The Statistical Analysis And Optimal Design Of Accelerated Life Testing Based On A Generalized Proportional Odds Model

The quality of products is the main force for enterprises to participate in market competition, it is also the lifeblood of business and the driving force for economic development. Reliability is an important indicator of product quality evaluation, and the Accelerated Life Test (ALT) is the key technology to assess the reliability of products. Accelerated life test data depends on the acceleration model to carry out statistical analysis. The choice of the acceleration model determines the accuracy of the reliability evaluation. Therefore, the study of the acceleration model is an important research direction in the field of reliability statistics.The acceleration models can be divided into two categories, which are physical acceleration models and statistical acceleration models, and statistical acceleration models are more suitable than physical acceleration models for the product reliability assessment based on accelerated life testing. Therefore, in the process of product reliability evaluation based on accelerated life testing, statistical acceleration models are more popular in the research. The statistical acceleration models can be divided into parametric models and non-parametric models. The Accelerated Time Failure model (AFT model) is the most typical parametric models. This model needs to specify the distribution types of product life, which is very difficult in practice. While the non-parametric models do not need to specify the lifetime distribution of the product, moreover, their calculation processes are relatively simple, so it has been widely used in the process of product reliability evaluation based on accelerated life testing. The Proportional Proportional model (PH model) and the Proportional Odds model (PO model) model are the common non-parametric acceleration models.In view of the importance of PO model in product reliability evaluation system based on accelerated life test, and on the basis of the PhD research project "Reliability analysis based on Bayesian survival statistical theory", in this paper, we propose a new acceleration model based on proportional odds model, and appliy the new model to analysis and optimization of the design process of accelerated life test. The research object is to optimize the design method and evaluation method of reliability test of product, and specific research work carried out as follows:1. On the basis of consult in a large number of relevant literatures, we systematically summarized and combing the research status and development trends of accelerated life test statistical analysis methods and accelerated life testing optimization design theory at home and abroad. We also analyzed and discussed at the forefront and Hot Issues of the field of and reliability research. Combined with the requirement of economic development and reliability engineering, we put the theory and practical application of innovation both as a starting point, and proposed the research proposition --- The Statistical Analysis and Optimal Design of Accelerated Life Testing based on a Generalized Proportional Odds Model.2. For the limitations of proportional odds model in applicating in accelerated life testing statistical analysis, we presented an extension form of the Proportional Odds model, which is called Generalized Proportional Odds (GPO). model. The GPO model takes into consideration the proportion odds effect, covariate effects and time scale effect, is an expansion of the PO model. Firstly, theoretical properties of the GPO model are discussed, proving that the PO model is a special form of the GPO model, thus confirming the application scope of the GPO model is more extensive than that of the PO model. Besides, through simulation examples, the same group of accelerated life the test data are analyzed seperatly based on the PO model and the GPO model, the results confirm that the reliability estimation based on the GPO model is more accurate than the reliability estimation based on the PO model. To validate the model, we fit the GPO model using simulated data sets and an experimental data set. The experimental data is obtained by Maranowski and Cooper (1999). The objective of their laboratory experiments is to study the effect of high electrical field and high temperature on the time-dependent-dielectric-breakdown (TDDB) of an n-type and p-type 6H-SiC MOS capacitors formed by thermal oxidation. We utilize PO model and our proposed GPO model to analysis the TDDB data, and the results show that the GPO model has a higher accuracy.3. The GPO model is applied to the statistical analysis process of the accelerated life test with truncation techniques. The artical firstly modeling the consored data based on the GPO model, and then estimate the model parameters using maximum likelihood estimate procedure. After parameters are estimated, the point estimate of reliability at a given time can be obtained. Simulation is preceded using the modified GPO model for non-censored failure data, and censored failure data with different percentage of censoring. The effects of censoring and the sizeof the data set are studied. Using 30 data sets, the estimated reliability mean is calculated at time t for each stress level.4. The confidence interval estimation method and the model verification method of the GPO model are