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

a.	Determine the p−p−, Sp, 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 in statistical control
	Process is out of statistical control

Answer 1

Solution:

Z = 1.96

Number of samples, N = 10

Sample size, n = 15

(a) P = Total number of defective items in the sample / (Number of samples x Sample size)

P = (2 + 3 + 1 + 3 + 1) / (10 x 15)

P = 0.067

Sp = SQRT [P x (1 - P)] / n

Sp = SQRT [0.067 x (1 - 0.067)] / 15

Sp = 0.065

UCL = P + [Z x Sp]

UCL = 0.067 + [1.96 x 0.065]

UCL = 0.194

LCL = P - [Z x Sp]

LCL = 0.067 - [1.96 x 0.065]

LCL = - 0.060 or 0 (Number of defects cannot be negative)

LCL = 0

(b) Since, the number of defective items in few of the samples is more than the Upper Control Limit (UCL = 0.194), the process is out of statistical control.