[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]

a) Determine the transition matrix of the process of sampling the part 3 pieces at the same time. Write the state space clearly

b) Suppose the inspector count the number of good product from the sampling which can be 0,1,2,3 Draw a transition matrix of process of sampling the part 3 pieces at the same time. Write the state space clearly

c) The inspector was told that the process will be judged in-control if the number of defect found is zero. Suppose that the inspector found is "0" defect at the present sample,
c-1. Find the distribution of the number of sample unit out-of-control is signal.

c-2. Find the mean number of sample unit out-of-control is signal ,and its variance.

c-3. Is this random variable a stochastic process? If it’s write down the transition matrix.

d) Use the matlab program and write function M-file to generate the stochastic process of problem c-2 and find the answer in c-3 Show the M-file command and the results.

Explanation / Answer

idk

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