A single-sampling plan by attributes is needed for a purchased component. Given the following information, what is the consumer's risk? Table G.1 is appended to this exam. Sample size = 125
Acceptance number (c) = 4
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.07
A) .057
B) .061
C) .065
D) .069

Question

Quizplus · Accepted Answer

The consumer's risk is the probability of accepting a lot that is actually defective. The consumer's risk is calculated using the following formula:Consumer's risk = P(Accepting a lot | Lot is defective)The probability of accepting a lot is calculated using the binomial distribution. The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent experiments, each of which has a constant probability of success.In this case, the number of successes is the number of defective items in the sample, and the probability of success is the lot tolerance proportion defective.The acceptance number is the maximum number of defective items that can be found in the sample for the lot to be accepted.The acceptance quality level is the proportion of defective items in a lot that is considered acceptable.The lot tolerance proportion defective is the proportion of defective items in a lot that is considered unacceptable.Using the information given in the question, we can calculate the consumer's risk as follows:Consumer's risk = P(Accepting a lot | Lot is defective)= P(X ≤ c | p = LTPD)= Σ(x=0 to c) (125 choose x) * (0.07)^x * (0.93)^(125-x)= 0.061Therefore, the consumer's risk is 0.061, which is closest to choice A.

A Single-Sampling Plan by Attributes Is Needed for a Purchased