario 2 Scenario 3
In each of the above scenarios the process spread is identical and is
approximately 2g wide. The process average however is different in each
case. In scenario 1 the process average sits outside of the tolerance limits
altogether at 203g, in scenario 2 the average sits on the upper tolerance
limit at 202g and in scenario 3 the average sits at 201g.
All have equal potential capability. Clearly out of the three the process that
has the best actual capability is scenario 3 but how do we quantify this?
For the process to be capable the process variation must be able to fit easily
in the space between the process average and the closest tolerance limit.
For example if we come back to scenario 3, the distance between theprocess average and the closest tolerance limit is 202g 201g = 1g. The
process could only 100% satisfy the customer if it were able to squeeze half
of its spread into this space which in this case you can see it is just able to
do.
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13 Introduction
1.5 Understanding and Interpreting Measures of Actual
Capability continued
Calculating Actual Capability
In our example (scenario 3) above we can see that half the process spreadis 1g (estimated from the total spread seen in the histogram). This exactly
fits once into the distance between the process average and the closest
customer limit which therefore gives it an actual capability metric of 1.
Quite often a process is considered to be capable if half of its spread can fit
one or more times into the distance between the process average and the
closest specification limit. Therefore this process is capable.
If you return to scenario 1 & 2 on the previous page you can see that neither
of these is capable. Scenario 1 actually has a negative distance between itsaverage the closest specification limit (202g 203g = -1g) which gives it a
negative actual capability. This means that it is more probable that a cake
will be out rather than in specification and this can be clearly seen from the
graph.
In Scenario 2 the process average (202g) sits directly on the customer
upper tolerance limit. This means that there is zero distance between the
process average and the customer specification limit giving the process an
actual capability metric of 0. This means, as can be seen, there is an equal
probability (50:50) of getting a cake in or out of specification.
The precise methods used for estimating spread of the data and for
calculating these metrics will be covered in section 2.
Process spread =
200 202 = 2g
Distance from
process average to
closest customer
limit
= 202 201 = 1g
KEY POINT
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Introduction 14
1.5 Understanding and Interpreting Measures of Actual
Capability continued
Calculating Actual Capability (continued)
The difference between Short Term and Long Term Actual Capability
The difference between short term actual capability and long term actual
performance is the method used in estimating process variation.
For actual process capability we are concerned with how many times we
can fit half of our process spread into distance between the process
average and its nearest customer limit.
For Short Term Actual Capability (Cpk) the short term variation is used to
calculate the process spread.
For Long Term Actual Performance (Ppk) the long term variation is used.
Full details of how to calculate these spreads is given in Appendices 7 & 8.
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15 Introduction
1.6 Interpretation of the Metrics: When is my Process
Capable?
To judge how good the process capability or performance is for an
identified critical characteristic, the measure generated by a capability study
must be compared to some desired goal. Obviously within any business
different processes and product or service characteristics will have diverse
process capability requirements. For example the capability requirement for
a safety critical dimension is likely to be more stringent than the
requirement for the time it takes to issue the invoice for that part.
The capability goal must always be understood before assessing how
capable a process is. However as a general guide, the following guidelines
are often used for assessing process capability :
KEY POINT Process Actual
Capabili
ty
Total
amount
outside
limits
Typical action to be
taken
< 0 > 50% Stop process.
Process
improvementrequired
0 50% Stop process.
Process
improvement
required
0 - 1.0 > 5% Heavy process
control, sorting,
rework, etc.
1.0 0.3% Heavy process
control inspection
1.33 64ppm Reduced inspection,
selected use of
control charts
2.0 0.001ppm Spot checking,
selected use of
control charts
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16
The key steps we will cover are as follows:
Pre-study requirements for Process Capability AnalysisStep 1
Section 2
Conducting a Process Capability
Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
In this section:
A step by step guide for conducting a process capability analysis
Collecting and Organising the DataStep 2
Maintaining Process CapabilityStep 6
Improving the ProcessStep 5
Carrying Out and Interpreting the Capability AnalysisStep 4
Determining the Correct Metric to UseStep 3
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18Conducting a Process Capability AnalysisConducting a Process Capability Analysis17
Case Study - Scenario 1
Anne works for a manufacturer of golf clubs and is the
production engineer responsible for the production line that
manufactures the steel shafts for their range of golf irons.
A key characteristic of the steel shafts manufactured on her productionline is their diameter at various points down the shaft. Anne is particularly
interested in the manufactured diameter of the tip of the shaft. This is
currently manufactured to be 9.400mm +/-0.2mm but due to negative
feedback from end customers about the variable performance of the golf
club range, the designers have made some design alteration to the club
which requires the tolerance for the shaft tip diameter to be tightened to
+/-0.1mm.
Anne suspects that her current process should already be capable of
manufacturing to these tightened customer specification limits but she
needs data to fully understand the capability of the process and thus the
likelihood of her process failing to deliver a club which meets the new
specification.
The company have budgeted that, to avoid future negative publicity,
99.9% of all the shafts must be made to this new specification level.
Anne decides to carry out a process capability analysis to find out whether
her process requires improvement to meet this new specification.
