V-optimality準則下之指數分散加速衰變模型的最適樣本數配置

Optimal Sample Size Allocation for Accelerated Degradation Test (based on Exponential Dispersion Model andV-optimality Criterion)

陳玟穎

指導教授 ： 曾勝滄

國立清華大學/理學院/統計學研究所/碩士(2012年)

摘要

加速衰變試驗 (accelerated degradation test, ADT) 是工業界常被使用來推估高可靠度產品的可靠度訊(如產品壽命第p百分位數或產品的平均失效時間 (mean-time-to-failure, MTTF ) 之重要分析工具，因此規畫有效率的加速衰變試驗，是可靠度工程師經常面臨的決策問題。李宜真 (2011) 曾建構指數分散衰變模型(exponential dispersion accelerated degradation model)，並探討最適樣本配置問題之解析解，其優點是指數分散衰變模型可涵蓋常見的衰變模型如速維納 (Wiener)、伽瑪 (Gamma) 及逆高斯 (Inverse Gaussian)等衰變模型。但美中不足的是該篇論文僅針對兩個應力水準下，獲得最適樣本配置之解析解，配置三個應力水準的情形則僅以數值方式求解，對於三個應力水準以上之決策問題，缺乏有系統的處理方法。本篇論文的研究主題是針對指數分散加速衰變模型中應力水準個數大於等於三個之最適樣本配置問題，做深入研究。
具體而言，本篇論文獲得以下研究結論：在指數分散加速衰變模型下，且配置三個應力水準時，最適樣本比例配置之必要條件是僅需將樣本數配置於其中兩個應力，且在常見加速衰變模型之最適應力配置情形如下：在伽瑪加速衰變模型下，樣本必配置於S1及S3兩應力水準上；當加速衰變模型為逆高斯或維納加速衰變模型時，其應力可能配置情形為 、 或 兩應力上。此外，最適樣本配置比例於此三種特定加速衰變模型下，亦可得到其充分條件。

關鍵字

加速衰變試驗 ； 指數分散加速衰變模型 ； V-optimality

並列摘要

Accelerated degradation test (ADT) is widely used to assess the lifetime information (e.g.,p-thquantileor mean-time-to-failure (MTTF))of highly reliable products. Hence,it is a challenging issue for reliabilityengineer to plan an efficientADT test. Recently, Lee (2011) proposedan exponential-dispersion accelerated degradation (EDAD) model and derived the analyticalsolution of optimal sample-size allocation. The advantage of this resultis that EDAD model covers well-knownmodels such as Wiener, Gamma and Inverse Gaussian accelerated degradation model. However, the results are very restricted to the case of the number of the stress levels equal to two. To overcome this difficulty, we will address the problem for the number of the stress levels greater than three.
In this thesis, we first demonstrate that anecessary conditionof the sample-size allocationfor 3-stress based on EDAD model is that we only need to assign testing units into two stresses level. Furthermore, we also obtained the optimal sample-sizeallocation formulafor thementioned-above accelerated degradation models. More specifically,under Gamma accelerated degradation model, we must assign testing units at stressesS1 and S3; for Wiener or Inverse Gaussian accelerated degradation model,we may arrange either the stress level in , or depending on different conditions.

並列關鍵字

accelerated degradation test ； exponential dispersion accelerated degradation model ； V-optimality

參考文獻

[15] 李宜真(2011)，“指數分散加速衰變模型最適樣本數配置之研究，”國立清華大學統計學研究所碩士論文。

[16] 姚禹丞 (2010)，“逆高斯與伽瑪衰變模型之誤判分析，”國立清華大學統計研究所碩士論文。

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