Assignment

Prob. 1

An assembly operation for trigger mechanisms of a semiautomatic spray gun produces a small percentage of defective mechanisms. Management must decide whether to continue the current practice of 100 percent inspection or to replace defective mechanisms after final assembly when all guns are inspected. Replacement at final assembly costs $30 each; inspection during trigger assembly costs $12 per hour for labor and overhead. The inspection rate is one trigger per minute.

(a) Would 100 percent inspection during trigger assembly be justified if there are (1) 4% defective? (2) 1%defective?
(b) At what point would management be indifferent between 100 percent inspection of triggers and only final inspection?

Prob. 2

Random samples of n = 20 circuit breakers are tested for damage caused by shipment in each lot of 4,000 received. Lots with more than one defective are pulled and subjected to 100 percent inspection.

(a) Construct the OC curve for this sampling plan.

(b) Construct the AOQ curve for this plan, assuming defectives found during 100 percent inspection are replaced with good parts. What is the approximate AOQL?

Prob. 3

A manufacturer receives shipments of several thousand parts from a supplier every week. The manufacturer has the option of conducting a 100 percent inspection before accepting the parts. The decision is based on a random sample of 15 parts. If parts are not inspected, defectives become apparent during a later assembly operation, at which time replacement cost is $6.25 per unit. Inspection cost for 100 percent inspection is $1per unit.

(a) At what fraction defective would the manufacturer be indifferent between 100 percent inspection and leaving discovery of defectives until the later assembly operation?

(b) For the sample size used, what is the maximum number of sample defectives that would cause the lot to be passed without 100 percent inspection, based on your answer to part (a)?

(c) If the shipment actually contains 5 percent defective items:

1. What is the correct decision?
2. What is the probability it would be rejected in favor of 100 percent inspection?
3. What is the probability that it would be accepted without 100 percent inspection?
4. What is the probability of a Type I error (α)? A Type II error (β)?

(d) Answer the question in part (c) for a shipment that contains 20 percent defective items.

Prob. 4

A single sampling plan is used to determine the acceptability of shipments of a bearing assembly used in the manufacture of skateboards. For lots of 500 bearings, samples of n = 20 are taken. The lot is rejected if any defectives are found in the sample.

(a) Suppose that AQL = 0.01 and LTPD = 0.10. Find the probability of α andβ.
(b) Is this plan more advantageous for the consumer or the producer?

Prob. 5

Samples of size 20 are drawn from lots of 1,000 items. The lot is rejected if there are more than two defectives in the sample. Using a binomial approximation, graph the OC curve as a function of p, the proportion of defectives in the lot. For an AQL of 0.01 and an LTPD of0.10, find Type I error (α) and Type II error (β).

(a) Graph the OC curve and indicate the Type I and Type II error probabilities on the graph.
(b) Graph the AOQ curve and identify the value of the AOQL.