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Statistical Process Statistical Process Control Control (SPC) (SPC) By By Zaipul Anwar Zaipul Anwar Business & Advanced Technology Centre, Business & Advanced Technology Centre, Universiti Teknologi Malaysia Universiti Teknologi Malaysia

Statistical Process Control (SPC)

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Statistical Process Control (SPC). By Zaipul Anwar Business & Advanced Technology Centre, Universiti Teknologi Malaysia. Aims and objectives. Explain the concept of SPC Understand variation and why it is important Manage variation in our work using SPC Learn how to do a control chart - PowerPoint PPT Presentation

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Page 1: Statistical Process Control (SPC)

Statistical Process ControlStatistical Process Control(SPC)(SPC)

By By Zaipul AnwarZaipul Anwar

Business & Advanced Technology Centre,Business & Advanced Technology Centre,Universiti Teknologi MalaysiaUniversiti Teknologi Malaysia

Page 2: Statistical Process Control (SPC)

Aims and objectivesAims and objectives

Explain the concept of SPCExplain the concept of SPC Understand variation and why it is Understand variation and why it is

importantimportant Manage variation in our work using Manage variation in our work using

SPCSPC Learn how to do a control chartLearn how to do a control chart Interpret the resultsInterpret the results

Page 3: Statistical Process Control (SPC)

What is SPC?What is SPC?

Statistical Process ControlStatistical Process Controlwe deliver our work through processeswe deliver our work through processeswe use statistical concepts to help us understand our workwe use statistical concepts to help us understand our workcontrol = predictable and stablecontrol = predictable and stable

branch of statistics developed by Walter branch of statistics developed by Walter Shewhart in the 1920s at Bell LaboratoriesShewhart in the 1920s at Bell Laboratories

based on the understanding of variationbased on the understanding of variation used widely in manufacturing industries used widely in manufacturing industries

for over 80 yearsfor over 80 years

Page 4: Statistical Process Control (SPC)

What is SPC for?What is SPC for?

A way of thinkingA way of thinking

Measurement for improvement - a simple Measurement for improvement - a simple tool for analysing data – easy and tool for analysing data – easy and sustainablesustainable

Evidence based management – real data Evidence based management – real data in real time – a better way of making in real time – a better way of making decisiondecision

Page 5: Statistical Process Control (SPC)

What does this show?What does this show?

QMS - 90%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

110.0%

week

10

- 10/

03

week

14

- 07/

04

week

18

- 05/

05

week

22

- 02/

06

week

26

- 30/

06

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- 28/

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34

- 25/

08

week

38

- 22/

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week

42

- 20/

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46

- 17/

11

week

50

- 15/

12

week

2 -

12/0

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week

6 -

09/0

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- 09/

03

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- 06/

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- 04/

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- 01/

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26

- 29/

06

week

30

- 27/

07

week

34

- 24/

08

week

38

- 21/

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42

- 19/

10

week

46

- 16/

11

week

50

- 14/

12

week

2 -

11/0

1

week

6 -

08/0

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week

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- 07/

03

week

14

- 4/4

week

18

- 02/

5

week

22

- 30/

5

week

26

- 27/

6

Page 6: Statistical Process Control (SPC)

Or this?Or this?

Page 7: Statistical Process Control (SPC)

NOTHING!NOTHING! This is inappropriate data This is inappropriate data

presentation presentation It tells us NOTHING It tells us NOTHING

Page 8: Statistical Process Control (SPC)

0

10

20

30

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F M A M J J A S O N D J F M A M J J A S O N D

Upper process

limit

Mean

Lower process

limit

Range

A typical SPC chartA typical SPC chart

Page 9: Statistical Process Control (SPC)

““A phenomenon will be A phenomenon will be said to be controlled when, said to be controlled when,

through the use of past through the use of past experience, we can predict, experience, we can predict, at least within limits, how at least within limits, how the phenomenon may be the phenomenon may be expected to vary in the expected to vary in the

future”future”Shewart - Economic Control of Quality of Shewart - Economic Control of Quality of

Manufactured Product, 1931Manufactured Product, 1931

Page 10: Statistical Process Control (SPC)

Walter A. ShewhartWalter A. ShewhartWhile every process displays variation:While every process displays variation:

some processes display some processes display controlled variationcontrolled variation stable, consistent and predictable pattern of stable, consistent and predictable pattern of

variationvariation constant causes / “chance”constant causes / “chance”

while others display while others display uncontrolled variationuncontrolled variation pattern changes over timepattern changes over time special cause variation/“assignable”special cause variation/“assignable”

Page 11: Statistical Process Control (SPC)

