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A quality control engineer wishes to study alternative
Chapter 3, Problem 183SE(choose chapter or problem)
Problem 183SE
A quality control engineer wishes to study alternative sampling plans: n = 5, a = 1 and n = 25, a = 5. On a sheet of graph paper, construct the operating characteristic curves for both plans, making use of acceptance probabilities at p = .05, p = .10, p = .20, p = .30, and p = .40 in each case.
a If you were a seller producing lots with fraction defective ranging from p = 0 to p = .10, which of the two sampling plans would you prefer?
b If you were a buyer wishing to be protected against accepting lots with fraction defective exceeding p = .30, which of the two sampling plans would you prefer?
Questions & Answers
QUESTION:
Problem 183SE
A quality control engineer wishes to study alternative sampling plans: n = 5, a = 1 and n = 25, a = 5. On a sheet of graph paper, construct the operating characteristic curves for both plans, making use of acceptance probabilities at p = .05, p = .10, p = .20, p = .30, and p = .40 in each case.
a If you were a seller producing lots with fraction defective ranging from p = 0 to p = .10, which of the two sampling plans would you prefer?
b If you were a buyer wishing to be protected against accepting lots with fraction defective exceeding p = .30, which of the two sampling plans would you prefer?
ANSWER:Solution :
Step 1 of 2:
Given a quality control engineer wishes to study alternative sampling plans is
n =5, a=1 and n=25, a=5.
Then the acceptance probabilities at p=0.05, p=0.10, p=0.20, p=0.30 and p=0.40.
Our goal is:
a). If we were a seller producing lots with fraction defective ranging from p=0 to p=0.10.
Then we need to find which of the two sampling plans would we prefer.
b). If we were a buyer wishing to be protected against accepting lots with fraction
defective exceeding p=0.30.
Then we need to find which of the two sampling plans would we prefer.
a).
If we were a seller producing lots with fraction defective ranging from p=0 to p=0.10.
Now we have to find which of the two sampling plans would we prefer.
We preferred n=25, a=5, because n=25, a=5 line above the n=5, a=1 line for p=0 to p=0.40.
Hence we preferred n=25, a=5.