1. Quality Control  Statistical Process Control (SPC) www.ePowerPoint.com

2. Step 5 – Control  Statistical Process Control (SPC)  Use data from the actual process  Estimate distributions  Look at capability - is good quality possible  Statistically monitor the process over time www.ePowerPoint.com

3. Quality Two types of variation www.ePowerPoint.com

4. Common Cause Variation (low level) Common Cause Variation (high level) Assignable Cause Variation Need to measure and reduce common cause variation Identify assignable cause variation as soon as possible What is common cause variation for one person might be assignable cause to the other Two Types of Variation www.ePowerPoint.com

5. Time Process Parameter Upper Control Limit (UCL) Lower Control Limit (LCL) Center Line Track process parameter over time - average weight of 5 bags - control limits - different from specification limits Distinguish between - common cause variation (within control limits) - assignable cause variation (outside control limits) Detect Abnormal Variation in the Process: Identifying Assignable Causes www.ePowerPoint.com

6. Statistical Process Control Capability Analysis Conformance Analysis Investigate for Assignable Cause Eliminate Assignable Cause Capability analysis What is the currently "inherent" capability of my process when it is "in control"? Conformance analysis SPC charts identify when control has likely been lost and assignable cause variation has occurred Investigate for assignable cause Find “Root Cause(s)” of Potential Loss of Statistical Control Eliminate or replicate assignable cause Need Corrective Action To Move Forward www.ePowerPoint.com

7.  Statistical process control (SPC) involves testing a random sample of output from a process to determine whether the process is producing items within a preselected range. www.ePowerPoint.com

8. Statistical Process Control (SPC) Charts UCL LCL Samples over time 1 2 3 4 5 6 UCL LCL Samples over time 1 2 3 4 5 6 UCL LCL Samples over time 1 2 3 4 5 6 Normal Behavior Possible problem, investigate www.ePowerPoint.com

9. Control Limits are based on the Normal Curve x 0123-3-2 z  Standard deviation units or “z” units. www.ePowerPoint.com

10. Control Limits Process Average UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL +3σ - 3σ- 3σ time Forming the Upper control limit (UCL) and the Lower control limit (LCL): www.ePowerPoint.com

11. Control Chart Basics Process Mean UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL +3σ - 3σ- 3σ Common Cause Variation: range of expected variability Special Cause Variation: Range of unexpected variability time www.ePowerPoint.com

12. Process Variability Process Mean UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL ±3σ → 99.7% of process values should be in this range time Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present www.ePowerPoint.com

13. In-control Process  A process is said to be in control when the control chart does not indicate any out-of-control condition  Contains only common causes of variation  If the common causes of variation is small, then control chart can be used to monitor the process  If the common causes of variation is too large, you need to alter the process www.ePowerPoint.com

14. Process In Control  Process in control: points are randomly distributed around the center line and all points are within the control limits UCL LCL time Process Mean www.ePowerPoint.com

15. Process Not in Control Out of control conditions:  One or more points outside control limits  8 or more points in a row on one side of the center line  8 or more points in a row moving in the same direction www.ePowerPoint.com

16. Process Not in Control One or more points outside control limits UCL LCL Eight or more points in a row on one side of the center line UCL LCL Eight or more points in a row moving in the same direction UCL LCL Process Average www.ePowerPoint.com

17. Out-of-control Processes  When the control chart indicates an out-of-control condition (a point outside the control limits or exhibiting trend, for example)  Contains both common causes of variation and assignable causes of variation  The assignable causes of variation must be identified  If detrimental to the quality, assignable causes of variation must be removed  If increases quality, assignable causes must be incorporated into the process design www.ePowerPoint.com

18. Types of Statistical Sampling  Attribute (Go or no-go information)  Defectives refers to the acceptability of product across a range of characteristics.  Defects refers to the number of defects per unit which may be higher than the number of defectives. (good or bad, function or malfunction, 0 or 1)  p -chart application  Variable (Continuous)  Usually measured by the mean and the standard deviation.  X-bar and R chart applications www.ePowerPoint.com

19. Example of Constructing a p -Chart: Required Data Sample No. No. of Samples Number of defects found in each sample www.ePowerPoint.com

20. Where is the fraction defective, is the standard deviation, is the sample size, is the number of standard deviations for a specific confidence. Typically, (99.7 percent confidence) or (99 percent confidence) Compute control limits: Statistical Process Control Formulas: Attribute Measurements ( p -Chart) Given: www.ePowerPoint.com

21. 1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample Example of Constructing a p-chart: Step 1 www.ePowerPoint.com

22. 2. Calculate the average of the sample proportions 3. Calculate the standard deviation of the sample proportion Example of Constructing a p -chart: Steps 2&3 www.ePowerPoint.com

23. 4. Calculate the control limits UCL = 0.0924 LCL = -0.0204 (or 0) Example of Constructing a p -chart: Step 4 www.ePowerPoint.com

24. Example of Constructing a p -Chart: Step 5 5. Plot the individual sample proportions, the average of the proportions, and the control limits www.ePowerPoint.com

25. Some notes for p-charts  The size of the sample must be large enough to allow counting of the attribute. A rule of thumb when setting up a p chart is to make the sample large enough to expect to count the attribute twice in each sample.  The assumption is that the sample size is fixed. If the sample size varies, the standard deviation and upper and lower control limits should be recalculated for each sample. www.ePowerPoint.com

26. Some notes for p-charts www.ePowerPoint.com

30. Process Control With Variable Measurements: Using X-bar and R Charts  Size of the samples (keep the sample size small, 4-5 is preferred)  the sample needs to be taken within a reasonable length of time  the larger the sample, the more it costs to take.  Number of samples (25 or so samples is suggested to set up the chart)  Frequency of samples  Control limits www.ePowerPoint.com

31. Example of x-bar and R Charts: Required Data www.ePowerPoint.com

32. Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges. www.ePowerPoint.com

33. Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values  E.L.Grant and R.Leavenworth computed a table, where n is the number of observations in subgroup, A2 is the factor for X-bar chart, D3 and D4 are factors for R chart. www.ePowerPoint.com

34. Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values UCL LCL Central Line www.ePowerPoint.com

35. Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot Values UCL LCL www.ePowerPoint.com

36. The R Chart  Monitors variability in a process  The characteristic of interest is measured on a numerical scale  Is a variables control chart  Shows the sample range over time  Range = difference between smallest and largest values in the subgroup www.ePowerPoint.com

37. The R Chart 1.Find the mean of the subgroup ranges (the center line of the R chart) 2.Compute the upper and lower control limits for the R chart 3.Use lines to show the center and control limits on the R chart 4.Plot the successive subgroup ranges as a line chart www.ePowerPoint.com

38. The X Chart  Shows the means of successive subgroups over time  Monitors process average  Must be preceded by examination of the R chart to make sure that the variation in the process is in control www.ePowerPoint.com

39. The X Chart  Compute the mean of the subgroup means (the center line of the X chart)  Compute the upper and lower control limits for the X chart  Graph the subgroup means  Add the center line and control limits to the graph www.ePowerPoint.com