Question

A quality engineer takes 40 subgroups of 100 transistors each from the output of an assembly line. Each transistor is tested and the number of defectives in each sample is recorded. The average proportion (fraction) defective is .0255. The lower and upper control limits for the p chart are

a. 0 and 0.100

b. 0.010 and 0.0413

c. 0 and 0.057

d. 0 and 0.0728

e. 0.001 and 0.050

Answer 1

Average proportion (fraction) defective = p-bar = 0.0255

Standard deviation of p-bar = sqrt((p-bar*(1-p-bar))/n) where n = sample size = 100

Standard deviation of p-bar = sqrt((0.0255*(1-0.0255))/100) = 0.015763803

UCL = 0.0255 + 3*0.015763803 = 0.072791409 = 0.0728 (Rounding to 4 decimal places)

LCL = 0.0255 - 3*0.015763803 = -0.021791409 = 0 (Adjusted to 0)

So, correct answer is d. 0 and 0.0728