Statistical Inference For Berkson Measurement Error Model And Its Application In Reliability Analysis

In this dissertation, we focus on the statistical inference of model with Berksonmeasurement error, and its application to degradation test in reliability analysis.As is well known, the true value of covariant is independent to its measurementerror in error-in-variable (EV) model in which the error could be thought as onesappearing after the test. However, if the assumed error appeared before the test,the observed value of covariant will be independent to the error. This is as knownas Berkson measurement error regression model, which has a wide range of ap-plications in the areas of industry, agriculture, epidemiology, economics, and soon.In industry, the accelerated degradation test is regularly used in the analysisof product reliability. It collects degradation data under high stress levels andestimates the reliability of product in normal condition. However, in many cases,when high stress level is applied, the output of stress carries out some measurementerrors for all kinds of reasons, which are Berkson measurement errors. Statisticalresearch shows that ignoring these errors may cause biased estimation of efectparameters, which might lead to deviation when predicting the lifetime of product.Combining with the inference of nonlinear regression model with Berksonmeasurement error, two kinds of degradation tests are studied in this dissertation.Firstly, accelerated destructive degradation test is discussed, in which the degrada-tion observations come from diferent products and are independent to each other.For the accelerated degradation test with random errors in the constant stresses, a nonlinear model with Berkson measurement error is employed, and an extendedminimum distance estimation method is proposed. Consistency and asymptoticnormality of the proposed estimator are obtained. The simulation result showsthat the performance of the estimator is better than the least-square estimator,which ignores the random errors of test stresses. When this method is applied tothe degradation data of an insulation material, it shows that the fitted degradationtrack matches the reality better.Secondly, accelerated non-destructive degradation test where a series of degra-dation observation can be obtained from a product along the test track is consid-ered. In this case, the degradation data become longitudinal data. A modelwith Berkson error for the longitudinal data is suggested for the accelerated non-destructive degradation test with random errors in the designed constant stresses,and an estimation method for the parameters in the model is proposed. Theobtained estimator is proved to be consistent and asymptotically normal as thesample sizes under each stress go to infinity. The properties of the estimator forfinite sample sizes are also justified by simulations.Finally, A multivariate ultra-structural Berkson measurement error regressionmodel is discussed and consistent estimators for this model parameters are pre-sented. The asymptotic distributions for the estimators are derived as well. Thismethod is applied to a simple ultra-structural Berkson measurement error regres-sion model. A real example and simulation results are provided for the illustrationof the method proposed in this paper.