[Information] Consider a process of sampling the part 3 pieces at the same time

Question

[Information]
Consider a process of sampling the part 3 pieces at the same time for every hour of production. The quality engineer wants to determine if the quality of the sampled product pass or fail. The specification is the "good product" has deviation not greater than 4 micron in magnitude.
The distribution of deviation is as follows
X deviation P(x)*100 percentages
-2.5 0.88
-1   1.77
-0.5     2.65
0        11.50
0.5      9.73
1.0      13.27
1.5      16.81
2.0      18.58
2.5      13.27
3.0      6.19
3.5      3.54
4.0      0.88
4.5      0.88
The sample inspection results will be labeled as (1,0,0) or (1,1,1), etc. depending on the test results ("1" means good product)

[Question]

Suppose the inspector has relaxed the criteria of inspection. The process will be jaded in-control if the number of the defect found is not greater one. If it's the process will be stopped for corrective action (This is called the absorbing stage).
After the process has been fixed, the process will begins as before

a) Write down the transition matrix

b) Find the mean number of sample taken until the process is stopped for corrective action given the inspector has found '0' as the present sample.

c) Find the mean number of sample taken until the process is stopped for corrective action given the inspector has found '1' as the present sample.

d) Write the M-file function (and show the command) how to calculate the answer of b)

Explanation / Answer

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