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Page 1: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

Statistical Process Control

The Control Chart

Part 1

Page 2: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

Change Management We develop and implement manufacturing strategies, quality systems and Health and Safety management systems to meet the requirements of the latest legislation. We can also provide project management services for similar large projects.

Manufacturing Strategy, Quality Management, Factory Layout, Health & Safety Management, Project Management.

Technical Writing

We develop technical literature to back-up or sell your products. These can be complex product manuals, specification guides or internal training information. All are designed to your needs and to a variety of formats from paper based to Help files or web pages. Product Manuals & Technical Information, Specification Guides, Help Files & Expert Systems, Public Relations & Article Generation, Quality Documentation Services, Web Site Generation and Management.

Training Seminars

We provide standard courses and also develop special courses to your specifications. Manufacturing Strategy, Quality Management, PVC-U Windows - Technical Aspects, How to specify PVC-U windows, Statistical Process Control, Potential Failure Mode Effects Analysis, Health & Safety, Project & Design Management.

Product Design

We help to design and produce new products. At the forefront of product developments for 20 years we can help to get your product to market.

Product Design & Management.

Field Service

We carry out a truly independent review and assessment of your needs for new machinery or systems.

Health Checks, Customer Set-up & Service, Information & Telephone Service.

COMPANY PROFILE

•Tangram Technology Ltd. was formed in 1996 as a technology based consultancy dealing with the needs of the plastics processing, plastics building products and PVC-U windows industries.

•Tangram provides high quality change management, technical writing, training, product design consultancy and field services for these diverse industries.

•Our client base consists of some of the largest plastics processing companies in the UK, window systems designers, window fabricators, specifiers, large contractors, hardware manufacturers and computer services companies. We carry out extensive work for the UK Government (DEFRA and DTI), the EC and the World Bank in a variety of fields.

•Tangram is technology based consultancy, not a management consultancy. We supply specialist technical knowledge needed by our client base.

TANGRAM TECHNOLOGY Ltd.

P.O. Box 24, HITCHIN, HERTS. SG5 2FP Tel: 07000 780 971 Fax: 07000 782 777 Email: [email protected] Web: www.tangram.co.uk

Specialist Consulting Engineers for Plastics Processing, Plastics Building Products and PVC-U Windows.

TANGRAM TECHNOLOGY LTD. - Products and Services

Page 3: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

Statistical Process Control

Part 1 The Control Chart

Dr Robin Kent Tangram Technology Ltd

Page 4: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

Tangram Technology Ltd.

PO BOX 24, HITCHIN, SG5 2FP

© 2004, Tangram Technology

Revision 1 - April 2007

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means - electronic, mechanical, photocopying, recording or otherwise - without the prior permission of the publisher, Tangram Technology Limited, PO Box 24, Hitchin, SG5 2FP, UK

Page 5: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

Statistical Process Control

A practical workbook for industry

The Control Chart

CONTENTS

1. What is Quality? ..................................................................................................... 10

2. Why do we want Quality? ...................................................................................... 12

3. How do we get Quality? ......................................................................................... 14

4. How do we build Quality into the Product?.......................................................... 16

5. Inspection Types .................................................................................................... 18

6. Statistical Process Control .................................................................................... 20

7. The Basic Statistics................................................................................................ 22

8. The Capability Study .............................................................................................. 24

9. The Normal Distribution......................................................................................... 26

10. Tolerances - Location............................................................................................. 28

11. Tolerances - Spread ............................................................................................... 30

12. How to get the Numbers - Spread ......................................................................... 32

13. How to get the Numbers - Location ...................................................................... 34

14. Process Setting - How not to do it! ....................................................................... 36

15. Setting the Range Process Control Chart ............................................................ 38

16. Setting the Average Process Control Chart ......................................................... 40

17. Using the Process Control Chart .......................................................................... 42

18. A Working Document ............................................................................................. 44

19. The Alarms .............................................................................................................. 46

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Scope and Objectives

This Workbook is designed to allow trainers to carry out a structured training session of approximately 1 hour. The session covers the basics of Statistical Process Control for all levels of staff.

