In this paper we study the moment generating function order and the new better than used in the moment generating function order (NBUMG) life distributions. A closure property of this order under an independent random sum is deduced, and stochastic comparisons among the block replacement policy, the age replacement policy, the complete repair policy, and the minimal repair policy of an NBUMG component are investigated.

A new burn-in procedure for a repairable component is proposed. During a burn-in period, the failed component is only minimally repaired rather than being completely repaired. This procedure is shown to be economical and efficient when the minimal repair method is applicable during a burn-in process. The properties of the optimal burn-in time b∗ and block replacement policy T∗ are also given.

When a mission is assigned, it often is the case that the component used to perform the task is required to work properly during the period of the mission time. In other words, the probability of the event that this component does not fail within the allowable mission time should be as large as possible. This problem is considered for the case when the lifetime of a component has a bathtub-shaped failure rate function, and it is found that burn-in procedure is beneficial. An application of this result to the problem of minimizing the mean number of failures in a given period of mission time is also considered.

Burn-in is a widely used method to improve quality of products after they have been produced. For a repairable component there are two common types of repair, complete repair and minimal repair. Preventive maintenance policies such as age replacement and block replacement are often employed in field operation. The present paper takes burn-in, maintenance and repair into consideration at the same time and considers related cost structures. The properties of the corresponding optimal burn-in times and optimal maintenance policies are discussed.