Question

A fraction nonconforming control chart with center line 0.10, UCL = 0.19, and LCL = 0.01 is used to control a process.

Find the average run length if the process fraction noncon- forming shifts to 0.20.

Answer 1

It is given that

Center line =0.10

U.C.L=0.19

L.C.L=0.01

We have to find average run length  if the process fraction noncon- forming shifts to 0.20

Whose formula is given as

Average running length=1/P(false alarm)=1/P (Type 1 error when P=0.20)

let us calculate P(Type 1 error when P=0.20)

Let us find the sample size

here P=0.1 and q=1-p=1-0.1=0.9

if 3 sigma was used

after calculation sample size=100

mean

U.C.L=100*0.01=1

L.C.L=100*0.19=19

let us find

=P(X=0)+P(X>19)

=

=0.000025+(1-0.87)

=0.124

Average running length=1/P(false alarm)=1/P (Type 1 error when P=0.20)=1/0.12=8.0