The Workbook provides internal or external trainers with all of the basic resources necessary to deliver a training session. The trainer should be either an internal trainer or an external professional trainer with a good knowledge of the sector.

This session covers the reasons for SPC and some of the basic steps to actually introduce SPC into a factory. The sessions and training only cover SPC for variables using average and range information. We have found this to be the best basis for introducing SPC into manufacturing. The use of SPC for attributes can always be introduced at a later stage when SPC variables is established and has proved it’s worth.

A second session (Part 2) covers reading control charts and getting the best information out of them.

Session timings

This training session is designed to take approximately 1 hour to run.

Changing the presentation

Trainers should feel free to modify the structure and content of the session to match the needs of the audience. Material that is not considered relevant may be deleted or additional material can be added to cover specific points that are felt to be particularly relevant.

The Workbook

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How to use the Workbook (Trainer’s Page)

Left Hand Page

Trainer Notes

and

sources of further information.

Right Hand Page

Displayed Information

(e.g. OHP slide)

and

Trainee Notes.

How to use this Workbook

This workbook is designed for use by internal trainers in the rubber industry to train employees of a company in the techniques of effective energy efficiency.

The workbook uses STOP format - this means ‘Single Theme On Page’. This is designed to provide the trainer with all the information they need to carry out effective training.

Use the training book with the pages as shown below:

Left Hand Page - The trainer’s page

The left hand page gives notes and discussion points for the trainer to cover whilst discussing this particular topic. It gives:

•A summary of the key points to be made.

•Some questions to ask of the delegates.

•Possible examples that will engage the delegates in the training.

•Sources of further information for the trainer - this is always in the box at the bottom of the page.

Right Hand Page - The delegate’s page

The right hand page will show what is to be on the overhead projector (OHP), on the PowerPoint screen or in the delegate’s copy of the Workbook (depending on the method of presentation chosen). The trainer can readily refer to this information and see exactly what the delegates are seeing.

Further Information

The Workbook series is designed to be self-sufficient and can be used with no other information other than internal company information where appropriate. Where trainers would like to have further information or explanation, this section of the trainer’s page contains signposts to other sources of information.

As a general rule, it is recommended that the trainer obtains the complete set of further information as part of preparing the training session.

Page 9: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

This right hand page contains all the required information for delegates.

The right hand pages do not have page numbers and the trainer can modify the order of the presentation to their own requirements.

Overhead projection slides

The right hand pages can be copied directly onto overhead projection slides to be shown to the delegates during the training session.

PowerPoint presentations

The information on this page is also contained in the Microsoft PowerPoint presentation that can be downloaded with the Workbook.

Delegate Workbooks

The right hand pages contain all the essential that the delegate needs to know. They can form a workbook for the delegate to retain and make notes. Print out only the odd numbered pages to quickly and easily create a Delegate Workbook.

How to use the Workbook (Delegate’s Page)

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Introduction

The trainer should introduce the session.

‘This training session has being specifically designed and developed for the plastics processing industry by Tangram Technology Ltd.’

Trainer Tip - Ask trainees to nominate a ‘Quality Car’. The chances are that they will nominate a Rolls Royce, a Ferrari etc.

Point out that quality has little to do with price and that what they have nominated are expensive cars. How would they rate a Ferrari that always broke down?

What is Quality?

Further Information:

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WHAT IS QUALITY? •••• Quality is:

•••• What gives complete customer satisfaction.

•••• ‘Fitness for purpose and value for money’

• ‘Conformance to requirement’

•••• Value for money = Quality for price

•••• Price is negotiable

•••• Quality is not negotiable

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Everybody wants quality

Quality products increase sales through increased customer satisfaction

Internally it gives less hassle!

Think how much work it would save if we only sold products that didn’t come back to customer's who did?

Think how much successful we would be if the customer's not only came back but brought a friend?

