Research On Failure Rate Functions Of Mixtures And The Monotonicity Of The Multivariate Mixed Distribution

Reliability engineering is the fight against product failure overall science and technology activities, while the reliability of mathematical theory of reliability has a special status. Product failure rate is an important concept in reliability theory. In practice, it is also the main index of product reliability. Many products that depend on the size of the failure rate to determine the level. Failure rate has been widely used in reliability, survival analysis, insurance, research and many other fields. The typical failure rate curve of the form "bathtub", commonly known as "bathtub curve." Reality, bathtub-shaped failure rate (BFR) model has very important significance.In many life distribution with bathtub-shaped failure rate of distribution is relatively small, so bathtub-shaped failure rate can often be constructed through a variety of ways. At present, there are already many ways to construct the bathtub-shaped failure rate, which, through the failure rate of the mixture to get the bathtub-shaped failure rate model is an important way.This paper studies three issues:First, in the three-parameter Weibull distribution and exponential distribution of the mixture failure rate model, how to use "practical" point of view to analyze the mixture failure rate curve, and get a real sense of the bathtub curve, and finally extended to other kinds of mixed failure rate curve analysis. Secondly, how to discuss the monotonicity of mixed failure rate curve. Mixing two or more distribution, often occur several Change point, in such circumstances, how to promote the Glaser's transition function to discuss the proposed mixed failure rate of the monotone case. Third, the distribution of mixed exponential distribution family made the failure rate of promotion. We expanded to four family mixed exponential distribution case, and made fit test, using the actual meaning of the second chapter of bathtub-shaped curve point of view, and the third chapter of the mixed monotone failure rate determination theory, the failure of mixed four distribution rates were compared with analysis of the situation.