Question

Problem 10-23

Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table:

SAMPLE	n	NUMBER OF DEFECTIVE ITEMS IN THE SAMPLE
1	15	2
2	15	1
3	15	1
4	15	1
5	15	3
6	15	1
7	15	0
8	15	2
9	15	1
10	15	0

a. Determine the p−p−, S_p, UCL and LCL for a p-chart of 95 percent confidence (1.96 standard deviations). (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal places.)

p−p−
Sp
UCL
LCL

b. What comments can you make about the process?

	Process is out of statistical control
	Process is in statistical control

Answer 1

Answer a:

Sample	defects	Observations
1	2	15
2	1	15
3	1	15
4	1	15
5	3	15
6	1	15
7	0	15
8	2	15
9	1	15
10	0	15
total	12	150
steps and formulas, for z=		1.96
Average Proportion of defects=P	total defects/total observations	0.0800
Q=	1-P	0.9200
N=	average sample size	15
Standard deviation, Sp	squareroot(P*Q/N)	0.070
UCL=	P + z*Sp	0.217
LCL=	P - z*Sp	-0.057
	defects cannot be negative, therefore negative LCL is taken as '0'	0.000

Answer b": The process is in control: As we can see that NO sample is beyond control limits in charts

Please ask, if you have any doubts through the comment section. Do rate the answer

Sample	defects	Observations	proportion of defect=defectives/observations	P	UCL	LCL
1	2	15	0.1333	0.0800	0.2173	0.0000
2	1	15	0.0667	0.0800	0.2173	0.0000
3	1	15	0.0667	0.0800	0.2173	0.0000
4	1	15	0.0667	0.0800	0.2173	0.0000
5	3	15	0.2000	0.0800	0.2173	0.0000
6	1	15	0.0667	0.0800	0.2173	0.0000
7	0	15	0.0000	0.0800	0.2173	0.0000
8	2	15	0.1333	0.0800	0.2173	0.0000
9	1	15	0.0667	0.0800	0.2173	0.0000
10	0	15	0.0000	0.0800	0.2173	0.0000