Component Failure Analysis: Selection of Appropriate Probability Model

In studying reliability of components or products, the chief concern is in selecting the most appropriate statistical model to describe the failure data. Some of the most commonly used statistical models are normal, lognormal, exponential and Weibull distributions. This concern has been met with analytical tools such as statistical goodness of fit test i.e., Chi-square test, moment test and Shapiro\u27s W test. However, the most popular tool is a graphical method called probability plot. This is so because it is easy to understand and implement. Despite its popularity, there is one shortcoming in this graphical method, its result is subjected to the individual judgement. Thus, it is good to have an analytical test to augment this method. This thesis mainly involves in analytical methods for testing the hypothesis of probability distribution models. Four of the most popular distributions used in reliability analysis, exponential, normal, lognormal and Weibull distribution, are presented in the thesis, including their forms, numerical characteristics and applications in some specific fields. Two methods to verify the assumed statistical methods - graphical and analytical test methods are compared with respect to the convenience, effectiveness and precision. An important methods of analytical test - W test is described in detail in the thesis. The concept and theory of W test are introduced in this thesis. Methods and procedures for application of W test are included for all four of the probability models. Depending on the basis of theoretical analysis, a software is developed to help users carry out W test. Because the software contains four methods for testing assumed statistical methods, it is possible for users to choose the most appropriate model through comparing the calculation results of two or more models. Making use of the software to test assumed model is time-saving and can avoid errors which may be introduced in manual calculation. The structure of the software presented m the thesis is reasonable and the calculation results of the examples demonstrated in the thesis are also satisfactory. Therefore, the software will be helpful in building statistical model of the failure of systems or components