Twenty-Six samples of 105 items each were inspected when a process was considere

ID: 3222321 • Letter: T

Question

Twenty-Six samples of 105 items each were inspected when a process was considered to be operating satisfactorily. In the 26 samples, 135 items were found to be defective. a. What is an estimate of the proportion defective when the process is in control? Round your answer to four decimal places. What is p = __________ b. What is the standard error of the proportion if samples of sue 105 will be used for statistical process control? Round your answer to four decimal places. Compute Sigma = _________ c. Compute the upper and lower control limits for the control chart. Round your answers to four decimal places. Compute the UCL = ___________ Compute the LCL = ___________

Explanation / Answer

There are 26 samples of size 105.

total number of sample points = 26*105 = 2730

no. of items to be defective = 135

estimate of the proportion defective (p) = 135/2730 = 0.049

standard error of the proportion when n = 105

SE = sqrt((p*q)/n)

q = 1 - p = 1 - 0.049 = 0.951

SE = sqrt((0.049*0.951)/105)) = 0.021

Therefore control limits for p-chart are :

UCL = p + SE = 0.049 + 0.021 = 0.071

LCL = p - SE = 0.049 - 0.021 = 0.028

CL = p = 0.049

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Twenty-Six samples of 105 items each were inspected when a process was considere

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