Quality and statistical process control ppt @ bec doms

1. Introduction to Quality and Statistical Process Control

3. Chapter Overview Quality Management and Tools for Improvement Deming’s 14 Points Juran’s 10 Steps to Quality Improvement The Basic 7 Tools Philosophy of Quality Tools for Quality Improvement Control Charts X-bar/R-charts p-charts c-charts

10. The Deming Cycle The Deming Cycle The key is a continuous cycle of improvement Act Plan Do Study

17. Process Variation Total Process Variation Common Cause Variation Special Cause Variation = + Variation is natural; inherent in the world around us No two products or service experiences are exactly the same With a fine enough gauge, all things can be seen to differ

18. Sources of Variation Total Process Variation Common Cause Variation Special Cause Variation = + People Machines Materials Methods Measurement Environment Variation is often due to differences in:

19. Common Cause Variation Total Process Variation Common Cause Variation Special Cause Variation = + Common cause variation naturally occurring and expected the result of normal variation in materials, tools, machines, operators, and the environment

20. Special Cause Variation Total Process Variation Common Cause Variation Special Cause Variation = + Special cause variation abnormal or unexpected variation has an assignable cause variation beyond what is considered inherent to the process

22. Control Chart Basics Process Average UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL LCL +3σ - 3σ Common Cause Variation: range of expected variability Special Cause Variation: Range of unexpected variability time

23. Process Variability Process Average UCL = Process Average + 3 Standard Deviations LCL = Process Average – 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

24. Statistical Process Control Charts Statistical Process Control Charts X-bar charts and R-charts c-charts Used for measured numeric data Used for proportions (attribute data) Used for number of attributes per sampling unit p-charts

29. Average of Subgroup Means and Ranges Average of subgroup means: where: x i = i th subgroup average k = number of subgroups Average of subgroup ranges: where: R i = i th subgroup range k = number of subgroups

32. Example: R-chart The upper and lower control limits for an R-chart are where: D 4 and D 3 are taken from the Shewhart table (appendix Q) for subgroup size = n

33. x-chart and R-chart UCL LCL time UCL LCL time R-chart x-chart

42. p-Chart Example Subgroup number Sample size Number of successes Proportion, p 1 2 3 … 150 150 150 15 12 17 … 10.00 8.00 11.33 … Average subgroup proportion = p

43. Average of Subgroup Proportions The average of subgroup proportions = p where: p i = sample proportion for subgroup i k = number of subgroups of size n where: n i = number of items in sample i  n i = total number of items sampled in k samples If equal sample sizes: If unequal sample sizes:

45. Standard Deviation of Subgroup Proportions The estimate of the standard deviation for the subgroup proportions is If equal sample sizes: If unequal sample sizes: where: = mean subgroup proportion n = common sample size Generally, is computed separately for each different sample size

50. c-Chart Control Limits The control limits for a c-chart are