Quality Control Part 2

1. Quality ControlPart 2 By Anita Lee-Post

2. Statistical process control methods • Control charts for variables: process characteristics are measured on a continuous scale, e.g., weight, volume, width • Mean (X-bar) chart • Range (R) chart • Control charts for attributes: process characteristics are counted on a discrete scale, e.g., number of defects, number of scratches • Proportion (P) chart • Count (C) chart • Process capability ratio and index

3. Control charts • Use statistical limits to identify whether a sample of data falls within a normal range of variation or not

4. Setting Limits Requires Balancing Risks • Control limits are based on a willingness to think that something is wrong when it’s actually not (Type I or alpha error), balanced against the sensitivity of the tool - the ability to quickly reveal a problem (failure is Type II or beta error)

5. Control Charts for Variable Data • Mean (x-bar) charts • Tracks the central tendency (the average value observed) over time • Range (R) charts: • Tracks the spread of the distribution over time (estimates the observed variation)

6. Mean (x-bar) charts

7. Mean (x-bar) charts continued • Use the x-bar chart established to monitor sample averages as the process continues:

8. An example The diameters of five C&A bagels are sampled each hour during a 8-hour period. The data collected are shown as follows:

9. An example continued • Develop an x-bar chart with the control limits set to include 99.74% of the sample means and the standard deviation of the production process (s) is known to be 0.2 Inches. Step 1. Compute the sample mean x-bar:

10. An example continued Step 2. Compute the process mean or center line of the control chart:

11. An example continued Step 3. Compute the upper and lower control limits: To include 99.74% of the sample means implies that the number of normal standard deviations is 3. i.e., z=3

12. An example continued • C&A collects the process characteristics (i.e., diameter) of their bagels in days 2 through 10. Is the process in control? The process is not in control because the means of recent sample averages fall outside the upper and lower control limits UCL = 4.25 LCL = 3.83

13. Range (R) charts

14. An example The diameters of five C&A bagels are sampled each hour during a 8-hour period. The data collected are shown as follows:

15. An example continued • Develop a range chart. Step 1. Compute the average range or CL:

16. An example continued Step 2. Compute the upper and lower control limits:

17. An example continued • C&A collects the process characteristics (i.e., diameter) of their bagels in days 2 through 10. Is the process in control? UCL = 0.57 The process is in control because the ranges of recent samples fall within the upper and lower control limits CL = 0.27 LCL = 0

18. Using both mean & range charts • Mean (x-bar) chart: measures the central tendency of a process • Range (R) chart: measures the variance of a process Case 1: a process showing a drift in its mean but not its variance  can be detected only by a mean (x-bar) chart

19. Using both mean & range charts continued Case 2: a process showing a change in its variance but not its mean  can be detected only by a range (R) chart

20. Construct x-bar chart from sample range

21. Control Charts for Attributes • p-Charts: • Track the proportion defective in a sample • c-Charts: • Track the average number of defects per unit of output

22. Proportion (p) charts • Data requirements: • Sample size • Number of defects • Sample size is large enough so that the attributes will be counted twice in each sample, e.g., a defect rate of 1% will require a sample size of 200 units.

23. Proportion (p) charts continued

24. Count (c) charts • Data requirements • Number of defects • Monitoring processes in which the items of interest (in this case, defects) are infrequent and/or occur in time or space, e.g., errors in newspaper, bad circuits in a microchip, complaints from customers.

25. Count (c) charts continued