Question

Please provide detailed solutions to the following problem.

A quality engineer took 40 samples of 100 transistors each from the output of an assembly line. Each transistor was tested and the number of defectives in each sample is recorded in the table below. Determine the control chart limits for a p-chart.

Sample	Number Defective	Sample	Number Defective
1	3	21	1
2	2	22	2
3	1	23	2
4	4	24	3
5	0	25	4
6	2	26	1
7	0	27	2
8	5	28	4
9	1	29	0
10	2	30	4
11	2	31	3
12	1	32	2
13	3	33	4
14	3	34	2
15	4	35	1
16	5	36	1
17	3	37	3
18	3	38	4
19	1	39	4
20	8	40	2

Answer 1

Given that, Sample Size = n = 100

Number of sample = 40

The P for every sample is computed as = Number of defectives / Sample size

The average value for P (known as Pbar) is computed as the mean of all P values for 40 samples.

The value for Pbar = 0.0255

n = 100 = sample size

The control limits for P chart are:

Upper Control limits = UCL = Pbar + [Pbar x (1 - Pbar)] / n

= 0.0255 + [0.0255 x (1 - 0.0255)] / 100

= 0.0255 + 0.0157

= 0.0413

Lower Control limits = LCL = Pbar - [Pbar x (1 - Pbar)] / n

= 0.0255 - [0.0255 x (1 - 0.0255)] / 100

= 0.0255 - 0.0157

= 0.0097