Problems

1. A 10-ampere fuse is a weak link in an electrical circuit; if the fuse is defective. It could fail to blow, even though the current exceeded 10 amps, thereby risking damage to equipment and personal injury. An electrical manufacturer uses enormous quantities of 10-ampere fuses in its products, which are purchased in lots of 100,000 from an outside supplier. The contract provides that each lot will be examined by the buyer according to this acceptance sampling plan: a random sample of 20 fuses will be drawn from the lot and tested by being subjected to a current of 10 amperes; if 0 or 1 of them fail to blow, the lot will be accepted; if 2 or more of them fail to blow, the lot will be returned.

1. Which probability distribution should be used here? Why?
2. Calculate some points on the operating characteristic curve for this sampling plan.
3. Draw the OC curve on a piece of graph paper. Use Table D in your textbook.
4. he acceptable quality level (AQL) is a 5 percent defective fuse. What type of sampling error might be made at the AQL?
5. What is the probability of suffering a sampling error at the AQL? What is the name of this probability?
6. The lot tolerance percent defective (LTPD) is 15 percent defective fuses. What type of sampling error might be made at the LTPD?
7. What is the probability of suffering a sampling error at the LTPD? What is the name of this probability?

2. The Major Convenience Appliance Company produces small appliances, such as drip coffee makers, for home and office use. It purchases the indicator lights, which indicate whether the appliance is off or on, from an outside supplier. Indicator lights are bought in lots of 10,000, the contract specifies that each lot will be examined by the buyer according to this acceptance sampling plan: a random sample of 150 indicator lights will be drawn from the lot and tested, if five (or fewer) defective lights are found, the batch will be accepted; if more than five defective lights are found, the batch will be returned.

1. Which probability distribution should be used here? Why?
2. Calculate some points on the operating characteristic curve for this sampling plan.
3. Draw the OC curve on a piece of graph paper.
4. The acceptable quality level (AQL) is 2 percent defective lights. What type of sampling error might be made at AQL?
5. What is the probability of suffering a sampling error at the AQL? What is the name of this probability?
6. The lot tolerance percent defective (LTPD) Is 6 percent defective lights. What type of sampling error might be made at the LTPD?
7. What is the probability of suffering a sampling error at the LTPD? What is the name of this probability?

3. Calculate some points on the AOQ curve for the acceptance-sampling plan in Problem 2.

1. Draw the AOQ curve on a piece of graph paper.
2. What is the approximate value of the average outgoing quality limit (AOQL)
3. What is the significance of the AOQL?

Solutions

1. a. Use the binomial distribution. This is attribute data with the categories of satisfactory and defective fuses, and the sample size is small.
b. Use Table D in your textbook.
Assumed Percentage
of Defective Fuses P(x < 1)
0% 1.0000
5% 0.7358
10% 0.3917
15% 0.1756
20% 0.0692
100% 0.0
c. Operating Characteristic Curve.
d. A Type I sampling error, consisting of rejecting a satisfactory batch.
e. p(Type I sampling error) = a = 1 - .7358 = .2642.
f. A Type II sampling error, consisting of accepting an unsatisfactory batch of fuses.
g. p(Type II sampling error) = ß = .1756.

2. a. Use the Poisson distribution. This is attribute data with the categories of satisfactory and defective indicator lights, and the sample size is large.
b. Use Table C in your textbook, with a mean, m = np.

3. Use the formula, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image291::/sites/dl/free/0072443901/24520/Image291.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image291 (1.0K)</a>Image291 , since the batch size is large compared to the sample size.

*Interpolate in Table C: (.720 + .686)/2 = .703.
a.
b. AOQL = 2.109% defective lights.
c. Because this acceptance sampling plan is applied to incoming indicator lights, those batches which are used in production will not include over 2.109% defective lights, on the average.