累積曝曬模型之逐步應力加速破壞衰變試驗

Step Stress Accelerated Destructive Degradation Test Based on Cumulative Exposure Model

游景涵(Jing-Han You)

指導教授 ： 蔡志群

淡江大學/理學院/數學學系數學與數據科學碩士班/碩士(2022年)

https://doi.org/10.6846/TKU.2022.00451

摘要

在可靠度領域中，當在測試樣品與設備不多時，為了探討高可靠度產品壽命資訊，逐步應力加速試驗是最常使用的方法。本文首先以聚合物資料為動機例子，使用累積曝曬模型 (cumulative exposure model) 的概念，建構出逐步應力加速破壞衰變模型，以推估產品在正常應力下的壽命，與其近似變異數。接著執行此試驗的最佳化設計，找出逐步應力最佳改變時間點，以精確推估高可靠度產品的壽命。最後本文進行模擬分析，探討最大概似估計量的大樣本特性，從模擬結果可知，當樣本數越大時，模擬結果會接近最大概似估計量的漸近結果。

關鍵字

逐步應力加速破壞衰變試驗 ； 累積曝曬模型 ； 最佳試驗配置

並列摘要

In the field of reliability, step stress accelerated testing is the most commonly used method for assessing the lifetime of highly reliable products when the available test sample and equipment are very few. Motivated by a polymer data, the article used the concept of cumulative exposure model to construct the step stress accelerated destructive degradation test model. Then, the products’ lifetime and the corresponding variance at normal environment can be obtained by extrapolation. And, the optimal change point time for stresses can be acquired precisely by minimizing the approximate variance of the estimated products’ lifetime. Finally, the simulation study was conducted to discuss the large sample property of the maximum likelihood estimator. The simulation result showed that the simulated values are quite close to the asymptotic values when sample sizes are large enough.

並列關鍵字

Step stress accelerated destructive degradation test ； Cumulative exposure model ； Optimal test plan

參考文獻

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