Question

# Random samples of size n= 400 are taken from a population with p= 0.15. a.Calculate the...

Random samples of size n= 400 are taken from a population with p= 0.15.

a.Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p
chart.

b.Suppose six samples of size 400 produced the following sample proportions: 0.06, 0.11, 0.09, 0.08, 0.14, and 0.16. Is the production process under control?

Ans(a)- given that

 Input: No. of samples 6 Sample size 400 Sigma limits(z) 3

using the p- chart formula

and CL =

using above formulas we get

Output:
 =
0.15
UCL = 0.20
LCL = 0.10

Ans(b)-

Calculations
Proportion
Sample Defective UCL
 LCL
1 0.060 0.15 0.2036 0.0964
2 0.110 0.15 0.2036 0.0964
3 0.090 0.15 0.2036 0.0964
4 0.080 0.15 0.2036 0.0964
5 0.140 0.15 0.2036 0.0964
6 0.160 0.15 0.2036 0.0964

graph-

p-chart-

we clearly see in this graph sample 1 lies below the LCL line since process is out of control.

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