Everybody wants quality from the company - not only the customers but also the employees.

Trainer Tip - Ask the trainees if they expect quality from the company? How would they feel if their wages were treated the way some employees treat the production? How would they react if the Wages Department thought that ‘Near enough was good enough’?

Trainer Tip - Ask the employees what the minimum amount of money they would complain about in their wages? Get this as a % of their wages.

Why do we want Quality?

Further Information:

• Caplen, PRACTICAL APPROACH TO QUALITY CONTROL, Business Books.

• Price, RIGHT FIRST TIME, Gower Press.

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WHY DO WE WANT QUALITY?

IF WE EXPECT QUALITY THEN WHY SHOULDN’T

OUR CUSTOMERS EXPECT IT?

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Types of defects

There are two types of defects. These are:

• Isolated defects - these occur only once or at random, e.g. surface damage in packaging, missing parts in package.

• Serial defects - these occur repeatedly until action is taken, e.g. surface lines in extrusion, underweight products etc.

The two types of defects have different types of causes and different techniques are needed to deal with them.

This course concentrates on serial defects.

Detection and prevention of defects

Detection finds defects after they have been created. Inspecting and sorting product does not make it a quality product.

You cannot inspect quality into a product.

Prevention stops defects before they are created.

You must build quality into a product.

Good quality product is good for everybody in the company. Good quality products decrease costs and increase sales. These make jobs more secure for everybody in the company.

Further Information:

• Caplen, PRACTICAL APPROACH TO QUALITY CONTROL, Business Books.

• Price, RIGHT FIRST TIME, Gower Press.

How to we get Quality?

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HOW DO WE GET QUALITY?

WE MUST BUILD QUALITY INTO THE PRODUCT

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Further Information:

• Juran, QUALITY CONTROL HANDBOOK, McGraw Hill.

Building quality into the product

There are 5 main influences on product quality:

• Men - the things that people do will have a large effect on the product quality, e.g. are operators careful or are they slipshod, do they care about the job and the product?

• Methods - the ways that people do things will have a large effect on the product quality, e.g. people may think they all work to the same procedures but do they? Does every operator have different method of assessing the product?

• Machines - the reliability and consistency of the machines we use will have a large effect on the product quality, e.g. is the machine right for the job? Is it an old machines that breaks down often?

• Materials - the types and consistency of the materials we use will have a large effect on the product quality, e.g. is the material the right one? Did the buyer get a discount for ‘off-specification material?

• Environment - the environment will have a large effect on the product quality, e.g. is the factory temperature consistent? Does the water temperature vary with the outside temperature?

All these factors need to be considered to start to build quality into the product.

The aim is to control the factors, measure the output to gain information on the process and to use this information to feed back as action on the process.

The ‘Plan - Do - Check - Act’ Action Cycle

When improving quality, we will always use the ‘Plan - Do - Check - Act’ Action Cycle to make sure that what we change actually improves the product quality.

This cycle is also part of the essential toolkit for BS EN ISO 9001: 2000.

How do we build Quality into the Product?

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HOW DO WE BUILD QUALITY INTO THE

PRODUCT?

PlanWhat to do &

how to do it

ActHow to improve

next time

DoDo what was

planned

CheckDid things go

to plan

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Sensory/physical

Sensory

• Judgement made by human senses.

• Difficult to set criteria.

Physical

• Judgement made by measuring devices.

Subjective/objective

Subjective

• Judgement made by person who did the work.

• Compromise/inattention.

Objective

• Judgement made by someone other than the operator.

Process internal/process external

Process internal

• Carried out at the same process.

• Rapid feedback and effective defect prevention.

Process external

• Carried out at a later process.

• Slow feedback and thus defect detection.

100% inspection/statistical sampling

100% inspection

• Every processed item checked (generally externally and objective).

• Costly.

• Boring.

• Can be effective if process internal.

• Inspection.

Statistical sampling

• Extrapolate from a small number of samples to make predictions.

• Economic.

