Twentyfive samples of 100 items each are inspected when a pr

Twenty-five samples of 100 items each are inspected when a process is considered to be operating satisfatorily. In the 25 samples a total of 135 items are found to be defective.

a) what is an estimate of the proportion defective when the process is in control?

b)what is the standard error of the proportion if samples of size 100 will be used for statistical process control?

c)compute the upper and lower control limits of the chart

please show your work

Solution

a.

total no. of items = 25*100

so

p = 135/(25*100) = 0.0540

b)

standard error =SE = sqrt(p*(1-p)/n) = sqrt(0.0540*(1-0.0540)/100) = 0.0226

c)

UCL = p + 3*SE = 0.0540+3*0.0226 = 0.1218

LCL = p - 3*SE = 0.0540-3*0.0226 = -0.0138