discussed. We construct a confidence interval estimate of the value of reliability based on the distribution of the parameters of the model by constructing a statistic that is related to the model parameters. We first establish the GPO model of the Fisher information matrix, through the Fisher information matrix to calculate the GPO model parameters and their asymptotic variance covariance matrix, which gives the model parameters evaluation value and confidence interval, and gives the estimation of product reliability confidence interval. In addition, we apply the PO model and GPO model to evaluate the same set of accelerated life test data, and construct the likelihood ratio statistic based on the evaluation results, then establish the method for verifying the validity of the GPO model. Finally, by numerical simulation, we show that the confidence interval of the accurate reliability estimation can be calculated by using the method proposed in this paper.5. The optimization design method of accelerated life test based on the GPO model is studied. Under the condition of multiple constant stresses and multiple step stresses, the optimization design method of accelerated life test based on GPO model is presented. We first describe the problem of optimizing the design of accelerated life tests under multiple constant stresses, and present the optimal design method based on the constrained optimization by linear approximations algorithm proposed by Powell (1992). Soon afterwards, we describe the multiple step stress accelerated life test of the optimization design problem program, according to the principle that minimum the asymptotic covariance of the reliability estimation under the design condition in a specified time, we give the optimal design scheme.6. For the demand for the actual reliability engineering, we use C language to develop a software package for "The statistical analysis process of accelerated life test based on generalized proportional odds model". The software package resolves the difficulty to estimate the parameters in reliability function and the confidence interval in product reliability evaluation process, and provides new ideas and tools for reliability assessment technology.Innovation of this dissertation can be summarized as follows:(1) A new accelerated model of accelerated life test is proposed, namely Generalized Proportional Odds (GPO) model.When accelerated life test data satisfies the proportional odds hypothesis, and there is no coefficient effect and time scale effect, the statistical analysis of accelerated life test data based on PO model can get a consistent estimator of the reliability index. But the accelerated life test data often have the time coefficient effect, and the time scale effect can not be ignored. Aiming at this problem, on the basis of the statistical analysis of accelerated life test based on PO model proposed by Zhang and Elsayed (2007), we propose a new acceleration model called Generalized Proportional Odds (GPO) model, which takes into consideration the proportion odds effect, covariate effects and time scale effect, is an expansion of the PO model. In addition, this paper also discusses the statistical properties of GPO model, and proves that the PO model is a special form of the model, so the model has a wider range of application than the PO model.(2) This dissertation applies the GPO model in the field of reliability statistics, and constructs the product reliability evaluation system which is based on the GPO model.The studies of the extension of accelerated models mostly concentrated in the PH models and the AFT models, research on the extension of the PO model is still very rare. Very few literatures have been involved in the application of PO model in medical research, but there are no studies on the expansion of the PO model, and its application in reliability evaluation. This dissertation proposed the GPO model, and studied its application in the statistical analysis of accelerated life test. Based on the GPO model, the product reliability evaluation framework of accelerated life test is established, and the application of the model in the process of reliability evaluation is analyzed comprehensively. In addition, through numerical simulation, under a variety of standard, the reliability estimation method based on GPO model is compared with the reliability estimation method based on the PO model, and the estimation results based on the GPO model is more accurate.(3) This dissertation presents the optimization design method of accelerated life test based on the GPO model.Although the accelerated life test can save the time and the cost, the reliability estimation obtained by extrapolation is not accurate enough. In order to obtain a more accurate estimate, an effective method is to design a test plan to make a reasonable distribution of the tested products at the appropriate level of stress. In other words, an optimal accelerated life test design plan will be more accurate to estimate the reliability of the design stress conditions. However, the single stress accelerated life test design may ignore other will result in product failure stress effects. In this paper, based on the GPO model, the optimal design of accelerated life test under the condition of multiple stresses is studied, under the two stress loading modes of constant stress and step stress, the optimum design of accelerated life test is presented.