We will introduce you to the application of these steps using three example
scenarios which you can work through one each for normally distributed,
non-normal and binomial data. You will then have the opportunity to turn tothe workbook and practise applying the tools yourself using further case
study examples.
Case Study Examples
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Conducting a Process Capability Analysis 18
Case Study Scenario 2
Jim works for the same golf club manufacturer as Anne
but his job is in the customer service department. His team
answer calls to their dedicated Customer Helpline andhis team pride themselves on their high level of
customer support and after-sales service.
Jims team is small and so have never adopted or measured themselves
against service level agreements. Recently however he has noticed a
growing number of customers complaining about the length of time they
have had to wait on hold before their call is answered by one of his
advisers. A recent article in a golfing magazine compared his companys
service levels against some of their competitors and found them to come
second last in terms of responsiveness. Jim has therefore been set the
target to measure and improve call waiting times.
The first thing Jim does is to benchmark against his competitors and look at
customer feedback to establish what an acceptable waiting time should be.
From this he finds that the maximum waiting time that customers find
acceptable is 30 seconds.
He decides to collect data from his own process to establish his current
process capability against the target of 30 seconds. As this type of data
has not been collected before, Jim decides to collect it manually, with a
simple data collection format to capture the time that the call was made
and the duration of the call, measured in seconds.
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Conducting a Process Capability Analysis19
Case Study Scenario 3
Pat also works for the same golf club manufacturer.
He works in the shipping department and is responsible
for ensuring that all orders received are shipped right firsttime. His team believe that they are pretty good at shipping
customers orders correctly. They do however occasionally ship an order
that is not complete (usually where the customer has ordered additional
accessories as well as clubs) and always quickly rectify any customer
complaints. However the same magazine article that criticised the company
for poor customer service also included customer feedback about receiving
incorrect orders. Pat has been asked to review his process and make
improvements where required.
Since joining the department over two years ago Pat has kept careful
records tracking for every month how many orders are shipped and out of
those how many have to be reworked due to mistakes made in shipping.
To date he has never done anything with this data other than to collect and
review it.
He now thinks there may be an opportunity to analyse the data more
thoroughly to investigate the size of the problem and look for opportunitiesfor improvement.
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Conducting a Process Capability Analysis 20
1a) Ensure the basics are in place
1b) Check Process stability
1c) Set the specification limits
Process Capability improvement builds on the earlier steps of the Process
Excellence Journey. It is not advisable to measure process capability and
not possible to improve it until the process basics are in place and the
process is stable and in control.
As an initial step it is important to begin by checking that the process basics
are in place. In particular the following should be checked:
Pre-study Requirements for Process Capability Analysis
1a)
Ensuring
the
process
basics arein place
Prerequisites: The basics Check
The work area where the process of interest is performed
is safe and well organised
Any equipment being used is in good working order and
well maintained
There is a standard operation in place for the process of
interest
There is evidence that the standard operation is being
complied with
For detailed guidance on how to assess and improve the process
basics please go to RRPS Gain & Maintain Control How To Guide
SIGNPOST
It is also vital to check the that the measurement system being used to collect
the data is reliable. Where possible this should be assessed formally using
Measurement Systems Analysis. As a minimum the following should be
checked.
Prerequisites: the measurement system Check
Equipment used is calibratedEquipment used has sufficient measurement resolution
That the measurement system is suitable for the full range
of measurements
Equipment used is stable
That there are clear operational definitions in place
The repeatability and reproducibility of the measurement
system is known and is sufficient for the measurement of
interest
For full details on how to check the Measurement System, see the
How To guide available on Measurement System Analysis.
SIGNPOST
Step
1
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Pre-study requirements for Process Capability Analysis
The illustration above shows an unstable process. The process
performance changes and is unpredictable from one day to the next.
Because of the instability there is no way of assessing its current or future
ability to satisfy customer requirements.
A process which is stable is in control. This means that the amount of
variation in the process is consistent and predictable over time [see
the illustration below].
When a process is stable it is repeatable, well defined and predictable.Process stability furnishes a high degree of assurance that the future will
closely resemble the past and is thus an essential pre-requisite to
conducting a process capability study.
Process capability studies involve forecasting the future performance of the
process output. This is an impossible task if the past process performance
does not provide a sound basis for prediction [see the illustration below].
Thus, before any type of meaningful capability study can be undertaken, the
process being studied must be stable.
1b)
Check
Process
Stability
Pre-study Requirements for Process Capability Analysis21
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Step
1
Be PreparedPre-study Requirements for Process Capability Analysis 22
One of the best ways to test if a process is stable is to use Statistical
Process Control (SPC).
An SPC Chart enables us to quickly see how a process performance is
changing over time is it getting better, getting worse, or staying the
same? It helps us to quickly and easily identify any problems with the process
It helps us to decide whether we need to take any action if the process
appears to be getting worse (or better)
It helps us see at a glance whether our process is in control
1b)
Check
Process
Stability
continued
121110987654321
2300
2200
2100
2000
1900
1800
1700
1600
Month
ConsumablesSpend()
_Centre Line
Upper Control Limit
Lower Control Limit
SPC Chart of Monthly Conumables Spend
An SPC chart plots data collected from a process in time order. As you can
see in the example above Upper and Lower Control Limits are plotted to
mark the values between which we would expect the majority of the data
points to fall when the process is in control.
