使用伽瑪過程之雙變數加速退化試驗之最適策略

Optimal Strategy for Two-Variable Accelerated Degradation Tests Using Gamma Process

宋文筠(Wen-Yun Sung)

指導教授 ： 蔡宗儒

淡江大學/商管學院/統計學系碩士班/碩士(2014年)

https://doi.org/10.6846/TKU.2014.00821

摘要

本論文使用伽瑪過程來配適高可靠度產品的衰退過程，並使用一個雙變數的加速退化試驗來加速高可靠度產品的品質衰退速度。假設加速變數與伽瑪過程的形狀參數間的關係服從廣義的Erying模式，我們分別使用 Birnbaum-Saunders分配和逆高斯分配來建立最大概似估計過程。文中使用蒙地卡羅模擬來研究加速退化試驗過程中樣本分配的敏感度。此外，針對本論文建議的加速退化試驗過程，我們建立了關於樣本分配及測量次數的最佳策略，此一最佳策略可極小化受測之高可靠度產品的平均失效時間的漸進變異數，並使得總成本不會超過給定的預算。文中也提出了一個演算法，以利最佳策略之達成。文末使用一個發光二極體的光衰資料為例子，說明所有提出的統計方法的執行過程。

關鍵字

廣義Eyring模式 ； 最大概似估計法 ； 費雪資訊矩陣 ； 均方誤 ； 平均失效時間

並列摘要

In this thesis, the Gamma process is used to describe the degradation of a highly reliable product, which is subject to a two-variable accelerated degradation test. The relationship between the stress variables and the shape parameter of Gamma process is assumed to follow a generalized Eyring model. Maximum-likelihood estimation process is established based on approximation methods using Birnbaum-Saunders distribution and Inverse Gaussian distribution, respectively. Sensitivity of sample allocation for degradation tests on the maximum-likelihood estimation process is studied using Monte Carlo simulations. Optimal strategy on the sample allocation and measurement frequency for the proposed accelerated degradation test method is developed to minimize the asymptotical variance of the mean time to failure of highly reliable products such that the total cost does not exceed a specified budget. An algorithm is provided to reach the proposed optimal strategy. Finally, a lumen degradation data set of light emitting diodes is presented to illustrate the proposed method.

並列關鍵字

Generalized Eyring model ； maximum likelihood estimation ； Fisher information matrix ； mean squared error ； mean time to failure

參考文獻

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