Inspection Types

Further Information:

• Juran, QUALITY CONTROL HANDBOOK, McGraw Hill.

Page 19: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

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INSPECTION TYPES •••• Sensory/physical

•••• Subjective/objective

•••• Process internal/process external

•••• 100% inspection/statistical sampling

The most effective inspection method is:

•••• physical

•••• subjective

•••• process internal

•••• statistical

This leads to Statistical Process ControlPC

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Who is responsible?

‘The person ultimately responsible for the quality of the product is the person producing that product’.

The person responsible cannot be the Quality Controller or Inspector, they are there only as a check.

In modern factories they should not be there at all. Operators should be responsible for quality and checking their own work and the Inspector should be there only to help if the process is ‘out-of-control’.

Two questions:

Can we make it OK?

This is all about whether the machine, tooling, material and process can ever make the products within tolerance. It is useless trying to make a product within tolerances which are too tight for the process.

We can assess this quickly using a ‘Capability Study’ to find out if we can reasonably expect the process to deliver product within the specifications. Capability studies can be carried out by anyone with a knowledge of the process and a good calculator - they are not difficult and tell us what we can expect from the process. Capability studies will generally be conducted by the machine and tooling supplier and verified by R&D/QC but most operators can do them to!

Are we making it OK?

Once we know that it is possible to make the product OK then it is necessary to know that we are actually making it OK on a regular basis. To find this out we use a ‘Control Chart’ to measure the output of the process.

Control charts are produced by operators, they only need simple measurements and a piece of paper but they allow operators to ‘see inside’ the process and to know when to take action and to call for help - more importantly they tell operators when to do nothing and when to leave the process alone.

Statistical Process Control

Further Information:

• Grant & Leavenworth, STATISTICAL QUALITY CONTROL, McGraw Hill.

• Price, RIGHT FIRST TIME, Gower Press.

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SPC

Statistical Process Control

‘The person ultimately responsible for the quality of

the product is the person producing that product’

Can we make it OK?

Capability Studies

Are we making it OK?

Control Charts

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Further Information:

Do not be afraid

The statistics of Statistical Process Control are really very simple. If an operator can use a simple pocket calculator then they can use SPC. In most cases it doesn’t even need a calculator and the arithmetic can be done in your head - at the simplest level SPC ultimately involves adding up 5 numbers and finding the average and then subtracting the smallest number from the largest number to find the range. This is not difficult!

Statistical definitions

All the statistical definitions needed are given on the slide, these are all you need to know. You are now a statistical expert because you know more about statistics then most people!

The Basic Statistics

Further Information:

• Grant & Leavenworth, STATISTICAL QUALITY CONTROL, McGraw Hill.

Page 23: Statistical Process Control 1 - tangram.co.uktangram.co.uk/TI-Statistical Process Control-Training Part 1.pdf · windows, Statistical Process Control, Potential Failure Mode Effects

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STATISTICAL DEFINITIONS

X

X

X

R

R

σ

A measurement value

X BAR - The average of a number of measurements

X DOUBLE BAR - The average of a number of averages.

RANGE - The difference between the largest

measurement and the smallest measurement in a group

of measurements.

R BAR - The average of a number of ranges.

SIGMA - The standard deviation - a measurement of

how wide a distribution is.

Population

Sample

All the parts in a batch or production run

A selection from the population

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Further Information:

What it is and isn’t

A Capability Study is simply a method of assessing if it is possible for a given machine or process to produce to a given specification.

It is not a statement of desire or lack of desire, simply an answer to the question ‘Can we make it OK?’.

Sampling and histograms

If we take a sample of parts from a machine (all produced at the same time) and measured a single property such as a dimension then we would expect a variation in the measurements. These sample results can be plotted on a bar chart (or histogram) and joined up to form a distribution of the results.

