The AQL and LTPD of a single sampling plan are 0.03 and 0.06, respectively. Your company...

 

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The AQL and LTPD of a single sampling plan are 0.03 and 0.06, respectively. Your company is more risk-averse than others in purchasing from suppliers and is interested in finding a single sampling plan such that the probability of rejecting a lot with a percentage nonconforming of 0.03 (i.e., the AQL) is 5% and the probability of accepting a lot with a percentage nonconforming of 0.06 (i.e., the LTPD) is 5%. Part (a) (6 Points): You need two equations that can be used to determine the two unknowns of the plan (n.c). Both of them are in the form of Equation (7.2) on page 289 of your textbook, with specific values for P, and p. (It is the most fundamental relationship that expresses the probability of acceptance Pa as a function of p, n and c in the context of binomial probability. CANVAS Quiz does not allow equation editor, and I cannot show you. But, you should be familiar with it.) For each of the two equations, specify the P, and p. You do not need to write down the equations. Part (b) (3 Points): What should be the single sampling plan? Approximate numbers will suffice. Draw on the nomograph provided at the end of this exam to show your work. (Do not attempt to solve the two equations for the two numbers n and c.) Part (c) (2 Points): When the lot size N is not very large when compared with the sample size n, is the binomial distribution used in the answer of Part (a) justified? If so, explain why. If not, what distribution should be used? Part (d) (1 Points): Returning lots to the vendor is obviously undesirable for the vendor; it may also negatively impact your company. Describe one negative impact in up to two sentences. Part (e) (3 Points): Use Minitab to find out the single sampling plan it suggests. The AQL and LTPD of a single sampling plan are 0.03 and 0.06, respectively. Your company is more risk-averse than others in purchasing from suppliers and is interested in finding a single sampling plan such that the probability of rejecting a lot with a percentage nonconforming of 0.03 (i.e., the AQL) is 5% and the probability of accepting a lot with a percentage nonconforming of 0.06 (i.e., the LTPD) is 5%. Part (a) (6 Points): You need two equations that can be used to determine the two unknowns of the plan (n.c). Both of them are in the form of Equation (7.2) on page 289 of your textbook, with specific values for P, and p. (It is the most fundamental relationship that expresses the probability of acceptance Pa as a function of p, n and c in the context of binomial probability. CANVAS Quiz does not allow equation editor, and I cannot show you. But, you should be familiar with it.) For each of the two equations, specify the P, and p. You do not need to write down the equations. Part (b) (3 Points): What should be the single sampling plan? Approximate numbers will suffice. Draw on the nomograph provided at the end of this exam to show your work. (Do not attempt to solve the two equations for the two numbers n and c.) Part (c) (2 Points): When the lot size N is not very large when compared with the sample size n, is the binomial distribution used in the answer of Part (a) justified? If so, explain why. If not, what distribution should be used? Part (d) (1 Points): Returning lots to the vendor is obviously undesirable for the vendor; it may also negatively impact your company. Describe one negative impact in up to two sentences. Part (e) (3 Points): Use Minitab to find out the single sampling plan it suggests.