Question

The following data represent samples that were taken on 10 separate days. Each day has a...

The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control.

 Day Sample Size Defects 1 100 6 2 110 4 3 190 10 4 190 7 5 240 15 6 255 8 7 105 3 8 175 6 9 245 22 10 265 27
1. Find the UCL.

b. Find the LCL.

c. Is the process in control? Why/why not?

 Day Sample Size Defects Pi 1 100 6 0.06 2 110 4 0.036364 3 190 10 0.052632 4 190 7 0.036842 5 240 15 0.0625 6 255 8 0.031373 7 105 3 0.028571 8 175 6 0.034286 9 245 22 0.089796 10 265 27 0.101887 total 1875 108 0.53425

sample proportion = 0.53425 / 10

=0.053425

STD DEV OF P = √( p(1-p)/n ) =  √(0.053425 (1- 0.053425)/ 10 ) = 0.071113

a)

UCL =  p + 3 * sd =  0.053425 + 3* 0.071113 = 0.266764

B)

LCL = p - 3 * sd =  0.053425 - 3* 0.071113 =-0.159914 = 0(The proportion cannot be negative)

C)

As, all the proportion are in between UCL and LCL sample process in control.

Please revert back in case of any doubt.

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