If we measured enough points to get the results for the whole population the in most cases we would end up with a smooth curve and it would probably look like the bell curve or normal distribution. The good thing about the normal distribution is that statisticians have been working with this for many years and know a lot about it. The normal distribution is found in many natural and industrial populations:

It can be used to describe (amongst other things):

• People's heights

• People’s intelligence

• The size of parts

• The weight of parts

The normal distribution isn’t always a simple symmetrical bell, sometimes it is skewed to one side and sometimes it is truncated (cut-off) at the ends or the middle.

A left skew might be seen if you measured the height of basketball players - they tend to be taller than the total population.

A right skew might be seen if you measured the height of jockeys - they tend to be smaller than the total population.

A truncated distribution might be seen if you sorted items before measuring them.

The important thing is that you need to be careful that your sample is from the population you want to control - if the population is skewed then the following numbers do not work and other techniques are needed. Fortunately for many industrial uses the normal distribution is applicable and works well.

The Capability Study

Further Information:

• Caplen, PRACTICAL APPROACH TO QUALITY CONTROL, Business Books.

• Juran, QUALITY CONTROL HANDBOOK, McGraw Hill.

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CAPABILITY STUDIES

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X

The critical numbers

Where the normal distribution is fully symmetrical, it is still possible for the shape of the curve to vary in both spread and location.

Variations in location

The actual location if the normal distribution can change so that it is the same shape but is moved sideways to the left or the right.

Variations in spread

The spread or width of the normal distribution can vary so that it is the same height but extends outwards further or less.

Describing the curve

Fortunately, despite the complex shape of the normal distribution, it is possible to fully describe it by using only 2 numbers, these are:

The average ( ): This is the centre line of the normal distribution and describes the location of the curve. If the average is higher the curve moves to the right and if it is lower then the curve moves to the left.

The standard deviation (σ) : This is a description of the amount of spread of the curve. A high standard deviation means that the curve is very wide and a low standard deviation means that the curve is thin.

The percentages of the normal distribution

The normal distribution also tells us the probability of finding a given value. For a normal distribution:

Therefore if the average of a population is 8 and the standard deviation is 1 then 99.73% of the population will have values between 5 (8-3) and 11 (8+3).

The Normal Distribution

Further Information:

• Juran, QUALITY CONTROL HANDBOOK, McGraw Hill.

• Price, RIGHT FIRST TIME, Gower Press.

σ±X contains 68.26% of the population.

σ2±X contains 95.44% of the population.

σ3±X contains 99.73% of the population.

σ4±X contains 99.99% of the population.

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THE NUMBERS

68.26%

95.44%

99.73%

99.994%

σ− σ+

σ2+σ2−

σ3+σ3−

σ4+σ4−

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X

Comparing location

Once the normal distribution for a process is established it is possible to compare the results with a set of tolerances as required by the customer or as established for good operation of the process.

The examples show how the location (as described by ) can easily vary and send parts into or out of tolerance.

The ideal result for location is an average which is equal to the nominal value of the dimension or value. We will describe a new number to identify this later.

Tolerances - Location

Further Information:

• Oakland, STATISTICAL PROCESS CONTROL, Heinemann.

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TOLERANCES

Accept RejectReject

T+T-

T+T-

T+T-

Accept RejectReject

Accept RejectReject

Poor location - parts will be

produced outside the lower

tolerance limit.

Good location - all parts will

be produced in tolerance.

Poor locations - parts will be

produced outside the upper

tolerance limit.

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Further Information:

Comparing spread

Once the normal distribution for a process is established it is possible to compare the results with a set of tolerances as required by the customer or as established for good operation of the process.

The examples show how the spread (as described by σ) can easily vary and send parts into or out of tolerance.

The ideal result for spread is a value which fits easily into the tolerance band. We will describe a new number to identify this later.

Tolerances - Spread

Further Information:

• Price, RIGHT FIRST TIME, Gower Press.

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TOLERANCES

T+T-

T+T-

T+T-

Accept RejectReject

Accept RejectReject

Accept RejectReject

Poor spread - parts will

always be produced outside

the tolerance limits.

