Question

William's assembly unit has decided to use a p-Chart with 2-sigma control limits to monitor the proportion of defective castings produced by their production process. The quality control manager randomly samples 150 castings at 10 successively selected time periods and counts the number of defective castings in the sample.

Sample Defects
1 9
2 14
3 9
4 9
5 13
6 8
7 12
8 10
9 12
10 11

Required:
a. What is the Center Line of the control chart?
b. What value of z should be used to construct the control chart?
c. What is the Upper Control Limit?
d. What is the Lower Control Limit?

Answer 1

Answer: attached below is the missing p chart

a) 0.07133

b) 2

c) 0.098

d) 0.045

Explanation:

sample size = 150 castings

number of periods = 10

a) Determine the center Line of the control chart

( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10

mean = 0.07133

standard deviation = 0.01335

b) Determine the value of Z to be used

Given that we are using 2sigma limits .

the value of Z to be used = 2

c) Upper limit control

= mean value + z-value * std

= 0.0713 + 2*0.01335 = 0.098

d) Lower Control Limit

= mean value - z-value * std

= 0.0713 - 2*0.01335 = 0.045