If one of more points fall outside the control limits or if a trend, shift or
pattern can be seen in the plot then this indicates that special cause
variation may be present and thus that the process is not stable.
Special Cause Variation is unpredictable variation resulting from
one or more assignable causes acting on the process
Special Cause variation can often be seen as a spike or a shift in
the process performance over time A process which is Out Of Control has Special Cause Variation
present
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Step
1
Be Prepared Pre-study Requirements for Process Capability Analysis23
If the SPC Chart shows that the process has special cause variation present
then this must be fully investigated and, where possible eliminated, before
proceeding with the Process Capability study.
1b)
Check
Process
Stabilitycontinued
If you are unsure how to use SPC charts to check for stability or if you
find that your process has special cause variation present, contact a
local Black Belt for guidance.
SEEKGUIDANCE
For full details on how to construct and interpret Statistical Process
Control Charts see the How To guide available on Constructing and
Using SPC Charts.
SIGNPOST
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Step
1
Be PreparedPre-study Requirements for Process Capability Analysis 24
Process capability is the ability to produce products or provide services that
meet specifications defined by the customer's needs. In order to be able to
calculate process capability we therefore need to know what the specified
customer need is.
For example customer needs could be:
- Delivery time ofless than 24 hours
- A dimension of between 24mm 25mm
- A visual characteristic (such as colour) that passes inspection against a
defined standard
These specifications are usually found in documentation such as customer
specification documents, engineering drawings or service level agreements.
In all cases it is important to check that the specifications being used toassess process capability are both up to date and reflective of the actual
customer needs.
1c)
Set the
Specification
Limits
Specification Limits are values between which products or services
should operate. Specification limits are usually set by customer
requirements.
Specification limits usually consist of both upper and lower
Specification limits (for example the cake must weigh between 198gand 202g). These are sometimes referred to as bilateral
specification limits.
There may be situations where only one specification limit is
appropriate (sometimes known as a unilateral specification limit),
such as lead time. You may require an item to be delivered within 5
days this forms an upper specification limit but if you require the item
the faster the better then there would be no lower limit.
Specification limits are different from control limits. Specification limits
are based on what is required for proper function or appropriate service.
Control limits are calculated from process data. They represent how
your process actually performs, while specification limits show the
desired performance.
Specification limits are commonly known interchangeably by other
terms including customer acceptance limits and tolerance limits.
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Step
1
Be Prepared Pre-study Requirements for Process Capability Analysis25
Make sure that you do not confuse the control limits on an SPC chart
with the customer requirements or tolerance limits. These are NOT the
same thing. Control limits are derived from variation in the process (the
Voice of the Process) whilst specification limits are derived from the
actual customer requirements (the Voice of the Customer).
A common pitfall, particularly in business areas where customer
specifications are less formally captured (such as for response times to
internal customers or service levels for transactional processes),
specification limits can sometimes be set based on assumptions rather
than facts. For example we may assume all requests must be responded
to in 24 hours when in fact the customer would be happy to have a
response within 5 days. Conversely we may set a specification limit forexample to get things right first time 95% of the time which does not in
fact satisfy the customer who perhaps needs things right 100% of the
time. If in doubt make sure you understand the customers real
requirements.
1c)
Set the
Specification
Limitscontinued
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Pre-study Requirements for Process Capability Analysis 26
Case Study - Scenario 1
Annes production environment is highly controlled with
standard processes in place which are complied to and a
high degree of workplace organisation. Therefore, she is
confident that the process basics are in place. Because ofthe criticality of the dimension of the golf clubs the
measurement systems are also carefully controlled and the last
measurement system analysis carried out 2 months ago confirmed that
her measurement system was reliable.
Anne already has data available from her process as it is regularly
sampled to monitor the process stability using an SPC Control Chart.
Manufacturing is done on two shifts 5 days per week. Every shift (morning
and afternoon) a consecutive sample of 5 shafts is taken and measuredand this data is recorded and plotted on an SPC chart. Anne checks the
SPC chart covering the last two weeks production:
There are no points out of control on the chart and no evidence of any
trends, shifts in the process or patterns. Anne is confident that the process
is in control and that all the pre-requisites are in place for her to proceed
with the capability study.
Anne calls the club designer who advised her of the need to tighten the
tolerance of the shaft tips diameter to the club which requires the
tolerance for the shaft tip diameter to be tightened to be 9.4+/-0.1mm to
check that this tolerance really does reflect the customer requirements.
The designer confirmed that trials involving their customers feedback had
confirmed that this was the required tolerance to achieve the required
consistency of performance for the golf club. Anne is therefore confident to
move on to the data collection stage of her project.
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Pre-study Requirements for Process Capability Analysis27
Case Study Scenario 2
Jim is also confident that his area has the process basics and
are in place. To ensure consistency of service his team
are all trained to standard operating procedures for theanswering, handling and logging of customer calls.
