ENSE 627 Quality Management in Systems

Homework Assignment 4

Chapter 3. Statistical Quality Control

3.4 Assignment Problems ( Page 3-81 ~3-82 )

3.4.4 A construction firm receives shipments of lots containing 20 steel rods to be used in the construction of a bridge. These lots must be checked to ensure that the breaking strength of the rods meets specifications. A lot will be rejected if it appears that more than 10% of the rods within the lot fail to meet specifications. Since testing a rod requires that it be broken, we cannot test each rod. Let us assume that a sample of size n=5 is selected for testing. Let us agree to reject the lot if more than 1 rod is found to be defective. Under this sampling plan, what is the producer's risk when the producer provides quality steel rods?

3.4.5. A single sampling plan calls for N=5,000, n=50, Ac=1. Based on the agreement, the producer should provide the products better than 0.5% defectives.
(1) What is the producer's risk when the producer is providing the quality at 0.5% defective level?
(2) What is the consumer's risk when the producer is providing the quality at 4.0% defective level?

3.4.6 You are given the following three inspection plans. Plan 1: N=100, n=10, Ac=3
Plan 2: N=200, n=20, Ac=3
Plan 3: N=300, n=30, Ac=3
(1) The incoming quality may vary from 0.0 to 0.15 regarding the percent defectives. Calculate the probabilities of acceptance at five selected quality level.
(2) Construction of the three OC curves using the results obtained in (1)
(3) Comments on the quality protection given by these three plans.

3.4.7. Our consumer who wants protection against accepting lots of 2.2% defective or worse insists that any 2.2% defective lots submitted shall have only a 0.1 probability of acceptance. Assume that product is submitted in lots of 1,000.
(1) Three engineers of quality control have proposed the following three plans.
Scheme 1: N=1000, n=100, Ac=0
Scheme 2: N=1000, n=170, Ac=1
Scheme 3: N=1000, n=240, Ac=2
You are asked to check if these three plans meet the consumer requirement. If you are not satisfied with these three plans, please propose one.
(2) Assuming that these three plans give the consumer equal protection against the acceptance of a 2.2% defective lot. You are informed that the product quality has been improved so that the incoming quality level is about 1% or 0.5% defectives. Which of the three plans provides the best protection for the MANUFACTURER.
(3) Do you agree with the claim that acceptance plans with the acceptance number equal to zero provide the best protection? Provide strong evidence to support your claim.

3.4.8 For the single sampling plan N=2,500, n=50, Ac=1, determine the AOQ for the lot percent defective values 0.1%, 0.2%, 0.3%, 0.4%, 0.8%, 1.0%, 1.2%, 1.4%, 1.8%, and 2.0%. Estimate the AOQL for this sampling plan and plot the AOQ curve vs incoming quality.

3.4.9. A consumer receives lots of 2,000 items and uses a single sampling plan to accept or reject the lots. the plan calls for 200 items to be inspected and for the lot to be accepted if two or less defectives are found. All rejected lots are screened by the consumer and the resultant costs is billed to the producer.
(1) Computer the average outgoing quality (AOQ) if 0.8% defective lots are submitted for inspection.
(2) Computer the average total inspection (ATI) if 0.8% defective lots are submitted for inspection
(3) Estimate the AOQL for this sampling plan and plot the AOQ curve vs incoming quality.