Total discharges

0

20

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60

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140

6/1/

2003

6/10

/200

3

6/19

/200

3

6/28

/200

3

7/7/

2003

7/16

/200

3

7/25

/200

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8/3/

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/200

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8/21

/200

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/200

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2003

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/200

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/200

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/200

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/200

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11/1

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11/1

9/20

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11/2

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Controlled variation

Page 12: Statistical Process Control (SPC)

220

240

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380

6/1/

2003

6/10

/200

3

6/19

/200

3

6/28

/200

3

7/7/

2003

7/16

/200

3

7/25

/200

3

8/3/

2003

8/12

/200

3

8/21

/200

3

8/30

/200

3

9/8/

2003

9/17

/200

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9/26

/200

3

10/5

/200

3

10/1

4/20

03

10/2

3/20

03

11/1

/200

3

11/1

0/20

03

11/1

9/20

03

11/2

8/20

03

Uncontrolled variation

Page 13: Statistical Process Control (SPC)

2 ways to improve a 2 ways to improve a processprocess

If uncontrolled variationIf uncontrolled variation - identify special causes (may - identify special causes (may be good or bad)be good or bad)

process is unstableprocess is unstable variation is extrinsic to processvariation is extrinsic to process cause should be identified and “treated”cause should be identified and “treated”

If controlled variationIf controlled variation - reduce variation, improve - reduce variation, improve outcomeoutcome

process is stableprocess is stable variation is inherent to processvariation is inherent to process therefore, process must be changedtherefore, process must be changed

Page 14: Statistical Process Control (SPC)

Process Improvement

Nominal

Common cause variation reduced

Process improved

Special causes present

Process out of control - unpredictable

Special causes eliminated

Process under control - predictable

Then improve nominal

Page 15: Statistical Process Control (SPC)

How to present dataHow to present data

Measures of locationMeasures of location averageaverage medianmedian modemode

Measures of dispersion/variationMeasures of dispersion/variation rangerange root mean square deviationroot mean square deviation standard deviationstandard deviation

Page 16: Statistical Process Control (SPC)

PRACTICAL INTERPRETATION OF THE STANDARD DEVIATION

Mean Mean + 3s

Mean - 3s

Page 17: Statistical Process Control (SPC)

Standard DeviationStandard Deviation• A measure of the range of variation from an average of a group of measurements. 68% of all measurements fall within one standard deviation of the average. 95% of all measurements fall within two standard deviations of the average

• The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you have a relatively large standard deviation. If you looked at normally distributed data on a graph, it would look something like this:

Page 18: Statistical Process Control (SPC)

3s and the Control Chart

6s

3s

3s

UCL

LCL

Mean

Page 19: Statistical Process Control (SPC)

2 dangers to beware of2 dangers to beware of

Reacting to special cause variation Reacting to special cause variation by changing the processby changing the process

Ignoring special cause variation by Ignoring special cause variation by assuming “it’s part of the process”assuming “it’s part of the process”

Page 20: Statistical Process Control (SPC)

TaskTask

Think of your normal routine for Think of your normal routine for coming to work every day. This is a coming to work every day. This is a process! process!

Discuss briefly on your tables:Discuss briefly on your tables: How long does it take on average?How long does it take on average? What factors might cause you to take What factors might cause you to take

longer (or shorter) than usual?longer (or shorter) than usual?

Page 21: Statistical Process Control (SPC)

0

20

40

60

80

100

120

Consecutive trips

Min.

Richard’s trip to work

Mean

Upper process limit

Lower process limit

Page 22: Statistical Process Control (SPC)

What Can It Do For Me?What Can It Do For Me?

to identify if a process is sustainableto identify if a process is sustainable are your improvements sustained over timeare your improvements sustained over time

to identify when an implemented to identify when an implemented change has improved a processchange has improved a process and it has not just occurred by chanceand it has not just occurred by chance

to understand that variation is normal to understand that variation is normal and to help reduce itand to help reduce it

to understand processes - this helps to understand processes - this helps make better predictions and improves make better predictions and improves decision makingdecision making

Page 23: Statistical Process Control (SPC)

Using ChartsUsing Charts Run chart records data points in time Run chart records data points in time

orderordermedian used as centre linemedian used as centre line

Control chart adds in estimates of Control chart adds in estimates of predictabilitypredictabilityprocess in controlprocess in controlmean used as the centre linemean used as the centre lineupper and lower process limits (3 sigma)upper and lower process limits (3 sigma)

Page 24: Statistical Process Control (SPC)

Using SPC in practiceUsing SPC in practice

Constructing an I chartConstructing an I chart Learning the rulesLearning the rules Examples of measurement for Examples of measurement for

improvement in practiceimprovement in practice

Page 25: Statistical Process Control (SPC)

Constructing the Constructing the I (XmR) chartI (XmR) chart

Don’t run here comes the Don’t run here comes the maths!!!maths!!!

