Uncertain Renewal Process And Its Application In The Maintenance Of Aircrafts

In the classic maintenance replacement policy, the lifetimes of units were usually assumed to be random variables, and some theories such as stochastic processes were used to study, in which the distribution of lifetimes of units or probability of failure can be obtained through a lot of sample data. However, in practical aviation maintenance, since many parts are costly, it is not realistic to conduct a lot of test to obtain data of the lifetimes of aircraft units. Therefore, there is no sufficient historical data to obtain the distribution of the lifetimes of the units. In this case, the only solution is to invite some experts to use their expertise and experience to give the lifetimes of the units and their belief degree. However, human beings tend to overweight unlikely events, which may make the belief degree have a much larger range than the real frequency. Thus if probability theory is still used to deal with the belief degrees of the experts, some faulty conclusions might be obtained. In order to solve this kind of problem, uncertainty theory arose at this historical moment, which has become a mathematical tool to deal with the belief degree of human beings. Based on uncertainty theory, the lifetimes of units are assumed to be uncertain variables, the main work of this paper is about age replacement policy and block replacement policy as follows:1. On the basis of uncertain age replacement model, the analytical expressions of the optimal replacement time are obtained when specific uncertainty distributions of the lifetimes of the units are given.2. The block replacement model with no replacement at failure is built in uncertain environment, the analytic expression of the optimal replacement time is obtained and the existence condition of the optimal replacement time is given.3. On the basis of chance theory, the lifetimes of the units are assumed as uncertain variables, and the cost per unit time of each failed unit is considered to be a random variable, the block replacement policy with no replacement at failure is studied. The analytic expression of the optimal replacement time is obtained and the existence condition of the optimal replacement time is given.4. The above-mentioned models are applied in the practice of civil aviation maintenance, the effectiveness and the feasibility are verified by concrete examples and sensitivity analyses are given. Numerical examples indicate that different parameters effect the optimal replacement time in different degrees.