Question: A component is replaced every T time units and upon its failure. The lifetimes of successive components are independent and identically distributed random variables with

A component is replaced every T time units and upon its failure. The lifetimes of successive components are independent and identically distributed random variables with PDF fX(x). A cost c1>0 is incurred for each planned replacement, and a fixed cost c2>c1 is incurred for each failure replacement.

What is the long-run average cost per unit time?

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