A Study On Change-point Problem Based On Reliability Characteristic Quantities

Change-point problem has been the hot topic of statistics since the 1950s.It has been widely applied in quality control,epidemiology,geographical science,economic.financial,reliability,and survival analysis.This dissertation mainly studies the change-point problem of the reliability characteristics.Based on the failure rate and the coefficient of varation,corresponding change-point statistical models are established Specially,our main contributions are as followsThe novel change-point model based on bathtub-shaped changes in the parameters of a sequence of exponential distributions is established.A likelihood ratio type test statistic and Schwarz information criterion statistics are proposed for detecting possible changes.The asymptotic distribution of the likelihood ratio type statistic under the null hypothesis and the testing procedure based on Schwarz information criterion are derived.Numerical critical values and powers of these two methods are tabulated for certain selected values of the parameters.The tests are applied to detect the change points in the predator data and Stanford heart transplant dataBathtub curve is an important curve in reliability and survival analysis.We propose an alternative approach based on the linear approximation to study the change-point problem of the failure rate function with the bathtub shape.The procedures based on the Schwarz information criterion and the modified information criterion are proposed to detect the change points in the piecewise linear failure rate function Consistency of the test is established and the asymptotic null distribution of the test statistic is also derived as the standard chi-square distribution.The performance of the test statistic is studied through the simulations.The proposed method is applied to a real example to illustrate the detecting procedureThe coefficient of variation is a reliability characteristic which is used to describethe failure mechanism.For different distributions,the coefficient of variation depends on different distribution parameters.The novel procedure based on the empirical likelihood is proposed to detect the change point in the coefficient of variation.For the one-sample test and the two-sample test of coefficient of variation,the corresponding test statistics are deduced and the asymptotic distributions are established.For the change-point problem of coefficient of variation based on the multi-sample test,the asymptotic null distribution of the test statistics is derived.Simulations indicate that the method based on the empirical likelihood performs very well under most situations.The method is applied to a real example.This dissertation aims at modelling the change-point problem in the reliability characteristics and proposing the change-point analysis methods.These methods are the theoretical basis of the subsequent reliability data analysis.