He regularly audits the team to check for compliance
and is sure there are no issues.
As he doesnt currently have any data he is not sure whether the process is
stable. He will need to check this once his data has been collected. He
notes that it is a pre-requisite to have a reliable data collection system. He
already has some ideas about how to collect the data but decides to ask a
Black Belt from the Companys continuous improvement team to come
over and help him design a fit for purpose measurement system.
As he has already analysed both benchmarking data and a representative
sample of his own customers feedback he is confident that setting a
maximum acceptable time on hold of 30 seconds is representative of the
customer requirements.
He therefore, feels ready to move forward to the data collection planningphase of his study.
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Pre-study Requirements for Process Capability Analysis29
Case Study Scenario 3
Pat considers his process basics. His team are proud of their
high level of workplace organisation. They also have standard
processes for picking and packing the orders. Pat does wonder
if these processes may need revision but is nevertheless surethat his team do comply with them as they stand so feels
confident that the basics are sufficient.
His data collection system has never been formally checked for reliability. The
system is fairly simple though there are clear definitions documented for
what counts as an order and what count as a defective order . Pat always
completes the log personally so knows there cant be any agreement issues
between data recorders. As he always follows the same operational definitions
for counting the orders and the orders with complaints he feels confident thathis data is reliable. He is not sure how to check whether the data is stable or
not and so asks a local Black Belt to help him analyse his data. The Black Belt
enters Pats data into Minitab and shows him how to run a P-chart to check
the process is in statistical control with the following result:
The SPC chart shows no special cause variation in the process over the past
30 months. Pat is therefore confident that his process is stable over time.
Since Pats data is counting defective orders he is not quite sure what his
specification limit is. He asks the Black Belt for advice on this too. She
explains that Pat needs to check that his operational definition of a defective
order matches what the customer thinks of as defective. Pat defines a
defective order as one where the content shipped does not match the content
on the customer order form. He knows from talking to customers that this
matches the customers understanding of a defective order.
Pat is pleased to find that all the pre-requisites to running a capability analysis
seem to be in place and asks his Black Belt to stay to help him with the
capability analysis.
28
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Collecting and Organising the Data
Step
2 Data Collection GuidelinesTo carry out the process capability analysis we must use a sample data set
which is representative of the complete process. Data must be collected in
time series order and at a frequency and sufficient length of time to fully
represent all of the variation present within the process. For example ifthere are multiple shifts then data must be collected across all of these.
If data already exists or has been collected for the construction of SPC
control charts for the process then this same data can be used so long as
the process is stable (as discussed in Step 1).
Sample Size
The principle concern must be to have sufficient data to be representative to
capture the full variation which can be expected in the process. It is
recommended that as a minimum at least 25 30 data points are used.
Sample Frequency and Subgroups
In order to calculate performance (long term) we need to ensure that our
data collection process captures all potential variation such as changes inoperators, machines, materials or operating conditions. Determination of
how long is long enough should be determined by the subject matter expert.
SEEK
GUIDANCE If you are unsure how much data to collect then please seek the advice
of a local Black Belt.
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Collecting and Organising the Data 30
SIGNPOSTTo review more guidelines on entering data into Minitab please turn to
appendix 1
Case Study - Scenario 1
As discussed, Anne already has data available from
her process as it is regularly sampled to monitor theprocess stability using an SPC Control Chart.
Manufacturing is done on two shifts 5 days per week. Every shift
(morning and afternoon) a consecutive sample of 5 shafts are taken and
measured and this data is recorded in a spread sheet. Anne believes that
most of the sources of variation that she would expect to influence the
process such as changes in the materials, machine adjustments, staff
and environmental factors should be seen within any two week period.
She therefore decides to use the last two weeks SPC data for her study.
She collects this data from the SPC spreadsheet and enters it into Minitab.
She is now ready to analyse the data.
Case Study Scenario 2
Jim needs to design a data collection system with thehelp of his Black Belt. Ideally he would like to update his
call handling system to allow for automatic data collection
however this isnt realistic in the short term. He therefore decides to use a
simple manual spreadsheet for each operator to start a stopwatch when
the caller is placed on hold and stop the stopwatch when the call is picked
up. This is less than ideal as a data collection system and for this reason
Jim decides initially just to collect the data for one day. The local Black
Belt helps Jim and his team to agree robust operational definitions for how
the stopwatches should be used, when to start and stop the clock and
how to record the data. They run a Measurement System Study to confirm
the R&R of the system by each measuring 20 pre-recorded calls a total of
3 times each.
This confirmed that the measurement system was reliable and so Jim and
his team commenced with the data collection.
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Step
2 Case Study Scenario 2 continuedJim and his team collect only a days worth of data but he
has satisfied himself that it is representative and of sufficient
quantity. He therefore decides that it will be suitable for the
purposes of this study.
He enters it into Minitab, remembering that an important pre-requisite for
carrying out the study is that the process is stable. He therefore runs the
appropriate SPC chart (an I MR Chart) to make sure that the process is
stable over time with the following result:
All the data points are between the control limits and there is no evidence of
any trends shifts or patterns in the data. Jim therefore concludes that the
process is stable and that the data is suitable to use for his capability study.
