الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 195 |  |  |
| | | from | 195 | | |
Abstract
Due to the rapid development of the advanced technology, the products and devices today become more and more reliable, and the products’ life gets longer and longer. For such highly reliable products, it is quite hard or even impossible to obtain the failure information under normal conditions. Therefore, accelerated life testing (ALT) is the most common way to obtain enough failure time data in a short period. Under such test settings, products are tested at higher than usual levels of stress to induce early failures. The failure time data collected from such accelerated tests are analyzed and extrapolated to estimate the life characteristics under normal operating conditions.
The stress loading in ALT is applied using different ways. Commonly used methods are constant-stress, step-stress, progressive-stress, cyclic-stress and random-stress. Here, we discuss the constant-stress, step-stress and progressive-stress models to obtain information about the parameters of the lifetime model more speedily than under normal operating conditions.
The thesis consists of six chapters:
Chapter 1
This chapter is considered as an opening chapter. It includes definitions and basic concepts that are used throughout this dissertation. A survey of the previous studies is presented such as accelerated life testing, statistical models for acceleration, constant-stress models, step-stress models, progressive-stress models, lifetime data, Bayesian analysis, and goodness of fit test. At the end of this chapter, a literature review of the previous studies is presented.
Chapter 2
In this chapter, we consider constant-stress ALT to study the estimation problem of the extension of the exponential distribution. Based on progressive type-II censoring, both maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained. The BEs are obtained based on both non-informative and informative priors. In addition, the interval estimation of the model parameters is obtained by finding the normal approximation, bootstrap and credible confidence intervals (CIs). Moreover, a real data set is analyzed to illustrate the proposed procedures. Furthermore, a real data set is used to show that the extension of the exponential distribution can be a better model than Weibull distribution and generalized exponential distribution. Finally, the MLEs and BEs of the parameters involved are compared via simulation studies. The results of this chapter were published at:
Metron, 2016, Vol. 74(2), 253-273.
Chapter 3
Chapter 3 presents the optimal plans for -level constant-stress ALT for Lindley failure data under complete sampling. The optimal test plans are developed under D and C-optimality criteria to determine the proportion of test units allocated to each stress level, assuming the general log-linear relationship between the life characteristic and stress. To illustrate the proposed procedures, we analyze two real data sets. Furthermore, the real data sets are used to show that Lindley distribution can be a better model than one based on the exponential distribution. Finally, we compare between the proposed optimal plans (D-optimal and C-optimal) and traditional plan through asymptotic variance of MLEs. The results of this chapter were accepted for publication at:
Journal of Testing and Evaluation, To appear.
Chapter 4
The aim of this chapter is to study the simple step-stress ALT under progressive type-II censoring. Assuming the cumulative exposure model when the lifetime of test units follows the extension of the exponential distribution, the MLEs and BEs of the model parameters are obtained. The BEs are obtained based on both square error (SE) loss function and linear exponential (LINEX) loss function. Also, the interval estimation of the model parameters is derived by using three types of CIs: normal approximation, bootstrap and credible CIs. In addition, a real data set is analyzed to illustrate the proposed estimation techniques. Lastly, the accuracy of the MLEs and BEs for the model parameters is investigated through the simulation studies. The results of this chapter were published at:
Communications for Statistical Applications and Methods, 2016, Vol. 23(4), 269-285.
Chapter 5
In this chapter, step-stress PALT under progressive type-II censoring is considered when the lifetime of the products follows power generalized Weibull distribution. Assuming the tampered random variable (TRV) model as a step-stress acceleration model, the MLEs and BEs of the model parameters and the acceleration factor are obtained. The BEs of the model parameters are obtained in the case of IP and NIP. In addition, normal approximation and credible CIs of the estimators are presented. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved. The results of this chapter were published at:
Advances in Statistics, 2015, Vol. 2015, 1-13.
Chapter 6
In this chapter, progressive-stress ALT is applied when the lifetime of the products under design stress follows the extension of the exponential distribution. The scale parameter of lifetime distribution satisfies the inverse power law and the cumulative exposure model holds for the effect of changing stress. Using type-II progressive censoring and MCMC algorithm, BEs of the unknown parameters based on SE and LINEX loss functions are obtained and compared with the MLEs. Furthermore, normal approximation and credible CIs for the unknown parameters are obtained. In addition, a real lifetime data set is used to illustrate the estimation methods. Finally, the different methods of estimation are compared via simulation studies. The results of this chapter were submitted to an international statistical journal.