Question

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	0
3	15	3
4	15	3
5	15	3
6	15	1
7	15	3
8	15	2
9	15	0
10	15	3

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	NUMBER OF DEFECTIVE ITEMS IN THE SAMPLE	SAMPLE SIZE (n)	p
1	2	15	0.133
2	0	15	0.000
3	3	15	0.200
4	3	15	0.200
5	3	15	0.200
6	1	15	0.067
7	3	15	0.200
8	2	15	0.133
9	0	15	0.000
10	3	15	0.200
Average of all 10 observations (p bar)	0.133

p = proportion of the defects in the sample = Number of defective items in the sample / n              

CL = p bar = mean or average of the proportions = 0.133

Sample size (n) = 15

z= no. of standard deviation from process average = 1.96 (for 95% confidence level)

p-p = CL = p bar = 0.1333

Sp = Standard Deviation (σ) = √[p bar * (1- p bar)]/n = 0.088

UCL= p bar + z*σ = 0.305

LCL= max(0,(p bar-z*σ)) = 0.000

Answer b)

Populate the data as shown below for plotting p-chart:

Sample	1	2	3	4	5	6	7	8	9	10
CL (p bar)	0.133	0.133	0.133	0.133	0.133	0.133	0.133	0.133	0.133	0.133
UCL	0.305	0.305	0.305	0.305	0.305	0.305	0.305	0.305	0.305	0.305
LCL	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
p	0.133	0.000	0.200	0.200	0.200	0.067	0.200	0.133	0.000	0.200

Plotted p-chart is as under:

0.350 0.300 0.250 CL (p bar) 0.200 UCL 0.150 LCL + Xp 0.100 0.050 0.000 1 2 3 4 5 6 7 8 9 10

Based on the above p-chart, the process is in statistical control as none of the value has breached the control limits.