Optimal Design for Gamma Degradation Processes with Random Effects

doi:10.1109/TR.2012.2194351

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/78485

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/78485

Title:	Optimal Design for Gamma Degradation Processes with Random Effects
Authors:	Tsai, Chih-chun;Tseng, Sheng-tsaing;Narayanaswamy Balakrishnan
Contributors:	淡江大學數學學系
Keywords:	Asymptotic normality;gamma process;model mis-specification;optimal design;random effects
Date:	2012-06
Issue Date:	2012-10-02 20:11:24 (UTC+8)
Publisher:	Piscataway: Institute of Electrical and Electronics Engineers
Abstract:	Degradation models are usually used to provide information about the reliability of highly reliable products that are not likely to fail within a reasonable period of time under traditional life tests, or even accelerated life tests. The gamma process is a natural model for describing degradation paths, which exhibit a monotone increasing pattern, while the commonly used Wiener process is not appropriate in such a case. We discuss the problem of optimal design for degradation tests based on a gamma degradation process with random effects. To conduct a degradation experiment efficiently, several decision variable (such as the sample size, inspection frequency, and measurement numbers) need to be determined carefully. These decition variables affect not only the experimental cost, but also the precision of the estimates of lifetime parameters of interest. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal decision variables are found by minimizing the asymptotic variance of the estimate of the 100p-th percentile of the lifetime distribution of the product. Laser data are used to illustrate the proposed method. Moreover, we assess analytically the effects of model mis-specification that occur when the random effects are not taken into consideration in the gamma degradation model.The numerical results of these effects reveal that the impact of model mis-specification on the accuracy and precision of prediction of percentiles of the lifetimes of products are somewhat serious for the tail probabilities. A simulation study also shows that the simulated values are quite close to the asymptotic values.
Relation:	IEEE Transactions on Reliability 61(2), pp.604-613
DOI:	10.1109/TR.2012.2194351
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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