Page 26: Statistical Process Control (SPC)

The I (XmR) chartThe I (XmR) chart I stands for IndividualI stands for Individual XmR stands for X moving Range XmR stands for X moving Range

the ‘I or X’ represents the data from the the ‘I or X’ represents the data from the process we are monitoring and corresponds process we are monitoring and corresponds to a single observation or individual valueto a single observation or individual value e.g. number of cancelled operations each daye.g. number of cancelled operations each day

the moving Range describes the way in the moving Range describes the way in which we measure the variation in the which we measure the variation in the processprocess

Page 27: Statistical Process Control (SPC)

Use individual values to calculate the Use individual values to calculate the MeanMean

Difference between 2 consecutive readings, always positive Difference between 2 consecutive readings, always positive = = Moving Range, mRMoving Range, mR

Calculate the Calculate the Mean mRMean mR

One Sigma/standard deviation = One Sigma/standard deviation = (Mean mR)/d2(Mean mR)/d2 ** s or σs or σ

Upper Process Limit (UPL)Upper Process Limit (UPL) = = Mean + 3 sMean + 3 s

Lower Process limit (LPL)Lower Process limit (LPL) = = Mean - 3 sMean - 3 s

** The bias correction factor, d2 is a constant for given subgroups The bias correction factor, d2 is a constant for given subgroups of size n (n = 2, d2 = 1.128)of size n (n = 2, d2 = 1.128)

H.L. Harter, “Tables of Range and Studentized Range”, Annals of Mathematical Statistics, H.L. Harter, “Tables of Range and Studentized Range”, Annals of Mathematical Statistics, 1960.1960.

Page 28: Statistical Process Control (SPC)

How to construct the How to construct the chartchart

Plot the individual valuesPlot the individual values Calculate the mean and plot itCalculate the mean and plot it Calculate a measure of the variation Calculate a measure of the variation

(sigma)(sigma) Derive upper and lower limits from Derive upper and lower limits from

this measure of variation (control this measure of variation (control limits)limits)

Page 29: Statistical Process Control (SPC)

1. Plot the individual 1. Plot the individual valuesvalues

Average wait in days

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120

Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Page 30: Statistical Process Control (SPC)

2. Calculate the mean 2. Calculate the mean and plot itand plot it

Average wait in days

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Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Page 31: Statistical Process Control (SPC)

3. Calculate a measure of 3. Calculate a measure of variation:variation:

the average moving rangethe average moving range Find out the difference between successive Find out the difference between successive

values (ignore the plus or minus signs!)values (ignore the plus or minus signs!) Find the average (mean) of these differences Find the average (mean) of these differences

(17.96)(17.96) Convert to 1 sigmaConvert to 1 sigma

(17.96 / 1.128 = 15.92)(17.96 / 1.128 = 15.92) Use 3 sigma to Use 3 sigma to

calculate the limits:calculate the limits: Mean +/- 3 x 15.92 Mean +/- 3 x 15.92

NB (Take Note): 1.128 is a standard bias correction factor (d2) used to calculate sigma valueNB (Take Note): 1.128 is a standard bias correction factor (d2) used to calculate sigma value

Value Difference8576 983 758 25

Page 32: Statistical Process Control (SPC)

4. Derive the limits and 4. Derive the limits and plot themplot them

Average wait in days

0

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Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov

Page 33: Statistical Process Control (SPC)

Things to Things to rememberremember

You only need 20 data points to set up a You only need 20 data points to set up a control chartcontrol chart

if one of initial 20 data points is out of process if one of initial 20 data points is out of process limits consider excluding that point from limits consider excluding that point from calculationscalculations

Sigma is not the same as the standard Sigma is not the same as the standard deviation of a normal distributiondeviation of a normal distribution

d2d2 constant means a sample size of 2 and constant means a sample size of 2 and refers to the sample size for moving range refers to the sample size for moving range (which is nearly always 2) (which is nearly always 2)

20 data points produces 19 moving ranges20 data points produces 19 moving ranges Data must be in time ordered sequenceData must be in time ordered sequence

Page 34: Statistical Process Control (SPC)

Benefits of process limits?Benefits of process limits?