Acceptable spread - Parts will

only be produced in tolerance

if the location is exactly

centred.

Good spread - parts will be

produced in tolerance for a

wide range of locations.

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X

Further Information:

Further Information:

How to get the Numbers - Spread

σ6

LSLUSLCp

−=

Procedure (see Essentials Sheet 1)

• Select 50 samples from a continuous run of product.

• Measure the desired feature and plot the results in a histogram using 6 bars.

• If the distribution is a normal distribution then proceed.

Note: If the distribution is not a normal distribution then other techniques are needed.

• Calculate the mean ( ) and the standard deviation (σ) for the 50 results using a standard calculator.

• Note: When using a standard calculator you should generally use the σn-1 key to get the σ for the population from a sample of results

• Estimate the process variability (relative to the specified tolerances) from the formula:

where:

USL = Upper Set Limit or Upper Acceptable Tolerance.

LSL = Lower Set Limit or Lower Acceptable Tolerance.

This value is a measure of the ‘process spread’.

• If Cp is less than 1.00 then the normal distribution width is greater than the tolerance band width. Defects will always be produced on the top or bottom of the tolerance band and it will not be possible for the process to produce parts within tolerance.

• If Cp is equal to 1.00 then the normal distribution width is equal to the tolerance band width. Only a small amount of defects will be produced if the process is exactly centred and if the process does not change. Otherwise it is extremely likely that defects will be produced.

• If Cp is greater than 1.33 then the normal distribution width is less than the tolerance band width. Defects will not be produced and exact centring is not necessary. In this case the process is said to be ‘capable’.

• As a general rule Cp must be not less than 1.33 to show acceptable process spread, this is to allow for minor variations in materials, men, methods, machines and environment.

• Cp only describes the spread, it does not describe the location and even with a small spread (Cp >1.33) it is possible to produce out of tolerance parts. We also need to be able to describe the location of the curve.

Further Information:

• Price, RIGHT FIRST TIME, Gower Press.

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HOW TO GET THE NUMBERS

Cp is greater than 1.33

The process spread is less than the tolerances. It will be possible to produce all the parts inside the tolerances even with process varia-tions.

Cp is equal to 1.00

It will be possible to produce 99.73% of the parts inside the tolerances but only if the process is exactly centred on the tolerance band and does not vary.

Cp is less than 1.00

The process is centred on the tolerances but it will never be possible to produce all the parts inside the toler-ance.

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σ

XUSLZUPPER

−=

σ

LSLXZLOWER

−=

minZ

3

minZ

C pk =

Further Information:

Further Information:

Further Information:

How to get the Numbers - Location

Procedure (see Essentials Sheet 1)

• Using the information from the 50 samples (the mean and standard deviation)

• Calculate ZUPPER and ZLOWER from the formulae below and find the smaller of the two:

is the smaller of and .

Calculate Cpk from the formula:

This value is a measure of the ‘process location’.

• As with Cp, if Cpk is less than 1.00 then it will not be possible for the process to produce parts within tolerance. The process will always be located such that out-of-tolerance parts are produced.

• If Cpk is equal to 1.00 then the process will be located such any small change in the process will result in defects being produced. It is extremely likely that defects will be produced.

• If Cpk is greater than 1.33 then the normal distribution will be located such that it is well within the tolerance band width. Defects will not be produced and exact centring is not necessary. In this case the process is said to be ‘capable’.

• As a general rule Cpk must be not less than 1.33 to show acceptable process location, this is to allow for minor variations in materials, men, methods, machines and environment.

• The values for ZUPPER and ZLOWER can be used with Pz tables to calculate the proportion of the output that will be beyond the specification limits but it is better to work on the process to get it better rather than calculate how many out-of-tolerance parts you are going to be producing.

Further Information:

• Price, RIGHT FIRST TIME, Gower Press.

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35

HOW TO GET THE NUMBERS

Cpk is greater than 1.33

The process is well within the tolerances and process variations can occur with no out of tolerance parts being produced.

