Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 13.8, Problem 41P
a
Summary Introduction
Interpretation:
Indifference value of the item with a free replacement warranty.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
b
Summary Introduction
Interpretation:
Whether the value of warranty larger or smaller than in exponential case.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
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Students have asked these similar questions
Large-scale integrated (LSI) circuit chips are made in one department of an electronics firm. These chips are incorporated into analog
devices that are then encased in epoxy. The yield is not particularly good for LSI manufacture, so the AQL specified by that department
is 17% while the LTPD acceptable by the assembly department is 47%. Assume the company is willing to accept a consumer's risk of 10
percent and a producer's risk of 5 percent.
a. Find the sample size. Use Exhibit 10.16. Note: If the exact value of the computed LTPD/AOQ ratio does not appear in Exhibit 10.16,
use the next higher ratio. (Round up your answer to the next whole number.)
Sample size
b. How would you tell someone to do the test?
Randomly sample LSI using the sample size from part a,
the lot if more than
defective.
TenTen Company manufactures video recorders. It is so certain of its quality control that it is offering a complete replacement warranty if the set fails within two years. Based upon compiled data, the company has a need that only 1% of its recorders fail during the first year and 5% fail during the second year. The warranty does not cover replaced recorders.
a) Formulate this problem as a Markov chain and determine the transition matrix.
b) Find the probability that the manufacturer will have to honor the warranty.
41. Consider the case in which the failure mechanism for the product does not obey
the exponential law. In that case, the cost under the free replacement warranty that
is indifferent to the cost of buying the item without a warranty is given by
C* = K[M(W\) + 1],
where M(t) is known as the renewal function.
If the time between failures, T, follows an Erlang law with parameters A and
2, then
At
M(t) = " - 0.25 + 0.25e¬211
2
for all t2 0.
(See, for example, Barlow and Proschan, 1965, p. 57.)
a. For Example 13.13, presented in this section, determine the indifference value
of the item with a free replacement warranty when the failure law follows an
Erlang distribution. Assume that A = to give the same value of E(T) as in the
еxample.
b. Is the value of the warranty larger or smaller than in the corresponding expo-
nential case? Explain the result intuitively.
Chapter 13 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 13.1 - Prob. 3PCh. 13.1 - Prob. 4PCh. 13.1 - Prob. 5PCh. 13.1 - Prob. 6PCh. 13.2 - Prob. 7PCh. 13.2 - Prob. 9PCh. 13.3 - Prob. 13PCh. 13.3 - Prob. 14PCh. 13.4 - Prob. 15PCh. 13.4 - Prob. 16P
Ch. 13.4 - Prob. 17PCh. 13.4 - Prob. 18PCh. 13.4 - Prob. 19PCh. 13.4 - Prob. 20PCh. 13.6 - Prob. 21PCh. 13.6 - Prob. 22PCh. 13.6 - Prob. 23PCh. 13.6 - Prob. 24PCh. 13.6 - Prob. 25PCh. 13.7 - Prob. 26PCh. 13.7 - Prob. 27PCh. 13.7 - Prob. 28PCh. 13.7 - Prob. 30PCh. 13.7 - Prob. 31PCh. 13.7 - Prob. 32PCh. 13.7 - Prob. 33PCh. 13.7 - Prob. 34PCh. 13.8 - Prob. 35PCh. 13.8 - Prob. 36PCh. 13.8 - Prob. 37PCh. 13.8 - Prob. 38PCh. 13.8 - Prob. 39PCh. 13.8 - Prob. 40PCh. 13.8 - Prob. 41PCh. 13 - Prob. 42APCh. 13 - Prob. 43APCh. 13 - Prob. 44APCh. 13 - Prob. 45APCh. 13 - Prob. 46APCh. 13 - Prob. 48APCh. 13 - Prob. 49APCh. 13 - Prob. 51APCh. 13 - Prob. 52APCh. 13 - Prob. 53AP
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