Question: 3.5.2 A component of a computer has an active life, measured in discrete units, that is a random variable T, where PrfT D kg D

3.5.2 A component of a computer has an active life, measured in discrete units, that is a random variable T, where PrfT D kg D ak for k D 1;2; : : : . Suppose one starts with a fresh component, and each component is replaced by a new component upon failure. Let Xn be the age of the component in service at time n. Then, fXng is a success runs Markov chain.

(a) Specify the probabilities pi and qi.

(b) A “planned replacement” policy calls for replacing the component upon its failure or upon its reaching age N, whichever occurs first. Specify the success runs probabilities pi and qi under the planned replacement policy.

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