Ten samples of 30 parts each were taken from an ongoing...

Ten samples of 30 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: (Please round to 4 decimal places) Sample n # of Def items Sample n # of Def items 1 30 2 6 30 2 2 30 1 7 30 1 3 30 1 8 30 3 4 30 0 9 30 0 5 30 2 10 30 1

Transcript

00:01 So for this problem to begin, i'll note that the upper control limit for p will be given by our average proportion plus 3 times the square root of average proportion times 1 minus the average proportion divided by the average sample size, n bar.

00:22 And the lower control limit for p would be p bar minus 3 times the square root of p bar times 1 minus p bar times 1 minus p.

00:32 Bar over n bar.

00:35 So with that information, i'll jump over into excel.

00:38 Problems like this typically are done using excel or some kind of statistical software, as opposed to being done by hand, like more theoretical problems.

00:47 All right, so i've copied down the data.

00:49 So we can see that we have n is constant for all of these.

00:53 So we don't need to worry about n bar.

00:54 It's just going to be equal to 30.

00:56 Then what we'll have to do is calculate the proportion of defective for each one of our samples.

01:03 So that's simply going to be equal to the number of defective divided by n.

01:08 So calculating that out for all of these, we have our individual sample proportion or proportions of defective.

01:15 So then we can find p bar simply by taking the average of all of those p values, noting that when we take a mean or a mean value, we add up all the individual values, then we divide by the number of measurements.

01:28 So we would have that the total, theoretically here, should be 43.

01:33 Then we divide by 100, or pardon me, a little bit off here.

01:38 The sum, if we look down at the bottom there, pardon me, no, the sum would be 0 .43...

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