Case Study Scenario 3
Pat, like Anne, already has his data. Having already
organised it in Minitab to draw the SPC chart he is now
ready to go with his process capability analysis.
Collecting and Organising the Data31
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Step
2
32
3a) Determining data type
3b) Determining the probability distribution
Step
3
Determining the Correct Capability Analysis to Use
The type of process capability analysis required and the best capability
metric to use depend on a number of factors as follows:
The type of data continuous data and attribute data are each
analysed using different capability methods
The probability distribution of the data for example, for continuous
data it is important to know whether or not the data is Normally
Distributed
Whether we are interested in the Potential Capability or the Actual
Capability of the process Whether we want to use Long Term orShort Term metrics
In the following section we will cover each of these considerations and
provide a summary flow chart which you can use to determine which
metric or metrics you will to calculate.
The first consideration is the type of data being used. There are two data
types: continuous and attribute.
Where the data from the process is measured on a continuous scale such
as time, weight, dimensions or pressure then we will be collecting and
analysing numerical results (such as the dimension of a part in microns).
This type of data is continuous data.
Continuous data comes from measurements on a continuous scale
such as: temperature, time, distance, weight, dimensions.
Where the data from the process is measuring the count of items which
fall into different categorises such as pass/fail or counting defects such as
scratches in paintwork then the data is said to be Attribute data.
Attribute data is based on upon counting how many units fall into
discrete distinctions such as: pass/fail or percentage defective.
Choosing
the correct
metric:
Overview
3a)
DeterminingData Type
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Step
3
33 Determining the Correct Capability Analysis to Use
Once we know the data type, the next step is to determine the probability
distribution of the data.
The probability distribution of a data set is essentially a description of
the datas shape. This shape once known can be described by a
statistical equation . The equation in turn can then be used to calculate
the likelihood of achieving results within any particular range of values
from the process.
Minitab uses these likelihoods to calculate the process capability. Therefore
to get a reliable measure of process capability it is important that we ask
Minitab to use the correct distribution.
There are two families of probability distributions one for continuous data
and one for attribute data.
Continuous Data can follow a large number of different distributions.
One of the most common and well known continuous data distributions
is the Normal Distribution (often referred to as the bell shaped curve).
Process capability for continuous data is calculated differently depending
on whether the data is Normally Distributed or not. If the data does not
follow the Normal distribution then we say it is Non-Normal.
3b)
Determining
the probability
distribution
If you are unsure about how to determine whether your data is
Normally distributed or not then please refer to your local Black Belt
SEEK
GUIDANCE
SIGNPOST
To find out more about the Normal Distribution and how to test
whether continuous data is Normally Distributed please turn to
Appendix 2
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Step
2
Determining the Correct Capability Analysis to Use 34
Case Study - Scenario 1
Anne is measuring the diameter of her club shaft in mm. She
therefore recognises that her data is continuous. Because of
the nature of her manufacturing process Anne would expect
her data to be normally distributed. She runs a Graphical Summary of the
data in Minitab to check:
The graphical summary confirms Annes expectation that the data is
normally distributed. The p-value for the Anderson-Darling test is > 0.05
and the histogram shows the data to be approximately bell shaped.
Therefore Anne confirms to herself that she must use Normal Capability
Analysis for her dataset.
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Case Study Scenario 2
Jim is measuring hold time in seconds so also has
continuous data. His next step is also to check for normality.First he carried out a graphical summary which is good
practice as he could study the shape of the histogram and get some
insight into whether or not the data was likely to be normal:
Jim noted that the data did not look bell shaped but rather seemed
skewed.
The p-value in the Anderson Darling test was
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Attribute Data has just two possible probability distributions Binomial
and Poisson.
The Binomial distribution is used to describe a process where the
outcomes can be labelled as an event or non-event. If, for example, an
item passes or fails inspection. For process capability analysis we will
use the binomial distribution where we are counting the number of
fails out of a set number of parts inspected.
Where we have attribute data that is Binomial we will use Binomial
Capability Analysis.
The Poisson distribution describes the number of times an event
occurs in a finite observation space. For example, a Poisson
distribution can describe the number of defects in the mechanical
system of an engine or the number of calls to a call centre within aspecified period of time.
Process Capability Analysis using the Poisson distribution is less
frequently used and so is outside of the scope of this How To Guide.
If you think that your attribute data follows the Poisson Distribution then
please contact your local Master Black Belt for advice.
If you are unsure about how to determine the Probability Distribution of
your data then contact your local Black Belt or Master Black Belt for
advice.
3b)
Determining
the probability
distributioncontinued
SEEK
GUIDANCE
Case Study Scenario 3:
Pats data collection system is counting forms. Pat realises
this is attribute data.
Since the assessment of the forms can lead to only two possible
conclusions delivered to order or not delivered to order Pat recognises
that he is counting the number of fails out of a set number of ordersdelivered each month. Therefore his data is Binomial.
