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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 Interpret the results What is SPC? 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 based on the understanding of variation used widely in manufacturing industries for over 80 years What is SPC for? A way of thinking 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 week 26 - 27/6 week 22 - 30/5 week 18 - 02/5 week 14 - 4/4 week 10 - 07/03 week 6 - 08/02 week 2 - 11/01 week 50 - 14/12 week 46 - 16/11 week 42 - 19/10 week 38 - 21/09 week 34 - 24/08 week 30 - 27/07 week 26 - 29/06 week 22 - 01/06 week 18 - 04/05 week 14 - 06/04 week 10 - 09/03 week 6 - 09/02 week 2 - 12/01 week 50 - 15/12 week 46 - 17/11 week 42 - 20/10 week 38 - 22/09 week 34 - 25/08 week 30 - 28/07 week 26 - 30/06 week 22 - 02/06 week 18 - 05/05 week 14 - 07/04 week 10 - 10/03 What does this show? QMS - 90% 110.0% 100.0% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% Or this? NOTHING! This is inappropriate data presentation It tells us NOTHING A typical SPC chart Range 80 Upper process limit 70 60 Mean 50 40 Lower process limit 30 20 10 0 F M A M J J A S O N D J F M A M J J A S O N D “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 Walter A. Shewhart While every process displays variation: some processes display controlled variation stable, consistent and predictable pattern of variation constant causes / “chance” while others display uncontrolled variation pattern changes over time special cause variation/“assignable” 11/28/2003 11/19/2003 11/10/2003 11/1/2003 10/23/2003 10/14/2003 10/5/2003 9/26/2003 9/17/2003 9/8/2003 8/30/2003 8/21/2003 8/12/2003 8/3/2003 7/25/2003 7/16/2003 7/7/2003 6/28/2003 6/19/2003 6/10/2003 6/1/2003 Controlled variation Total discharges 140 120 100 80 60 40 20 0 11/28/2003 11/19/2003 11/10/2003 11/1/2003 10/23/2003 10/14/2003 10/5/2003 9/26/2003 9/17/2003 9/8/2003 8/30/2003 8/21/2003 8/12/2003 8/3/2003 7/25/2003 7/16/2003 7/7/2003 6/28/2003 6/19/2003 6/10/2003 6/1/2003 Uncontrolled variation 380 360 340 320 300 280 260 240 220 2 ways to improve a process If uncontrolled variation - identify special causes (may be good or bad) process is unstable variation is extrinsic to process cause should be identified and “treated” If controlled variation - reduce variation, improve outcome process is stable variation is inherent to process therefore, process must be changed Process Improvement Common cause variation reduced Special causes eliminated Process improved Special causes present Process under control - predictable Process out of control - unpredictable Then improve nominal How to present data Measures of location average median mode Measures of dispersion/variation range root mean square deviation standard deviation PRACTICAL INTERPRETATION OF THE STANDARD DEVIATION Mean - 3s Mean Mean + 3s 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: 3s and the Control Chart UCL 3s 3s 6s Mean LCL 2 dangers to beware of Reacting to special cause variation by changing the process Ignoring special cause variation by assuming “it’s part of the process” Task Think of your normal routine for coming to work every day. This is a process! Discuss briefly on your tables: How long does it take on average? What factors might cause you to take longer (or shorter) than usual? Richard’s trip to work 120 100 Upper process limit Mean 80 Lower process limit Min. 60 40 20 0 Consecutive trips What Can It Do For Me? to identify if a process is sustainable to identify when an implemented change has improved a process are your improvements sustained over time and it has not just occurred by chance to understand that variation is normal and to help reduce it to understand processes - this helps make better predictions and improves decision making Using Charts Run chart records data points in time order median used as centre line Control chart adds in estimates of predictability process in control mean used as the centre line upper and lower process limits (3 sigma) Using SPC in practice Constructing an I chart Learning the rules Examples of measurement for improvement in practice Constructing the I (XmR) chart Don’t run here comes the maths!!! The I (XmR) chart I stands for Individual 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 e.g. number of cancelled operations each day the moving Range describes the way in which we measure the variation in the process Use individual values to calculate the Mean Difference between 2 consecutive readings, always positive Moving Range, mR Calculate the Mean mR One Sigma/standard deviation = (Mean mR)/d2 * = s or σ Upper Process Limit (UPL) = 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. How to construct the chart Plot the individual values Calculate the mean and plot it Calculate a measure of the variation (sigma) Derive upper and lower limits from this measure of variation (control limits) 1. Plot the individual values Average wait in days 120 100 80 60 40 20 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov 2. Calculate the mean and plot it Average wait in days 120 100 80 60 40 20 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov 3. Calculate a measure of variation: the average moving range Find out the difference between successive values (ignore the plus or minus signs!) Find the average (mean) of these differences (17.96) Convert to 1 sigma (17.96 / 1.128 = 15.92) Value Difference Use 3 sigma to 85 calculate the limits: 76 9 83 7 Mean +/- 3 x 15.92 58 NB (Take Note): 1.128 is a standard bias correction factor (d2) used to calculate sigma value 25 4. Derive the limits and plot them Average wait in days 120 100 80 60 40 20 0 Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Things to remember 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 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) 20 data points produces 19 moving ranges Data must be in time ordered sequence Benefits of process limits? Measure variability of process over time NOT probability or confidence limits Work well even if measurements not normally distributed How to interpret the charts and results Rules, Patterns and Signals The Empirical Rule 99-100% will be within 3 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 In real life, only the first of these is of any real benefit Rules for special causes 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 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 Special causes - Rule 1 Point above UCL X UCL X X X UCL X X X X X X MEAN X X X X X X MEAN X X X LCL X Point below LCL LCL Special causes - Rule 2 Seven points above centre line UCL X X X X X X X X UCL X X X MEAN X X X X X MEAN X X X X X LCL LCL Seven points below centre line Special causes - Rule 2 Seven points in a downward direction UCL UCL X X X X X X X X X X X X X X X X X X X MEAN X MEAN X LCL LCL Seven points in an upward direction Special causes - Rule 3 Cyclic pattern Trend pattern UCL X X X X X X X X X X X X X X X X X X X X UCL X X X X X X X LCL X X X X X X X X X X X X LCL Special causes - Rule 4 Considerably less than 2/3 of all the points fall in this zone X X Considerably more than 2/3 of all the points fall in this zone UCL UCL X X X XX 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 X X X X X X X X X LCL LCL USING SPC TO SHOW IMPROVEMENT What is Statistical Process Control (SPC)? 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) - branch of statistics founded on understanding variation - used for over 80 years in manufacturing industries - plots real data in real time 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 650 600 number of patients 550 500 450 Run of seven or more on same side of centreline picks up a small but consistent change in the process 400 350 300 Period 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 26/10/2003 05/10/2003 14/09/2003 24/08/2003 03/08/2003 13/07/2003 22/06/2003 01/06/2003 11/05/2003 20/04/2003 30/03/2003 09/03/2003 16/02/2003 26/01/2003 05/01/2003 15/12/2002 24/11/2002 03/11/2002 13/10/2002 22/09/2002 01/09/2002 11/08/2002 21/07/2002 30/06/2002 09/06/2002 19/05/2002 28/04/2002 Lower control limits 07/04/2002 250 Summary What is SPC and why it is a useful tool Understanding variation Presenting data as control charts Understanding the results Useful SPC references 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 Raymond G Carey. Improving healthcare with control charts. ASQ Quality Press, 2003 Mal Owen. SPC and continuous improvement: IFS Publications 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: 121225. www.steyn.org