Cpk is equal to 1.00

The process is exactly on the tolerance at either the upper or the lower set limit. It will only just be possible to pro-duce in tolerance parts if the process does not change.

Cpk is less than 1.00

The process is outside the tolerances at either the upper or lower set limits. It will never be possible to pro-duce all the parts inside the tolerance.

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Further Information:

Further Information:

Further Information:

How it happens

The operator selects one sample (which happens to be at the top end of the distribution) and finds that it is ‘high’. The process is set with this single high reading despite the fact that the process is actually totally fine.

The process is adjusted downwards by the same amount that it was running high - therefore pushing the process so that it produces parts outside specification. The process is again measured and found to be running low.

The process is again adjusted and this time overshoots so that it is running high and parts are again produced outside of specification.

The cycle continues and see-saws in and out of control.

This situation happened day after day in industry.

Even worse (perhaps) is when the operator selects a sample that shows the process to be OK when it is mostly outside the tolerance limits - the process is then operated with out-of-tolerance parts being produced while the operator thinks that everything is OK.

Think about it.

How it should happen

To set a process you should never rely in a single sample result. Always make at least 5 measurement and set the process on the basis of the average of the 5 measurements.

Process Setting - How not to do it!

Further Information:

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37

PROCESS SETTING

T+T-

T+T-

T+T-

Offset 1

Adjustment 1

Offset 2

Adjustment 2

The process is set with a

single reading. If this is

located at the top of the

distribution then it will appear

that the process is running

high. This is despite the fact

that the process is actually

totally fine.

The process is adjusted

downwards by the same

amount that it was running

high - therefore pushing the

process so that it produces

parts outside specification.

The process is again

measured and found to be

running low.

The process is again adjusted

and this time overshoots so

that it is running high and

parts are again produced

outside of specification.

This situation happened day

after day in industry.

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R

Starting out

• Using a running and stable process, take 5 samples from the process each hour.

• Record the average and the range (- the difference between the highest and lowest measurements) for the set of 5 samples.

• Continue until 25 sets of data are available.

Range Control Charts

• Plot the results for the range on a preliminary Control Chart

• Calculate the control limits for R by:

Find the average of the 25 values for R. This is and

The control limits are given by

Lower Control Limit for R:

Upper Control Limit for R:

Where D3 and D4 are constants that vary with the sample size as below:

For a sample size of 5 (see Step 1) the Control Limits are then

Lower Control Limit for R:

Upper Control Limit for R:

• Plot the average for the range ( ) and the Upper and Lower Control Limits (UCLR and LCLR) on the Control Chart.

• Interpret the Range Control Chart for control (see below).

These calculations will normally be done by the Quality Control Department.

Further Information:

Further Information:

Further Information:

Further Information:

• Oakland, STATISTICAL PROCESS CONTROL, Heinemann.

Setting the Range Process Control Chart

R25

valuesR of Sum=R

RDLCLR ×=3

RDUCLR ×=4

Sample Size 2 3 4 5 6 7 8 9 10

D3 0 0 0 0 0 0.08 0.14 0.18 0.22

D4 3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78

0=RLCL

RUCLR ×= 11.2

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THE RANGE CHART

R

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40

X

XUCL

XLCL

X

RAXLCLX

×−=2

X

X

Starting out

• Using a running and stable process, take 5 samples from the process each hour.

• Record the average and the range (- the difference between the highest and lowest measurements) for the set of 5 samples.

• Continue until 25 sets of data are available.

Average Charts

• Plot the results for the average on a preliminary Control Chart

• Calculate the control limits for by:

Find the average of the 25 values for . This is and

The control limits are given by

Lower Control Limit for :

Upper Control Limit for :

Where A2 is a constant that varies with the sample size as below:

Use A2 = 0.58 for a sample size of 5 (see Step 1) and calculate the Control Limits.

• Plot the average of the averages ( ) and the Upper and Lower Control Limits ( and ) on the Control Chart.

• Interpret the Average Control Chart for control (see below).

