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 


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