偏常態加速破壞衰變模型之貝氏方法

Bayesian Approach for Skew-Normal Accelerated Destructive Degradation Model

陳奕汝(I-Ju Chen)；吳裕振(Yuh-Jenn Wu)；蔡志群(Chih-Chun Tsai)

高可靠度產品 ； 加速破壞衰變試驗 ； 偏常態分配 ； Highly reliable products ； Accelerated destructive degradation tests ； Skew-normal distribution

中國統計學報

61卷3期（2023 / 09 / 01）

207 - 230

繁體中文;英文

高可靠度產品使用傳統的加速壽命試驗技巧，在給定合理測試時間內，往往無法獲得足夠的失效資料，使得產品壽命推估上造成困難。加速衰變試驗（accelerated degradation test, ADT）測量產品隨著時間衰變的品質特徵值（quality characteristics, QC），藉由這些品質特徵值衰變訊息，可提供較精準的產品壽命推估。某些特定實驗的樣本量測，需經過破壞測試樣本，才可測得其品質特徵值，此加速衰變資料的實驗，稱之加速破壞衰變試驗（accelerated destructive degradation test, ADDT）。針對聚合物材料（polymer material）之ADDT資料，所建構出的非線性偏常態ADDT衰變模型，本文以貝氏方法（Bayesian method），提高估計的精確度，進而有效地估得產品壽命，與描述聚合物材料的衰變路徑。最後以模擬分析方式，與傳統的最大概似估計法（maximum likelihood estimator, MLE）進行比較，來探討所提出模型之參數估計的精準性。

Nowadays, it is difficult to have a precise assessment for the reliability of highly reliable products within a reasonable amount of testing time by using traditional accelerated life tests (ALTs). In such cases, accelerated degradation tests (ADTs) can be conducted to measure the quality characteristics of the products at higher stresses, then the product's reliability at the design stress can be obtained by extrapolation. In some applications, the degradation measurement process would destroy the physical characteristic of tested units, so that only one measurement can be made on each tested unit during the degradation testing. Accelerated degradation tests with such a degradation data are called as accelerated destructive degradation tests (ADDTs). Motivated by polymer data, the article used Bayesian method to improve the precision of the estimation effectively on the nonlinear ADDT degradation model with skew-normal error term that has been proposed to describe the degradation path of the materials. Finally, a simulation study was conducted to compare the performance of the maximum likelihood approach with the Bayesian approach.

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