Reliability Analysis Of Repairable Mechanical System Based On Markov Process

Reliability theory is a comprehensive and edge science which takes life of the product as the main object of study, reliability has become an important indicator to measure the quality of products. In order to further improve product quality, repairable design become the development direction of modern design, that has put forward higher requirements for reliability analysis of repairable system. Existing reliability analysis methods of repairable system is carried out under the premise that the component life is exponentially distributed, but life distribution of the actual parts maybe much biased towards the exponential distribution. This article tries to study the reliability analysis methods of repairable system, when the parts life obeys a general distribution.In this article, for a start, establish the stress-life model to calculate fatigue reliability of mechanical components under constant amplitude stress. That is to say we obtain dynamic reliability model of components. The next, fitting the time-reliability function in a new form which is easy to follow-up calculate, using Guass-type numerical integration methods. Once again, regarding component using process as a Markov process consisted of work state and maintain state, deduce the formula of the reliability indexes including the first time to failure of the system, the instantaneous availability of the system, average steady-state availability of the system, the number of faults of the system and steady-state failure frequency in single unit system. Finally, deduce the formula of the reliability indexes including the first time to failure of the system, the instantaneous availability of the system, average steady-state availability of the system, the number of faults of the system and steady-state failure frequency in series system and parallel system using the similar methods, including series system with two same units, parallel system with two same units, series system with two different units and parallel system with two different units. After obtain the formula, calculate the specific results taking the assumption that stress obeys lognormal distribution as an example, integrated using Matlab software and complex function formulas.Two main methods in this article are Matlab software and Markov method. Two main contents of this article are fitting the time-reliability function and deducing the formula of reliability indexes.