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

3. Aims and objectives Explain the concept of SPC Explain the concept of SPC Understand variation and why it is important Understand variation and why it is important Manage variation in our work using SPC Manage variation in our work using SPC Learn how to do a control chart Learn how to do a control chart Interpret the results Interpret the results

4. What is SPC? Statistical Process Control Statistical Process Control we deliver our work through processes we use statistical concepts to help us understand our work control = predictable and stable branch of statistics developed by Walter Shewhart in the 1920s at Bell Laboratories branch of statistics developed by Walter Shewhart in the 1920s at Bell Laboratories based on the understanding of variation based on the understanding of variation used widely in manufacturing industries for over 80 years used widely in manufacturing industries for over 80 years

5. What is SPC for? A way of thinking A way of thinking Measurement for improvement - a simple tool for analysing data – easy and sustainable Measurement for improvement - a simple tool for analysing data – easy and sustainable Evidence based management – real data in real time – a better way of making decision Evidence based management – real data in real time – a better way of making decision

6. What does this show?

7. Or this?

8. NOTHING! This is inappropriate data presentation This is inappropriate data presentation It tells us NOTHING It tells us NOTHING

9. Upper process limit Mean Lower process limit Range A typical SPC chart

10. “A phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to vary in the future” Shewart - Economic Control of Quality of Manufactured Product, 1931

11. Walter A. Shewhart While every process displays variation: some processes display controlled variation some processes display controlled variation stable, consistent and predictable pattern of variation stable, consistent and predictable pattern of variation constant causes / “chance” constant causes / “chance” while others display uncontrolled variation while others display uncontrolled variation pattern changes over time pattern changes over time special cause variation/“assignable” special cause variation/“assignable”

12. Controlled variation

13. 220 240 260 280 300 320 340 360 380 6/1/2003 6/10/20036/19/20036/28/2003 7/7/2003 7/16/20037/25/2003 8/3/2003 8/12/20038/21/20038/30/2003 9/8/2003 9/17/20039/26/200310/5/2003 10/14/200310/23/2003 11/1/2003 11/10/200311/19/200311/28/2003 Uncontrolled variation

14. 2 ways to improve a process If uncontrolled variation - identify special causes (may be good or bad) process is unstable process is unstable variation is extrinsic to process variation is extrinsic to process cause should be identified and “treated” cause should be identified and “treated” If controlled variation - reduce variation, improve outcome process is stable process is stable variation is inherent to process variation is inherent to process therefore, process must be changed therefore, process must be changed

15. 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

16. How to present data Measures of location Measures of location average average median median mode mode Measures of dispersion/variation Measures of dispersion/variation range range root mean square deviation root mean square deviation standard deviation standard deviation

17. PRACTICAL INTERPRETATION OF THE STANDARD DEVIATION MeanMean + 3sMean - 3s

18. Standard 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:

19. 3s and the Control Chart 6s 3s UCL LCL Mean

20. 2 dangers to beware of Reacting to special cause variation by changing the process Reacting to special cause variation by changing the process Ignoring special cause variation by assuming “it’s part of the process” Ignoring special cause variation by assuming “it’s part of the process”

21. Task Think of your normal routine for coming to work every day. This is a process! Think of your normal routine for coming to work every day. This is a 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 longer (or shorter) than usual? What factors might cause you to take longer (or shorter) than usual?

22. Richard’s trip to work Mean Upper process limit Lower process limit

23. What Can It Do For Me? to identify if a process is sustainable to identify if a process is sustainable are your improvements sustained over time are your improvements sustained over time to identify when an implemented change has improved a process to identify when an implemented change has improved a process and it has not just occurred by chance and it has not just occurred by chance to understand that variation is normal and to help reduce it to understand that variation is normal and to help reduce it to understand processes - this helps make better predictions and improves decision making to understand processes - this helps make better predictions and improves decision making

