capability howto

7/30/2019 Capability Howto

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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


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


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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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




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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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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



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



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


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


35/80

Pre-study Requirements for Process Capability Analysis 26


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.


36/80



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.


37/80



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.


39/80

Collecting and Organising the Data 30

SIGNPOSTTo review more guidelines on entering data into Minitab please turn to

appendix 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.


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.


40/80

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.


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


42/80

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


43/80

Step

2

Determining the Correct Capability Analysis to Use 34


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.


44/80


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


45/80

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


46/80

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.


49/80

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


Step 4: Analysing and Interpreting Gauge R&R StudiesStep 4: Carrying out and interpreting Normal Process Capability Analysis

40


50/80

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).


Interpreting the Process Data


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


51/80

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.


Interpreting the Graph


4b)

Interpret

graphicaloutput

42


52/80

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.


Interpreting the Capability Metrics


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.


Interpreting the Capability Metrics continued


4b)

Interpret

graphicaloutput

continued

44


54/80

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.


Interpreting the Performance Metrics


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).




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.



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



48



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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

capability howto

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