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    Title: 加速破壞衰變試驗之最佳化設計
    Other Titles: Optimal Design for Accelerated Destructive Degradation Tests
    Authors: 蔡志群
    Contributors: 淡江大學數學學系
    Keywords: 高可靠度產品;加速破壞衰變試驗;Arrhenius方程式;最佳試驗配置;Highly reliable products;Accelerated destructive degradation tests;Arrhenius equation;Optimal test plan
    Date: 2012-08
    Issue Date: 2015-05-13 09:11:29 (UTC+8)
    Abstract: 衰變分析(degradation analysis) 是工業界最常使用來推估高可靠度產品的可靠度資訊(如產品壽命第p 百分位數) 之重要分析工具,亦即量測與產品壽命相關之品質特徵值(quality characteristics, QC),且此QC會隨時間逐漸衰變(degrade),再藉由其衰變路徑來推估產品壽命。有些產品在正常使用狀況下衰變速率非常緩慢,此時可提昇環境應力,來加速產品衰變過程,並藉由產品壽命與應力變數之間的關係式,推估正常應力使用下產品的壽命。某些特定測試樣本的量測,需經過破壞測試樣本的特性才可獲得。因此,每一個測試樣本,只可量測到一個QC,此種衰變資料型態,配合加速衰變試驗的過程,稱之加速破壞衰變試驗(accelerated destructive degradation test, ADDT)。本計劃以聚合物材料(polymer material) 之ADDT資料為動機,欲探討如何建構一個非線性的ADDT衰變模型,來描述聚合物材料的衰變路徑,進而求得其第p百分位數壽命。此外,執行一ADDT有許多決策變數,例如在每個溫度與時間下,須取幾個測試片(coupons) 進行破壞量測,須間隔多少時間進行量測,與在每各應力下須量測的總次數等,這些變數皆會影響聚合物材料壽命推估的精確度與試驗成本。因此,實驗者經常面臨如何執行一個符合成本效益的ADDT實驗,以精確地推估產品的壽命。故本計劃亦探討如何在有限的試驗總成本下,設計一最佳的ADDT,以精確地推估聚合物材料的第p百分位數壽命;換言之,極小化產品第p百分位數估計值之近似變異數,以獲得最佳的試驗配置。最後,本計劃探究模型參數對於最佳試驗配置的敏感度分析(sensitivity analysis),與以模擬分析來深入了解樣本數對於理論推導出的漸近結果之影響。
    Degradation tests are powerful and useful tools for lifetime assessment of highly reliable products. In some applications, the degradation measurement process would destroy the physical characteristic of tested units at higher than usual stress levels of an accelerating variable such as temperature, so that only one measurement can be made on each tested unit during the degradation testing. An accelerated degradation test with such a degradation data is called an accelerated destructive degradation test (ADDT). The specification of the size of the total sample, the frequency of destructive measurements, the number of measurements at each stress level, and other decision variables is very important to plan and conduct an ADDT efficiently. A wrong choice of these decision variables may not only result in increasing the experimental cost, but also in an imprecise estimate of the reliability of the product at the use condition. Motivated by a polymer data, this research deals with the problem of designing an ADDT with a nonlinear model. Under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal test plan is obtained by minimizing the asymptotic variance of the estimated 100pth percentile of the product’s lifetime distribution at the use condition. A sensitivity analysis is also carried out to examine the effects of changes in the decision variables on the precision of the estimator of the 100pth percentile. A simulation study further was expected to show that the simulated values are quite close to the asymptotic values when the sample sizes are large enough.
    Appears in Collections:[數學學系暨研究所] 研究報告

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