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研究生:程紀堯
研究生(外文):Chi-Yao Cheng
論文名稱: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
論文名稱(外文):Designing an accelerated degradation testing where the product’s lifetime follows a two-parameter exponential distribution
指導教授:胡伯潛胡伯潛引用關係
指導教授(外文):Po-Chien Hu
學位類別:碩士
校院名稱:國立虎尾科技大學
系所名稱:工業工程與管理研究所
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:86
中文關鍵詞:加速壽命試驗加速衰變試驗二參數指數分配均方誤
外文關鍵詞:accelerated life testingaccelerated degradation testingtwo-parameter exponential distributionmean-square error
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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。
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.
中文摘要 --------------------------------------------- i
英文摘要 --------------------------------------------- ii
誌謝 --------------------------------------------- iv
表目錄 --------------------------------------------- vii
圖目錄 --------------------------------------------- viii
第一章 緒論----------------------------------------- 1
1.1 研究背景與動機------------------------------- 1
1.2 設限資料------------------------------------- 2
1.3 加速壽命試驗--------------------------------- 3
1.4 衰變試驗------------------------------------- 4
1.5 加速衰變試驗--------------------------------- 5
1.6 研究範圍與限制------------------------------- 6
1.7 論文架構------------------------------------- 7
第二章 二參數指數分配之加速壽命模式----------------- 8
2.1 二參數指數分配------------------------------- 8
2.2 加速壽命試驗假設----------------------------- 10
2.3 τ之估計-------------------------------------- 12
2.4 τ均方誤之計算-------------------------------- 14
2.5 加速壽命試驗的最佳化設計--------------------- 15
2.6 加速壽命試驗範例----------------------------- 18
2.7 各參數變動對MSE(τ)之敏感度分析--------------- 21
2.7.1 最大和最小應力水準變動下對MSE(τ)之敏感度分析- 21
2.7.2 中間應力變動下對MSE(τ)之敏感度分析----------- 25
2.7.3 不同Cb值下對MSE(τ)之敏感度分析--------------- 27
2.7.4 不同p值下對MSE(τ)之敏感度分析---------------- 28
第三章 加速衰變分析--------------------------------- 30
3.1 衰變模式------------------------------------- 30
3.2 加速衰變試驗假設----------------------------- 31
3.3 τ之估計-------------------------------------- 33
3.4 τ均方誤之計算-------------------------------- 39
3.5 最佳化模型----------------------------------- 40
3.6 加速衰變試驗範例----------------------------- 44
3.7 各參數變動對 之敏感度分析-------------------- 52
3.7.1 最大和最小應力水準變動下對MSE(τ)之敏感度分析- 52
3.7.2 中間應力變動下對MSE(τ)之敏感度分析----------- 54
3.7.3 不同Cb值下對MSE(τ)之敏感度分析--------------- 56
3.7.4 不同p值下對MSE(τ)之敏感度分析---------------- 57
第四章 結論與未來研究方向--------------------------- 59
4.1 結論----------------------------------------- 59
4.2 未來研究方向--------------------------------- 60
參考文獻 --------------------------------------------- 61
附錄一 --------------------------------------------- 64
附錄二 --------------------------------------------- 69
附錄三 --------------------------------------------- 77
附錄四 --------------------------------------------- 80
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