產品壽命服從二參數指數分配之加速衰變試驗的最佳設計

Designing an accelerated degradation testing where the product’s lifetime follows a two-parameter exponential distribution

程紀堯(Chi-Yao Cheng)

指導教授 ： 胡伯潛

國立虎尾科技大學/管理學院/工業工程與管理研究所/碩士(2009年)

摘要

在現今工業生產技術的快速進步下，產品壽命越來越長，由傳統的壽命試驗不容易獲得完整的壽命資訊。本研究的目的即是探討產品壽命服從二參數指數分配之加速衰變試驗的最適設計。首先，本研究針對產品壽命服從二參數指數分配的情況，經由證明，可知試驗時間足夠大時，由衰變資料求得的壽命估計量會近似服從二參數指數分配。在成本控制在不超過預算，和試驗時間已達足夠大的條件下，極小化產品壽命分配第 100p 個百分位數估計量之均方誤，以決定加速衰變試驗下，各應力的最佳樣本數、最佳量測間隔時間和最佳量測次數。

此外，本研究針對加速應力水準配置、試驗總預算和 值之決定，對產品壽命估計精準度之影響大小進行敏感度分析，由分析結果我們可發現幾個趨勢如下：在不改變產品失效模式下，當最大應力和最小應力的間距越大，可獲得較精準的估計結果；在三個應力的試驗下，當中間的應力水準越接近最大或最小應力時，估計結果越精準；在總預算提高的情況下，可以採用更多的樣本進行試驗，因此，可獲得更好的估計結果；約在0.01~0.04之間，p有一定值存在，可使得產品壽命分配的第100p 個百分位數估計量的均方誤最小。

關鍵字

加速壽命試驗 ； 加速衰變試驗 ； 二參數指數分配 ； 均方誤

並列摘要

The product’s lifetime is getting longer when the technology of the industry production is improving nowadays. It is difficult to assess the lifetime data by using the traditional life-test method. This paper deals with the problem of designing an accelerated degradation testing in which the product’s lifetime follows a two-parameter exponential distribution. First, we will prove that the estimator of lifetime approximates the real lifetime while the experiment time is large enough. Using the criterion of minimizing the mean-square error of the estimator of the 100p th percentile of the product’s lifetime subject to the constraint that the total experiment cost does not exceed a predetermined budget and the distribution of the estimator of lifetime approximate the distribution of the real lifetime very much, we determine the optimal solution of the sample size, the measure of time and the number of measurements.

Moreover, we will do the analysis of the sensitivity of the changeable parameter versus the mean-square error of the estimator of the 100p th percentile of the lifetime distribution. There are four concluding remarks given as follows：(1) In the condition of unchanging the failure model of the product, we can get a better estimate result precisely while the range of the highest stress and the lowest stress is getting larger. (2) When the middle level of stress is close to the highest or the lowest among the three stresses of the experiments, we can get a good precision of the estimate of a product’s lifetime. (3) If the predetermined budget is higher, we can set a lot of samples in the accelerated test. Also, we receive a better result. (4) The value between 0.01 and 0.04 can minimum the mean-square error of the estimator of the 100p th percentile of the product’s lifetime and the estimator of the product’s lifetime is the lowest.

並列關鍵字

accelerated life testing ； accelerated degradation testing ； two-parameter exponential distribution ； mean-square error

參考文獻

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