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	2
3	15	2
4	15	0
5	15	2
6	15	1
7	15	3
8	15	2
9	15	1
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):

P bar

Sp

UCL

LCL

Answer 1

Total number of defects across the 10 samples = 2+2+2+0+2+1+3+2+1+3 = 18

a)

p bar = 18 / (15*10) = 0.12

Sp = sqrt(0.12*(1-0.12)/15) = 0.0839

UCL = Pbar + z*Sp = 0.12+1.96*0.0839 = 0.2845

LCL = Pbar - z*Sp = 0.12-1.96*0.0839 = -0.0445 =~ 0   (LCL = 0, if the calculated value is negative)