24. Using Charts Run chart records data points in time order Run chart records data points in time order median used as centre line Control chart adds in estimates of predictability Control chart adds in estimates of predictability process in control mean used as the centre line upper and lower process limits (3 sigma)

25. Using SPC in practice Constructing an I chart Constructing an I chart Learning the rules Learning the rules Examples of measurement for improvement in practice Examples of measurement for improvement in practice

26. Constructing the I (XmR) chart Don’t run here comes the maths!!!

27. The I (XmR) chart I stands for Individual I stands for Individual XmR stands for X moving Range XmR stands for X moving Range the ‘I or X’ represents the data from the process we are monitoring and corresponds to a single observation or individual value the ‘I or X’ represents the data from the process we are monitoring and corresponds to a single observation or individual value e.g. number of cancelled operations each day e.g. number of cancelled operations each day the moving Range describes the way in which we measure the variation in the process the moving Range describes the way in which we measure the variation in the process

28. Use individual values to calculate the Mean Use individual values to calculate the Mean Difference between 2 consecutive readings, always positive = Moving Range, mR Difference between 2 consecutive readings, always positive = Moving Range, mR Calculate the Mean mR Calculate the Mean mR One Sigma/standard deviation = (Mean mR)/d2* One Sigma/standard deviation = (Mean mR)/d2* s or σ s or σ Upper Process Limit (UPL) = Mean + 3 s Upper Process Limit (UPL) = Mean + 3 s Lower Process limit (LPL) = Mean - 3 s Lower Process limit (LPL) = Mean - 3 s * The bias correction factor, d2 is a constant for given subgroups of size n (n = 2, d2 = 1.128) H.L. Harter, “Tables of Range and Studentized Range”, Annals of Mathematical Statistics, 1960.

29. How to construct the chart Plot the individual values Plot the individual values Calculate the mean and plot it Calculate the mean and plot it Calculate a measure of the variation (sigma) Calculate a measure of the variation (sigma) Derive upper and lower limits from this measure of variation (control limits) Derive upper and lower limits from this measure of variation (control limits)

30. 1. Plot the individual values

31. 2. Calculate the mean and plot it

32. 3. Calculate a measure of variation: the average moving range Find out the difference between successive values (ignore the plus or minus signs!) Find out the difference between successive values (ignore the plus or minus signs!) Find the average (mean) of these differences (17.96) Find the average (mean) of these differences (17.96) Convert to 1 sigma (17.96 / 1.128 = 15.92) Convert to 1 sigma (17.96 / 1.128 = 15.92) Use 3 sigma to calculate the limits: Mean +/- 3 x 15.92 Use 3 sigma to calculate the limits: Mean +/- 3 x 15.92 NB (Take Note): 1.128 is a standard bias correction factor (d2) used to calculate sigma value NB (Take Note): 1.128 is a standard bias correction factor (d2) used to calculate sigma value

33. 4. Derive the limits and plot them

34. Things to remember You only need 20 data points to set up a control chart You only need 20 data points to set up a control chart if one of initial 20 data points is out of process limits consider excluding that point from calculations if one of initial 20 data points is out of process limits consider excluding that point from calculations Sigma is not the same as the standard deviation of a normal distribution Sigma is not the same as the standard deviation of a normal distribution d2 constant means a sample size of 2 and refers to the sample size for moving range (which is nearly always 2) d2 constant means a sample size of 2 and refers to the sample size for moving range (which is nearly always 2) 20 data points produces 19 moving ranges 20 data points produces 19 moving ranges Data must be in time ordered sequence Data must be in time ordered sequence

35. Benefits of process limits? Measure variability of process over time Measure variability of process over time NOT probability or confidence limits NOT probability or confidence limits Work well even if measurements not normally distributed Work well even if measurements not normally distributed

36. How to interpret the charts and results Rules, Patterns and Signals

37. The Empirical Rule 99-100% will be within 3 sigmas either side of mean 99-100% will be within 3 sigmas either side of mean 90-98% will be within 2 sigmas either side of mean 90-98% will be within 2 sigmas either side of mean 60-75% of data within 1 sigma either side of the mean 60-75% of data within 1 sigma either side of the mean In real life, only the first of these is of any real benefit

