Maintenance, Replacement and Reliability

"A car rental company has kept records on a particular vehicle component. Although failure of the component is random, it is a function of vehicle use. Data on 1000 failures have been collected and analyzed, and through using a 2 goodness-of-fit test, the conclusion is reached that the time to failure of the component can be described adequately by a uniform distribution. Table 2.17 gives the distribution of the expected frequencies of the 1000 failures. The total cost of a preventive replacement of the component is $100. A failure results in a penalty cost being incurred, and in total, the cost of a failure replacement is $200. It is reasonable to assume that the times taken to carry out either a preventive or failure replacement are negligible. The car rental company wishes to consider implementing a preventive replacement policy. The particular policy it is interested in is frequently termed an age-based policy; that is, it is one in which preventive replacement occurs only when a component has reached a specific age, say, tp; otherwise, a failure replacement is made. Considering tp values of 10,000, 20,000, 30,000, and 40,000 km, which one gives the smallest expected total cost per 1000 km? Clearly explain the derivation of any model you use and your line of reasoning in reaching a conclusion." (Tsang & Jardine, 2013)

TABLE 2.17 Component Failure Frequency Data Thousands of kilometers to failure 0-10 10-20 Expected frequency 250 250 20-30 250 30-40 250 TABLE 2.17 Component Failure Frequency Data Thousands of kilometers to failure 0-10 10-20 Expected frequency 250 250 20-30 250 30-40 250