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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

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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

    44

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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

    47

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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.

    49

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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


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