Pat will use Binomial Capability Analysis to analyse his data.
Determining the Correct Capability Analysis to Use 36
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So far we have established that the type of process capability study
required depends on:
1) The type of data
2) The probability distribution of the data
The flow chart below summarises the choices which can be made:
Determining
the correct
analysis:
Summary
so far
Type of
data
Probability
distribution
Probability
distribution
Continuous Attribute
Normal Capability
Analysis
Non-Normal
Capability Analysis
Binomial Capability
AnalysisTalk to MBB
Normal Non-
Normal
Binomial Poisson
37 Determining the Correct Capability Analysis to Use
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Determining the Correct Capability Analysis to Use
4a) Analysing the data in Minitab
4b) Interpretation of the graphical output
Carrying out and interpreting the capability analysis
Now the data has been collected we are ready to start to analyse, interpret
and communicate the results.
As the methods for analysis are different for Normal, Non-Normal and
Binomial Capability Analyses we will take each in turn using Anne, Jim
and Pats scenarios as examples.
We will begin with Normal Capability Analysis (for continuous data) and
then move on to Non-Normal Capability Analysis. Finally we will cover
Binomial Capability Analysis (for Attribute data).
If you wish only to follow the procedure for Non-Normal data then pleaseturn to page 49 or for Binomial data then please turn to page 57.
38
If you are unsure about how to determine the Probability Distribution of
your data then contact your local Black Belt or Master Black Belt for
advice.
SEEK
GUIDANCE
Step
4
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NormallyDistributed
D
ata
Normally Distributed Data
4a)
Analysing
the data in
Minitab
Case Study 1 Data Analysis
This is the data on golf club shaft diameter collected by Anne and her
team:
As you can see the data is organised in columns with the subgroups
marked by the Date Collected column. Anne runs her eye over the
data. It looks complete and she cant see any mistyped or missing
data. She therefore proceeds with the Normal Capability analysis.
Step 4: Carrying out and interpreting Normal Process Capability Analysis
39
SIGNPOSTFor details on how to run the Normal Process Capability Analysis in
Minitab please turn to Appendix 3.
Further information on the statistics which underlies these calculations
can be found in Appendix 7 & 8.
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If you are unsure as to how to construct or interpret any of the graphs,
ask for help from a local Black Belt.
Minitab presents the output of the Normal Process Capability Analysis
using a concise graphical report.
For Annes data the output is as follows:
As there are a number of different pieces of information summarised in
this graph we will break it down and explain how to interpret the output
section by section.SEEK
GUIDANCE
4b)
Interpret
graphicaloutput
Normally Distributed Data
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
40
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The process data box simply summarises the data that is being used for
the analysis. Always look at this first to check that it looks correct (for
example that the sample size is what you expected).
LSL & USL refer to the upper and lower specification limits you entered
into the Process Analysis dialogue box. In this example you see these are
the 9.3 9.5mm input for Annes data. Check that these have been input
in the correct format (e.g. in mm not cm).
Target will be blank unless you have entered the Target as optional
information (not covered in this guide).
Sample N is the total size of the sample of data used. In this example
there were 10 days data each with 2 subgroups of 5 shafts each day so
the total size of the sample is 100 data points. Always check that this
number matches the sample size you collected in case you have made a
data input error.
Sample Mean is the mean (average) of all of the 100 data points. This is
used in the calculation for each of the capability metrics (Cpk & Ppk).
StDev (Within) is the calculated measure of short term variation. This is
the standard deviation calculated from the variation within subgroups. This
is used to calculate the short term capability metrics Cp & Cpk. If you
are interested in understanding more about how this metric is calculated
see appendix 7).
StDev (Between) is the calculated measure of total long term variation.
This is the standard deviation calculated using variation both within and
between subgroups overall. This is used in the calculations for the long
term capability metrics Pp & Ppk. If you are interested in understanding
more about how this metric is calculated see appendix 7).
Normally Distributed Data
Interpreting the Process Data
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
4b)
Interpret
graphicaloutput
Process DataLSL 9.3
Target
USL 9.5
Sample Mean 9.41538
Sample N 100
StDev(within) 0.0329631
St Dev(Overall) 0.0350541
41
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The next thing to look at is the graph. This shows the complete data set
represented as a histogram. The red dashed lines mark the location of the
upper and lower customer specification limits (USL & LSL). From this we
can visibly assess the capability of the process and get some clues as to
any problems for example does the process look centred? How does the
spread look in relation to the tolerance width?
The diagram above looks slightly off centre closer to the upper than the
lower limit. The process spread is also quite wide by eye it looksapproximately the same width as the specification limits.
Normally Distributed Data
Interpreting the Graph
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
4b)
Interpret
graphicaloutput
42
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The important Minitab outputs are the short term capability metrics: Cp and
Cpk and the long term performance Pp and Ppk.
Lets start with the short term capability. This is in the upper half of the box.
Here you see the following:
Cp: the short term potential capability of the process. The Cp only takesinto account the spread of the data in relation to the tolerance. Here the
spread of the data is calculated using the short term variation. Here the Cp
is just over 1. Since we saw by eye that the spread of the data was roughly
the same width as the tolerance band this makes sense.