Measure variability of process over Measure variability of process over timetime

NOTNOT probability or confidence limits probability or confidence limits

Work well even if measurements not Work well even if measurements not normallynormally distributeddistributed

Page 35: Statistical Process Control (SPC)

How to interpret How to interpret the charts and the charts and

resultsresultsRules, Patterns and SignalsRules, Patterns and Signals

Page 36: Statistical Process Control (SPC)

The Empirical RuleThe Empirical Rule

99-100% will be within 3 sigmas either side of 99-100% will be within 3 sigmas either side of meanmean

90-98% will be within 2 sigmas either side of mean90-98% will be within 2 sigmas either side of mean

60-75% of data within 1 sigma either side of the 60-75% of data within 1 sigma either side of the meanmean

In real life, only the first of these is of any real In real life, only the first of these is of any real benefitbenefit

Page 37: Statistical Process Control (SPC)

Rules for special causesRules for special causes Rule 1Rule 1 - Any point outside the control limits - Any point outside the control limits

Rule 2Rule 2 - Run of 7 points or more all above or all - Run of 7 points or more all above or all below below the mean, or all increasing or all the mean, or all increasing or all decreasingdecreasing

Rule 3Rule 3 - An unusual pattern or trend within the - An unusual pattern or trend within the control control limits limits

Rule 4Rule 4 - Number of points within the middle third - Number of points within the middle third of of the region between the control the region between the control limits differs limits differs markedly from two-thirds markedly from two-thirds of the total number of the total number of points of points

Page 38: Statistical Process Control (SPC)

XX

X

X

X

X

X

X

X

LCL

UCL

MEAN

X

X

X

X

XX

X

X

X

X

LCL

UCL

MEAN

X

Point above UCL

Point below LCL

Special causes - Rule 1

Page 39: Statistical Process Control (SPC)

MEAN MEAN

Seven points above centre line

Special causes - Rule 2

LCL

UCL

LCL

UCL

XX

X

X

X X

X

XX

XX X

X

XX

X X

X

XX

X

Seven points below centre line

Page 40: Statistical Process Control (SPC)

MEAN MEAN

Seven points in a downward direction

Special causes - Rule 2

LCL

UCL

LCL

UCL

XX

XX

X

XX

X

X X

X

XX X

XX

XX

X

X

X

Seven points in an upward direction

Page 41: Statistical Process Control (SPC)

Special causes - Rule 3

X

X

X

X

X

X

XX X

X

X

X

X

X

X

X

X

X

X

X

Cyclic pattern

X

X X

XX

XX

X

X

X

X

X

X

X

X X

X

X

XLCL

UCL

LCL

UCL

Trend pattern

Page 42: Statistical Process Control (SPC)

Special causes - Rule 4Considerably less than 2/3 of all the points fall in this zone

X

XX X X

X

X

X

X

X

XX

XX

X

XX

LCL

UCL

X

X

X

X

X

X

XX

X

X

X

XX

X

XX

X

X

XX

X X

X

X

XX

LCL

UCL

Considerably more than 2/3 of all the points fall in this zone

Page 43: Statistical Process Control (SPC)

USING SPC TO SHOW IMPROVEMENTUSING SPC TO SHOW IMPROVEMENT

What is Statistical Process Control (SPC)?

- branch of statistics founded on understanding variation

- used for over 80 years in manufacturing industries

- plots real data in real time

250

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Period

num

ber

of p

atie

nts

Special cause –a single point falling outside a control limit – a rare event with a probability of occurring by chance of 3 in a thousand

Control limits define the estimated variation inherent within the process (common variation or common cause) and are calculated using the difference between each successive value in time order (shown by the red lines). They are centred on the mean value for the data set (shown by the green line)

Lower control limits

Upper control limits

Seven or more values steadily increasing or decreasing indicates a change in the process – this usually requires recalculation of the mean and the control limits as it indicates a new process – this is called a step change

Run of seven or more on same side of centreline picks up a small but consistent change in the process

Page 44: Statistical Process Control (SPC)

SummarySummary

What is SPC and why it is a useful What is SPC and why it is a useful tooltool

Understanding variationUnderstanding variation Presenting data as control chartsPresenting data as control charts Understanding the resultsUnderstanding the results

Page 45: Statistical Process Control (SPC)

Useful SPC referencesUseful SPC references

Walter A ShewhartWalter A Shewhart. . Economic control of quality of Economic control of quality of manufactured product. New York: D Van Nostrand 1931.manufactured product. New York: D Van Nostrand 1931.

Donald WheelerDonald Wheeler. . Understanding Variation. Knoxville: SPC Understanding Variation. Knoxville: SPC Press Inc, 1995 Press Inc, 1995

Raymond G CareyRaymond G Carey. . Improving healthcare with control Improving healthcare with control charts. ASQ Quality Press, 2003charts. ASQ Quality Press, 2003

Mal Owen. Mal Owen. SPC and continuous improvement: IFS SPC and continuous improvement: IFS PublicationsPublications

WE DemingWE Deming. . Out of the crisis. Massachusetts: MIT 1986Out of the crisis. Massachusetts: MIT 1986 Donald M BerwickDonald M Berwick. . Controlling variation in health care: a Controlling variation in health care: a

consultation from Walter Shewhart. Med Care 1991; 29: consultation from Walter Shewhart. Med Care 1991; 29: 1212-25.1212-25.

www.steyn.orgwww.steyn.org