Analysis of Degradation Tests for Highly Reliable Products

• Main Authors: Chien-Yu Peng, 彭健育
• Other Authors: Tseng, S. T.
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/23708605367512936443

博士 === 國立清華大學 === 統計學研究所 === 96 === Degradation models have been widely used to assess the lifetime information of highly reliable products. The performance of a degradation analysis strongly depends on the modeling of product’s degradation path. For designing and analyzing the degradation tests of highly reliable products, we study the following four topics in this thesis. (i) Motivated by a real data set, we propose a general linear degradation model in which the unit-to-unit variation and time-dependent structure are simultaneously considered. For this model, the product’s mean-time-to-failure (MTTF) can be obtained under some regular conditions. Furthermore, we also address the effects of model mis-specification on the prediction of product’s MTTF. It shows that the effect of model mis-specification on product’s MTTF predictions is not critical when the sample size is large enough. However, when the sample size and termination time are not large enough, a simulation study shows that these effects are not negligible. (ii) Under the proposed linear degradation model, we study the problem of optimal test plans. Under the constraint that the total experimental cost does not exceed a pre-determined budget, the optimal decision variables such as sample size, sample frequency and terminational time are solved by minimizing the variance of the estimated MTTF of the lifetime distribution of the product. Moreover, we also assess the robustness of this degradation model through sensitivity analysis and address the effects of variety of parameters and cost conditions on the optimal test plans. (iii) Motivated by a laser data, we relax the normal assumption of random-effect to fit realistic data sets. In this topic, we construct a skew-Wiener linear degradation model and derive the closed-form expression of the lifetime distribution. Because the likelihood functions for such a degradation model are analytically intractable, we develop an EM type algorithm to efficiently obtain the maximum likelihood estimators for this model. (iv) For highly reliable products with very few test units on hand, we use the concept of cumulative exposure model to formulate a typical progressive stress accelerated degradation test (PSADT) problem. An analytical expression of the product’s lifetime distribution can then be obtained by using the first passage time of its degradation path. Next, an analytical performance comparison between the PSADT and the constant stress degradation test under same special cases is present. The comparison includes the product’s MTTF, median lifetime, and variations of lifetime during different stresses.