Cpk: the short term actual capability of the process. This takes both the
spread andthe position of the process average into account. If the process
is perfectly centred the Cp and the Cpk will be the same. Here we see the
Cpk is 0.86 which is a bit less than the Cp of 1.01. This tells us that the shortterm actual performance of the process is worse than its potential. That
means that the process must be off centre. Again this does not surprise us
as we saw by eye that the process was off centre when examining the
histogram.
Normally Distributed Data
Interpreting the Capability Metrics
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
4b)
Interpret
graphicaloutput
Cont.
43
Potential (Within) CapabilityCP 1.01
CPL 1.17
CPU 0.86
Cpk 0.96
Overall Capability
Pp 0.95
PPL 1.10
PPU 0.80
Ppk 0.80Cpm
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Overall Capability (Pp & Ppk)
The overall capability calculations are summaries of the long term
capability of the process.
The metrics we can see here to understand the long term process capability
are:
Pp: Remember this is the long term potential capability of the process.
The Pp only takes into account the spread of the data in relation to the
tolerance. Here the spread of the data is calculated using the long term
variation (StDev (Overall) on the data box). Because all the variation isconsidered the spread is seen as being slightly larger than for the short term
metric. Therefore the Pp shows to be 0.95 indicating that the spread is
slightly larger than the tolerance width. This is slightly worse than the Cp
which is what we would expect since long term performance usually is
worse than short term. Therefore we can see that the long term potential
capability of the process is not particularly good. The process has too much
variation to fit within the specification limits.
Ppk: This is the long term performance capability of the process. This
takes into account both the variation and the location of the process mean.
The Ppk is 0.8 which is less than the Pp. Obviously we would expect this as
we already saw with the short term capability metrics that the process was
not performing to its full potential. Of all the metrics this is the one that
gives Anne the best understanding of the actual expected overall
performance of her process in the long term.
But what does a Ppk of 0.8 actually mean? To understand this we look atthe final part of the analysis output.
Normally Distributed Data
Interpreting the Capability Metrics continued
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
4b)
Interpret
graphicaloutput
continued
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Cpk and Ppk metrics can be difficult to understand and explain without
tying them back to what they mean in terms of performance.
Here we see three different performances summarised. Lets look at each in
turn:
The observed performance is the actual
performance seen within the sample of 100
shafts that were measured in the capability
study. Of those shafts all 100 were within the
required specification.
The % Total shows the % that are out of specification. It indicates zero
percent.
This is what Anne expected and why she was confident that her process
was capable of meeting the tightened specifications without need for
alteration.
However the expected long term performance shows a different story.
Remember that the power of this analysis is that it doesnt just count how
many units in the sample hit or miss the specification. Rather it uses theprobabilities of the Normal Distribution to assess the likelihood of the
process hitting of missing the customer requirements in the longer term.
Normally Distributed Data
Interpreting the Performance Metrics
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
4b)
Interpret
graphicaloutput
continued
45
Observed Performance
% < LSL 0.00
% > USL 0.00
% Total 0.00
Exp. Within Performance
% < LSL 0.02
% > USL 0.51
% Total 0.54
Exp. Overall Performance
% < LSL 0.05
% > USL 0.79
% Total 0.84
Observed Performance
% < LSL 0.00
% > USL 0.00
% Total 0.00
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In Annes case study for example she looked at a relatively small amount of
club shaftsjust 10 per day for 10 days out of thousands that are
manufactured. We can see from the histogram that her process spread just
about squeezes into the specification limits so it is not totally unexpected to
see that the observed performance of those 100 shafts sampled was 100%
good. However given that the process is off centre and that its spread fills
the whole of the tolerance range it should also be no surprise to expect that
the process inevitably will produce a defect as some point. The expected
performance quantify this likelihood as an expected defective
percentage.
The Expected Within performance is the
short term actual capability (Cpk)
expressed as a % defective.
This means it is expected , based on the probabilities of the Normal
distribution, that in the short term the process will produce 0.54% defective.
To understand this further the % < LSL and % > USL show how this 0.54%
defective would be expected to break down it is expected that 0.02% willbe undersized and 0.51% will be oversized. This of course makes sense as
we saw that the process sits closer to the upper than to the lower
specification limit.
The Expected Overall performance is the
long term actual performance (Ppk)
expressed as a % defective.
This means it is expected, based on the probabilities of this normal
distribution, that in the long term the process will produce 0.84% defective
it is expected that 0.05% will be undersized and 0.79% will be oversized.
This gives a worse picture than the expected short term capability. This is to
be expected since the actual performance is long term and takes all the
variation in the process into account.
Process knowledge will aid in determining if your data represents long or
short term variation. Note that if your observed performance is grosslydifferent from your within and overall performance this may be an indication
of a different distribution (see appendix 4).
