Question

The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control.

Day	Sample Size	Defects
1	100	6
2	110	4
3	190	10
4	190	7
5	240	15
6	255	8
7	105	3
8	175	6
9	245	22
10	265	27

1. Find the UCL.

              b. Find the LCL.

              c. Is the process in control? Why/why not?

Answer 1

	Day	Sample Size	Defects	Pi
	1	100	6	0.06
	2	110	4	0.036364
	3	190	10	0.052632
	4	190	7	0.036842
	5	240	15	0.0625
	6	255	8	0.031373
	7	105	3	0.028571
	8	175	6	0.034286
	9	245	22	0.089796
	10	265	27	0.101887
total		1875	108	0.53425

sample proportion = 0.53425 / 10

=0.053425

STD DEV OF P = √( p(1-p)/n ) =  √(0.053425 (1- 0.053425)/ 10 ) = 0.071113

a)

UCL =  p + 3 * sd =  0.053425 + 3* 0.071113 = 0.266764

B)

LCL = p - 3 * sd =  0.053425 - 3* 0.071113 =-0.159914 = 0(The proportion cannot be negative)

C)

As, all the proportion are in between UCL and LCL sample process in control.

Please revert back in case of any doubt.