We have taken 12 samples of 400 letters each from a typing p

We have taken 12 samples of 400 letters each from a typing pool and found the following proportions of defective letters: .01, .02, .02, .00, .01, .03, .02, .01, .00, .04, .03, .02. A letter is defective when one or more errors are detected.

A. Calculate the control limits for a p chart. B. A sample of 400 letters has just been taken, and 6 letters are defective. Is the process still in control?

Solution

A.The control limits for a p chart can be calculated as

control limit=(.01+.02+.02+.00+.01+.03+.02+.01+.00+.04+.03+.02)/12

= (0.21)/12

= 0.0175

B. UCL=control limit(cl)+3square root(cl*(1-cl)/n)

= 0.0175+3*sqrt(0.0175*(1-0.0175)/400)

= 0.037169

LCL=control limit(cl)-3square root(cl*(1-cl)/n)
= 0.0175-3*sqrt(0.0175*(1-0.0175)/400)
=-0.00217

=0

YES,the process still in control.