statistical process control (spc) by zaipul anwar business & advanced technology centre,...
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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
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
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
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
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%
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- 07/
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NOTHING!NOTHING! This is inappropriate data This is inappropriate data
presentation presentation It tells us NOTHING It tells us NOTHING
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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
““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
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”
Total discharges
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/200
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/200
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/200
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/200
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Controlled variation
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2003
7/16
/200
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7/25
/200
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8/3/
2003
8/12
/200
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8/21
/200
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8/30
/200
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9/8/
2003
9/17
/200
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9/26
/200
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/200
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10/1
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10/2
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11/1
/200
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11/1
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11/1
9/20
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11/2
8/20
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Uncontrolled variation
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
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
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
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:
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”
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?
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Consecutive trips
Min.
Richard’s trip to work
Mean
Upper process limit
Lower process limit
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
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)
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
Constructing the Constructing the I (XmR) chartI (XmR) chart
Don’t run here comes the Don’t run here comes the maths!!!maths!!!
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
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.
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)
1. Plot the individual 1. Plot the individual valuesvalues
Average wait in days
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Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov
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
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
4. Derive the limits and 4. Derive the limits and plot themplot them
Average wait in days
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Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov
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
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
How to interpret How to interpret the charts and the charts and
resultsresultsRules, Patterns and SignalsRules, Patterns and Signals
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
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
XX
X
X
X
X
X
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X
LCL
UCL
MEAN
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X
X
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X
X
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X
LCL
UCL
MEAN
X
Point above UCL
Point below LCL
Special causes - Rule 1
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
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
Special causes - Rule 3
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X
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XX X
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Cyclic pattern
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X X
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X
X X
X
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XLCL
UCL
LCL
UCL
Trend pattern
Special causes - Rule 4Considerably less than 2/3 of all the points fall in this zone
X
XX X X
X
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X
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XX
LCL
UCL
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X
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X X
X
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XX
LCL
UCL
Considerably more than 2/3 of all the points fall in this zone
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
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Period
num
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of p
atie
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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
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
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
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