Theory And Method For Time-Depedent Reliability Models Of Components And Systems

Reliability, as one of the most important quality indices, has been embodied in all the stages of new products, such as development, manufacturing, test, operation, transportation, storage, maintenance and so on. Therefore, for the design and manufacture, safety operation and life cycle management of components and systems, it is of importance to develop the scientific and rational theory and method for the reliability analysis.In the conventional reliability models, the load-strength interference theory is directly applied to calculate the reliability of components or systems when these probability distribution of stress (or load) and strength are known. However, these reliability models can't reflect how the reliability and the failure rate of components and systems changes with the times of load action and time. The probability calculated through these models is actually the reliability when random load acts only once or for the specified times, and it is also a static reliability. In fact, random loads which act on components or systems in service are always repetitious, and the reliability and failure rate of components and systems should vary with the times of load action or time. At the same time, the failure rate calculation of components and systems in the conventional methods is always based on the life distribution function. That is, the life distribution function is obtained through the statistical analysis of product failure data, and then the failure rate function is derived. Obviously, this method of calculating the failure rate is based on a lot of product fail data, and it can't be applied to guide the design of new products directly in the development stage.For mechanical systems, dependent failure is their general character and it will lead to considerable errors or even misleading conclusions that neglect the failure dependence which exsits in the components of systems and the failure modes of components, and assume independent failure in the analysis and calculation of reliability of components and systems.In this paper, we develop the time-depedent reliability models of components and systems with stress-strength interference model, order statistic theory, Poisson stochastic process and probability differential equation. Firstly, common cause failure, as one mode of dependent failure, is considered and the reliability models of components with multiple failure modes and systems are derived with the load-strength interference model and without the assumption of independent failure. Based on analyzing the reliability models of systems proposed, we develop the concept of system strength and derive the probability cumulative distribution functions and the probability density functions of strength for series system, parallel systems and k-out-of-n system. It is pointed out that the reliability models of systems have the same structure as those of components. The different kinds of systems, which have different number and different combination forms of components, have different strength distributions and can represent different reliability under the same random load. Then, the failure mechanism of components and systems under repeated random load is studied, and the probability cumulative distribution function and the probability density function of equivalent load are derived with the order statistic theory when random load acts for multiple times. Further, we develop the reliability models of components and systems under random repeated load, and for components and systems we discuss the relationship between reliability and times of load action and that between failure rate and times of random load action. The loading process is described with Poisson stochastic process, and the time-depedent reliability models of components and systems without strength degeneration and those with strength degeneration are developed respectively. Finally, for components and systems, the relationship between the reliability and time and that between the failure rate and time are discussed.The result shows that when strength doesn't degenerate and strength degeneration can be neglected, the reliability and the failure rate of components and systems decreases with time, and the failure rate curves of components and systems both have the partial feature of the bathtub curve, namely, the early failure period and the random failure period. When strength degenerates, the reliability of components and systems decreases with time more obviously and the failure rate curves of components and systems have the whole feature of the bathtub curve. It should be noticed that the early failure and the higher failure rate of components and systems are not caused by their initial flaw only, but determined by both random load action and strength together.The time-depedent reliability models of components and systems developed in this paper can reflect the change of the reliability and the failure rate with time time-depedentally. When the probability distribution of strength and load and the rule of strength degeneration are known, we can calculate the reliability and the failure rate of components and systems at any time. Thus, the reliability models proposed may be applied to the life cycle management of components and systems and it is very useful to guide the design, to determine the testing time and the reliable operation life and to make the rational maintenance schedule of components and systems.