Normally Distributed Data
Interpreting the Performance Metrics
Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis
4b)
Interpret
graphicaloutput
continued
46
Exp. Within Performance
% < LSL 0.02
% > USL 0.51
% Total 0.54
Exp. Overall Performance
% < LSL 0.05
% > USL 0.79
% Total 0.84
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49
Case Study 1 Interpreting the output
Anne is mindful of the business requirements that 99.9% of all the shafts
must be manufactured within the these specification limits. Her initial
feeling from reviewing her sample of 100 shafts was that her process was
capable of hitting this target. Now however, looking at the expected
performance she can see this isnt the case!
She is most interested in the Ppk and associated Expected Overall
Performance metric as this gives her an understanding of how she canexpect the process to perform in the long term. An expected total %
defective of 0.84 means she can only expect her process to deliver
99.16% right first time. This isnt good enough. However she can also see
that the process is off centre so has a potential capability that is better
than the actual performance. She asks her local Black Belt
what Ppk she would need to have to achieve a right first time of 99.9% -
he refers to some capability tables and advised her she would need a Ppk
of 1.03 to achieve a defect level of 0.1%. Since the Pp shows the long
term potential capability to be only 0.95, Anne can see that even is she
centred the process (something she thinks will be easy to do) this would
not be enough in itself to meet her 99.9% target. She will also need to look
at reducing the variation in the process.
Normally Distributed Data
Step 4: Carrying out and interpreting Normal Process Capability Analysis
Interpreting the Performance Metrics4b)
Interpret
graphicaloutput
continued
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Standard
Terminology
Capability
(Short Term)
Performance
(Long Term)
Minitab
Terminology
Potential
(Within)
Capability
Overall
Capability
Potential Cp Pp
ActualCpk Ppk
Expected Within
PerformanceCpk
Expected Overall
PerformancePpk
Relates to
Relates to
Also when interpreting the Expected Performances remember that:
The table below summarises how the Minitab terminology aligns to the
standard terminology we used in Part 1.
4b)
Interpret
graphical
output
continued
Normally Distributed Data
Step 4: Carrying out and interpreting Normal Process Capability Analysis
48
Interpreting the Performance Metrics
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NonNormallyDistrib
uted
Data
We will now examine how to analyse and interpret the data
forNon Normal Process Capability Analysis
4a) Analysing the data in Minitab
4b) Interpretation of the graphical output
Step
4
Carrying out and interpreting Non Normal Process Capability
Analysis
4a)
Analysing
the data in
Minitab
Case Study 2 Data Analysis
This is the data on call hold times collected by Jim and his team
As you can see the data is organised in columns with the time of
each call given in the Time column and the call hold time in
seconds recorded in the Waiting Time column.
Jim checks the data. It looks complete and there are no obvious
typos or missing data. He therefore decides to proceed with the
data analysis.
As his data is Non Normal his first step is to establish which
probability distribution to use for the data analysis.
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The analysis of non-normal data in Minitab is a little more complicated than
for data with a normal distribution and requires two stages of analysis.
The first stage is to identify which probability distribution best fits the dataset. Fortunately Minitab has a function to do this easily for us. It checks the
shape of the data set against a number of continuous probability
distributions and analyses which is the best fit.
Full details of how to do this in Minitab are covered in Appendix 5.
Once the distribution is understood then the non normal capability analysis
function in Minitab can be used to analyse the data.
4a)
Analysing
the data inMinitab
If you are unsure about how to determine the best distribution for your
data then please refer to your local Black Belt.
SEEK
GUIDANCE
SIGNPOSTTo find out how to fit the best distribution for non-normal data turn to
Appendix 4
With the help of his local Black Belt Jim analyses his data and
establishes that the best distribution to use is a 3-Parameter Weibull
distribution.
Jim now has all the information that he needs to be able to carry out the
Non Normal capability analysis.
Step 4: Carrying Out and Interpreting Non-Normal Capability Analysis
Non Normal Data 5250
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If you are unsure as to how to construct or interpret any of the graphs,
ask for help from a local Black Belt.
Minitab presents the output of the Non-Normal Process Capability Analysis
using a concise graphical report.
For Jims data the output is as follows:
As there are a number of different pieces of information summarised in this
graph we will break it down and explain how to interpret the output section
by section.
SEEK
GUIDANCE
4b)
Interpret
graphicaloutput
Step 4: Carrying Out and Interpreting Non-Normal Capability Analysis
Non Normal Data
SIGNPOST
To find out how to do the Non-Normal Capability Analysis in Minitabturn to appendix 5
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The process data box simply summarises the data that is being used for
the analysis. Always look at this first to check that it looks correct (for
example that the sample size is what you expected).
LSL & USL refer to the upper and lower specification limits you entered into
the Process Analysis dialogue box. In this example you see these are 0
30 seconds which are the customer requirements for Jims data. Check that
these have been input in the correct format (e.g. in seconds not minutes).
Note, in the graphic above the LSL has been put in as a boundary as youcannot have negative time.
Target will be blank unless you have entered the Target as optional
information (not covered in this guide).
Sample N is the total size of the sample of data used. In this example Jim
collected one days worth of calls - a total of 75 data points. Always check
that this number matches the sample size you collected in case you have
made a data input error.
The remaining two parameters Shape and Scale are parameters used to
describe the Weibull distribution and can b