sanad57Lv1

12 Dec 2022

Problem 3 (35 pts.)

In a production process, parts are processed with a mean diameter of µ=100 mm and a standard deviation of σ=2 mm. assuming that a sample of size n=4 units would be taken for quality control process, answer the following questions.

     

1. Set up a control chart with 3sx control limits.

      UCL =

      CL =

      LCL =

 

1. What is probability of type I error for the control chart above.

 

Prob. (Type I Error, α) =

 

1. Determine the average run length and the average time to signal (assuming a sample is taken every 30 minutes) when the process is in control.

     ARL0 =

     ATS0 =

 

1. What is probability of type II error if the process mean shifts to 00 mm?

 

Prob. (Type II Error, β) =          

 

1. Determine the average run length and the average time to signal (assuming a sample is taken every 30 minutes) when the process mean shifts to 00 mm.

      ARL1 =

      ATS0 =

 

1. Set up a control chart with α=0.003 probability limits (Note: Find Zα/2 and use this as the number of sigma units you will be away from center line for upper and lower control limits)

UCL =

        LCL =

 

1. Plot the following points (mean diameter values of samples) on the control chart developed in (a) and determine if any point is out of control by the Western Electric Specify the point and the rule.