These calculations will normally be done by the Quality Control Department.

Further Information:

Further Information:

Further Information:

Further Information:

• Oakland, STATISTICAL PROCESS CONTROL, Heinemann.

Setting the Average Process Control Chart

25

valuesX of Sum=XX

RAXUCLX

×+=2

Sample Size 2 3 4 5 6 7 8 9 10

A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31

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THE AVERAGE CHART

X

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42

Recording on the charts

• Use the previously created Control Charts (see Sheet 2) with the Average and the Upper and Lower Control limits marked on them.

• Measure 5 samples every hour and calculate:

• The average of the 5 measurements (add them up and divide by 5)

• The range of the 5 measurements (subtract the lowest from the highest).

• Plot the average and the range on the relevant Control Chart during the production run.

• Join the new result to the previous result with a straight line.

Interpret the Range Control Chart

• It is essential to interpret the range chart before the average chart - if the range chart is not in control then no meaningful information can be obtained from the average chart.

• Look for any of the following patterns:

• No points outside the control limits (upper or lower).

• No run of 7 consecutive points above or below the average line.

• No run of 7 consecutive points upward or downward.

• No pattern with 2/3 of the points in the middle 1/3 of the control limits.

• No pattern with 2/3 of the points in the outer 2/3 of the control limits.

• If any of these patterns is present then the process is out of control for the range.

• Investigate for special causes and correct as required.

• If the Range Control Chart is in order then interpret the Average Control Chart

Interpret the Average Control Chart

• Look for the same patterns in the Average Control Chart as in the Range Control Chart.

• If any of the patterns is present then the process is out of control for the average.

• Investigate for special causes and correct as required.

Part 2 has more details on how to interpret the range and average charts and what to took for.

Further Information:

Further Information:

Further Information:

Further Information:

• Oakland, STATISTICAL PROCESS CONTROL, Heinemann.

Using the Process Control Chart

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43

PROCESS CONTROL

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44

Important points

• Operators should carry out the measurements and record them on the chart themselves - this is not to be done by ‘Quality Control’, it is an operator task.

• Operators should join the recorded and calculated points together with a straight line to the previous result.

• Operators should always initial and date the Control Chart when they make the measurements.

• Operators should always record significant events (materials batch changes, operator changes, colour changes etc) on the Control Chart - it makes finding the special causes easier to find and rectify.

• Control Charts are working documents, not works of art.

• Unless the Control Chart indicates one of the above patterns then the process should never be adjusted by the operator. Parts are being produced in tolerance and the process is in control - there is no need for adjustment.

• Hint: To drive this home, make adjusting the machine without a Control Chart warning a disciplinary offence.

• Do not be in a rush to adjust the machine - always study the process carefully before making any adjustments to the machine.

• Control Charts provide a ‘common language’ for operators, managers and reporting. They are the glue that holds a factory together.

• Control Charts can be used to detect ‘special causes’ these can be fixed or eliminated by local action.

• The detection and elimination of ‘common causes’ (the reason for the Upper and Lower Control Limits) is generally much more difficult. Eliminating ‘common causes’ generally requires management action and possibly even investment in the process.

Further Information:

Further Information:

Further Information:

Further Information:

• Oakland, STATISTICAL PROCESS CONTROL, Heinemann.

A Working Document

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45

PROCESS CONTROL The Process Control Chart is a working document - it is not a work of art.

Mark on it, write on it but keep it safe.

Unless the Control Chart tells you to take action you do nothing.

Note on the chart any of the following:

• materials batch changes.

• operator changes.

• machine changes.

• anything that could have an effect in quality.

•••• Any time ‘HELP’ was called and the action taken by the person helping.

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46

Alarms test answers:

Further Information:

Further Information:

Further Information:

Further Information:

The Alarms

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

A B

C D

E F

G H

OK OK

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THE ALARMS

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

Upper Control Limit (UCL)

Lower Control Limit (LCL)

X

A B

C D

E F

G H

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