Stochastic comparisons of maintenance policies and Bayesian imperfect repair model

The types of repairs considered in this research are: (i) perfect repair, (ii) imperfect repair and (iii) minimal repair. When a failed unit is repaired, it is returned to the good-as-new state (perfect repair), is restored to its condition just prior to failure (minimal repair) and is either perfectly repaired with a probability p or minimally repaired with a probability q = 1 $-$ p (imperfect repair). In Chapter II, we compare three maintenance policies which are based on perfect repairs, minimal repairs and imperfect repairs. We study the stochastic processes generated by three policies and obtain some results for their relations. Also, we find the total expected cost for repairs during a finite interval (0,t) for each policy. Finally, we extend our result to the case of infinite time span and obtain the expected cost per unit time for each model. Chapter III is devoted to propose a new repair model where the probability of perfect repair, P, is considered to be a random variable and, hence, has a prior distribution $\Pi(p).$ We define a new repair model and call it Bayesian Imperfect Repair Model. We obtain the distribution, H, of waiting time to the first perfect repair starting with a new item and its corresponding failure rate, $r\sb{H}.$ We investigate the preservation properties for classes of life distributions. We also obtain monotonicity properties and inequalities for various parameters and random variables of stochastic process incurred by our model. Examples are given to illustrate our results. In Chapter IV, we develop nonparametric tests for Increasing (Decreasing) Mean Residual Life alternatives against exponentiality when the proportion, p, of population that dies at or before the change point of Mean Residual Life is known. The proposed test statistics are L-statistics. The asymptotic normality of our test statistics is established by using the L-statistic theory. Monte Carlo experiments are performed to investigate the speed of convergence of our test statistics to normality and the power of our test