Question

Twenty samples of n = 200 were taken by an operator at a workstation in a production
process. The number of defective items in each sample were recorded as follows

Sample	number of defectives		Sample	number of defectives
						1	12		11	16
2	18		12	14
3	10		13	12
4	14		14	16
5	16		15	18
6	19		16	20
7	17		17	18
8	12		18	20
9	11		19	21
10	14		20	22

1- develop a P-chart using 3-sigma , set p the P chart and plot the observations to determine if the process was out of control at any point.

2- if the management want to use the pattern tests using 1-sigma , 2- sigma and 3-sigma to further determine if the process is in control . Determine the " up-and-down" and " above -and -below" runs and zone observations to make your recommendation using the control chart.

Answer 1

Ans. 1)

Sample	No. of Defective (di)	P = (No. of defect/ Sample size)
1	12	0.06
2	18	0.09
3	10	0.05
4	14	0.07
5	16	0.08
6	19	0.095
7	17	0.085
8	12	0.06
9	11	0.055
10	14	0.07
11	16	0.08
12	14	0.07
13	12	0.06
14	16	0.08
15	18	0.09
16	20	0.1
17	18	0.09
18	20	0.1
19	21	0.105
20	22	0.11

Ans 2)

P value of all samples are within control limit.

Rule 2 - Zone A - For sample 2 and 3, there is sudden change in the p value. It is a special cause or one time occurence event.

Rule 3 - Zone B - From sample 4-7, there is a one directional shift with small changes

Rule 4 - Zone C - From sample 14-20 there is a long one directional shift with small changes.

Possible cause of error for Zone A might be because of wrong setup or new person doing the job. It can be prevent by havindg robust standard operating procedure.

Possible cause of error for Zone C might be because of change in Raw Material or Change in Setup procedure. It can be prevent by adjust the process in line with the other changes.