1. /k Variation thinking 2WS02 Industrial Statistics A. Di Bucchianico

2. /k SPC: Philosophy Let the process do the talking: Goal: realize constant quality by controlling the process with quantitative information Constant quality means: quality with controlled and known variation around a fixed target Operator should be able to do the routine controlling

3. /k Variation I

4. /k Variation II

5. /k Variation III

6. /k 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Example: Dartec disqualification when outside range

7. /k Examples of variation patterns 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

8. /k Metric for sample variation: range easy to compute (pre-computer era!) rather accurate for sample size < 10 minimum maximum range

9. /k Metric for sample variation: standard deviation 2nd formula easier to compute by hand 2nd formula less rounding errors correct dimension of units n-1 to ensure that average value equals population variance (“unbiased estimator”)

10. /k Visualisation of sample variation Box-and Whisker plot histogram

11. /k all observationsfirst 60 observations

12. /k Variation and stability Can variation be stable? yes, if we mean that observations –follow fixed probability distribution –do not influence each other (independence) stability -> predictability How to handle a stable production process?

13. /k Why stable processes? behaviour is predictable processes can be left on itself: intervention may be expensive

14. /k Deming’s funnel experiment

15. /k Lessons from funnel experiment tampering a stable process may lead to increase of variation adjustments should be based on understanding of process (engineering knowledge) we need a tool to check for stability

16. /k Attributive versus variable two main types of measurements: –attributive (yes/no, categories) –variable (continuous data) hybrid type: –classes or bins use variable data whenever possible!

17. /k Statistically in control Constant mean and spread Process-inherent variation only Do not intervene Measurement Tijd X X X X X X X X X X X X X X X X X Intervene?

18. /k Statistically versus technically in control “Statistically in control” –stable over time /predictable “Technically in control” –within specifications

19. /k Statistically in control vs technically in control statistically controlled process: –inhibits only natural random fluctuations (common causes) –is stable –is predictable –may yield products out of specification technically controlled process: –presently yields products within specification –need not be stable nor predictable

20. /k Priorities what is preferable: –statistical control or –technically in control ?? process must first be in statistical control

21. /k Variation and production processes Shewhart distinguishes two forms of variation in production processes: common causes –inherent to process –cannot be removed, but are harmless special causes –external causes –must be detected and eliminated

22. /k Chance or noise How do we detect special causes ? use statistics to distinguish between chance and real cause

23. /k Shewhart control chart graphical display of product characteristic which is important for product quality Upper Control Limit Centre Line Lower Control Limit

24. /k Control charts

25. /k Why control charts? control charts are effective preventive device control charts avoid tampering of processes control charts yield diagnostic information

26. /k Basic principles take samples and compute statistic if statistic falls above UCL or below LCL, then out-of-control signal: e.g., how to choose control limits?

27. /k Normal distribution often used in SPC “justification” by Central Limit Theorem: –accumulation of many small errors

28. /k Meaning of control limits limits at 3 x standard deviation of plotted statistic basic example: UCL LCL

29. /k Example diameters of piston rings process mean: 74 mm process standard deviation: 0.01 mm measurements via repeated samples of 5 rings yields:

30. /k Specifications vs. natural tolerance limits never put specification limits on a control chart control chart displays inherent process variance during trial run charts (also called tolerance chart of tier chart) often yields useful graphical information