[1] A manufacturing process involved in the production of plastic molds for a specific automotive application is under study. To control the meanthickness of this (normally distributed) process with a standard deviation, s = 3.0, chart is used with n = 5, LCL = 14.15, and UCL = 15.85. If the process means shifts to 15.2, find the probabilitythat the shift will be detected on the:

(a) first subsequent sample of 5 observations

(b) second subsequent sample of 5 observations

[3] Given the following information with regards to ( , S)-chart with n = 4:

-chart: UCL = 510, Center line = 500, and LCL = 490

S-chart: UCL = 12.9709, Center line = 6.5842, and LCL = 0.19753

(a) what fraction of items are nonconforming if specifications call for 501 ± 5?

(b) find the ARL if the process mean shifts to 493.

Please see the attached file.

Solution 1

Here it is given that the process standard deviation s = 3, subgroup size n = 5, LCL = 14.15 and UCL = 15.85

Now the Central Line (mean) is CL =(UCL+LCL)/2 =15

Let denote the process mean. Suppose the process mean shift from 15 to 15.2.

Let and denote the sample mean of first and second subsequent sample of 5 observations.

Now the probability that the shift will be …

The solution describes the method to find the average run length and probability of detecting a shift in a manufacturing process.