Statistical Inference On Several Structural Reliability Models

Reliability is a very important index of describing the quality of products, which represents the ability of keeping its performance index. Reliability runs through the whole life cycle, which means it will be related to every department and every course. Their common purpose is to improve the reliability of products quantificationally and to guarantee effectiveness and prevent loss. Therefore some related people must be aware of the knowledge of reliability to make the products achieve the desired reliability. The study of reliability begined with electronic products which is based on the safety factor not the probability of failure. Some project planners thought it could improve the reliability of products if we make the safety factor high enough. In fact the same safety factor can lead to corresponding wide reliability, unless you accumulated a lot of experience. Consequently, there came a probability method to design the structural reliability, taking the place of the original method.Structural reliability is the branch of reliability, whose products can be described by stress-strength model. In the study of reliability, there are three methods to solve the problem of confidence interval:Classical、 Bayes and fiducial methods. This article adopts the classical method, which is used most widely. In classical method, the estimated parameter is a constant and the confidence interval is random, which can be explained with probability. As for the simple structural reliability models, their probability expressions are simple and can be calculated immediately. But for the complicated models, for example, Weibull distribution and extreme value distribution, their reliabilities contain double integral, whose computation courses are hard to compute. In this situation, many articles settle it under some assumptions. As for Weibull distribution, they assume that the two shape parameters are equal to study the ratio of the two scale parameters. This article adopts generalized pivotal quantity method; we use the generalized confidence interval, which makes the computing course more convenient and direct. The key and difficult point is how to choose and construct proper pivotal quantity.This article mainly studies three structural reliability models: exponential-normal distributions、Weibull-normal distributions and extreme value-normal distributions. We use MLE to get reliability point estimation and use generalized pivotal quantity method to get reliability generalized confidence interval, then using simulation method we get the deviation and MSE of the point estimation and also study the frequency property of generalized confidence interval. Eventually we find that the difference between the fact coverage of generalized confidence interval and that of nominal coverage is little even in small sample, which means that generalized confidence interval is in good frequency explanation.