38. Rules for special causes Rule 1 - Any point outside the control limits Rule 1 - Any point outside the control limits Rule 2 - Run of 7 points or more all above or all below the mean, or all increasing or all decreasing Rule 2 - Run of 7 points or more all above or all below the mean, or all increasing or all decreasing Rule 3 - An unusual pattern or trend within the control limits Rule 3 - An unusual pattern or trend within the control limits Rule 4 - Number of points within the middle third of the region between the control limits differs markedly from two-thirds of the total number of points Rule 4 - Number of points within the middle third of the region between the control limits differs markedly from two-thirds of the total number of points

39. X X X X X X X X X LCL UCL MEAN X X X X X X X X X X LCL UCL MEAN X Point above UCL Point below LCL Special causes - Rule 1

40. MEAN Seven points above centre line Special causes - Rule 2 LCL UCL LCL UCL X X X X X X X X X X X X X X X X X X X X X Seven points below centre line

41. MEAN Seven points in a downward direction Special causes - Rule 2 LCL UCL LCL UCL X X X X X X X X X X X X X X X X X X X X X Seven points in an upward direction

42. Special causes - Rule 3 X X X X X X X X X X X X X X X X X X X X Cyclic pattern X X X X X X X X X X X X X X X X X X X LCL UCL LCL UCL Trend pattern

43. Special causes - Rule 4 Considerably less than 2/3 of all the points fall in this zone X X X X X X X X X X X X X X X X X LCL UCL X X X X X X X X X X X X X X X X X X X X X X X X X X LCL UCL Considerably more than 2/3 of all the points fall in this zone

44. USING 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 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

45. INTERPRETING A RUN CHART A TREND - Seven or more values steadily increasing or decreasing indicates a change in the process A RUN – one or more consecutive data points on the same side as the median. The median is the green line. There are 7 runs on this chart. If there are too few or too many runs on a chart then the process is unstable. To find out how many runs should be present consult box 1. A = no. of points on chart B = min no of runs C = max no of runs A SHIFT – if a run is too long ie contains seven or more points this signifies a special cause or ‘shift’ in the process 0 5 10 15 20 25 1234567891011121314151617181920212223242526 consecutive events number of events What is a run chart? - This is a running record of a process over time - A minimum of 16 points is needed for a run chart - The advantage of a run chart is that is it is easy to construct and doesn’t require a computer programme to interpret the data CBA 12516 13517 13618 14619 15620 15721 16722 16823 19927 18926 17925 17824 BOX 1

46. Summary What is SPC and why it is a useful tool What is SPC and why it is a useful tool Understanding variation Understanding variation Presenting data as control charts Presenting data as control charts Understanding the results Understanding the results

47. Useful SPC references Walter A Shewhart. Economic control of quality of manufactured product. New York: D Van Nostrand 1931. Walter A Shewhart. Economic control of quality of manufactured product. New York: D Van Nostrand 1931. Donald Wheeler. Understanding Variation. Knoxville: SPC Press Inc, 1995 Donald Wheeler. Understanding Variation. Knoxville: SPC Press Inc, 1995 Raymond G Carey. Improving healthcare with control charts. ASQ Quality Press, 2003 Raymond G Carey. Improving healthcare with control charts. ASQ Quality Press, 2003 Mal Owen. SPC and continuous improvement: IFS Publications Mal Owen. SPC and continuous improvement: IFS Publications WE Deming. Out of the crisis. Massachusetts: MIT 1986 WE Deming. Out of the crisis. Massachusetts: MIT 1986 Donald M Berwick. Controlling variation in health care: a consultation from Walter Shewhart. Med Care 1991; 29: 1212- 25. Donald M Berwick. Controlling variation in health care: a consultation from Walter Shewhart. Med Care 1991; 29: 1212- 25. www.steyn.org www.steyn.org www.steyn.org