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.
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.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2fb5ce7-0178-4c15-b8b1-c44be074791b%2F3aa2c182-c8cf-4968-a404-4f730e46ec00%2Fzodlza.png&w=3840&q=75)
Transcribed Image Text: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.
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