Optimal Replacement Policy For Repairable System And The System Steady State Availability Of Interval Estimates

This thesis is finished during my Master of science and it consists of three chapters, in which we discuss the optimal replacement policy for a repairable system and the confidence interval for steady state availability of a specially system.Chapter Ⅰ shows the background of the reliability theory, and the organization and structure of this thesis.In Chapter Ⅱ, we introduce the optimal replacement policy for a repairable system, and it has four parts. First part, we introduce the simplest repairable system with one component. We discuss a new kind of replacement policy T of the system based on the total repair time, and give three kinds of object functions. Under some conditions, we can prove that the three object functions are equal. Second part, we bring a preventive maintenance into the above system and consider the replacement policy T, which is based on the age of the system. In the third part, we discuss a bivariate optimal replacement policy for a cold standby repairable system with two components. The policy is based on the working age of component 1 and its failure times. We prove that the bivatate policy (T,N) is better than the policy N .In the last part, amonotone process model for a one component system with s+1 states is studies, and we consider the policy T, which is based on the age of thesystem. When we introduce the definition of the harmonic mean, we can show that the model is equivalent to a geometric process model for a two-state one component system, because both of them have the same long-run average cost per unit time under the same policy T.In Chapter HI, through the generalized p-value method, we discuss the hypothesis problem and confidence interval for steady state availability of a system with extreme value operating time and lognormal repair time.