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*1  K[M(W1)  1], where M(t) is known as the renewal function.

If the time between failures, T, follows an Erlang law with parameters  and 2, then M(t)  



2 t

  0.25  0.25e2t for all t  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 to give the same value of E(T) as in the example.

b. Is the value of the warranty larger or smaller than in the corresponding exponential case? Explain the result intuitively