Single-unit Multi-state Markov Repairable System With Fatigue Effect Omission

This article establishes a single component repair system with three states based on the actual background of the road system, which is called the original system. By assuming that the short state of the original system is not observed or it is no influence on the normal work of system, we introduce two kinds of models for fatigue influence omission and delayed, which are the new system. Finally, it gives reliability indexes of the original system and the new system by using the stochastic process, reliability theory and the probability theory method.This paper mainly can be discussed from the following four aspects. The first chapter is the introduction, which introduces the research background and main contents. Second chapter defines the original and new system model, respectively. Assuming that the system have a repairman and three states (normal work, fatigue working or semi-working and failure), its life are obey exponentially distributed and independent each other, and established the original system model by using the Markov process theory. Two kinds of new system models (including four models) are established on the basis of the original system. Model1-ignore fatigue time r is a nonnegative constant; model2---ignore fatigue time r is a nonnegative random variables; model3---eary influence and the expiration influence can be neglected model; model4---eary influence and the expiration influence can be lagged model. The third chapter assuming the system is repairable, reliability analysis of the original and the new system respectively by using methods of Markov process theory, and obtained system reliability indicators and maintainability indicators. In concluded, conclusion and outlook, it is the innovation of this paper or can be resolved the problem in practice.The normal working hours, half the work time and repair time of the original system are exponentially distributed random variables, The entire operation process, it has Markov property. Based on the original system model, four new system model is established, it no longer has the property, which is a worthwhile research of the problem for the existing reliability index derivation and proof. In addition, the performance indicators of these new systems to make the right decisions for some managers, use for some enterprises reasonable or maintenance of equipment, and provide a theoretical basis on improving economic efficiency.