壽命具指數分配之串聯系統恆定應力與階段應力加速壽命試驗的比較

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邱柏龍(Bo-Lung Chiu) 查詢紙本館藏

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統計研究所

論文名稱

壽命具指數分配之串聯系統恆定應力與階段應力加速壽命試驗的比較
(Comparison of Constant-Stress and Step-Stress Accelerated Life Tests for Series Systems under Exponentila Life Distribution)

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摘要(中)

在可靠度分析中, 加速壽命試驗是指將受測物件置於較正常使用下嚴厲的環境應力中,
以縮短試驗時間的一種方法。本文考慮受測物件是由兩個零件串聯而成, 且零件平均壽
命服從獨立的指數分配, 分別在V-準則、D-準則與A-準則下, 探討兩應力水準恆定
應力加速壽命試驗(two-level constant-stress ALT , CSALT) 與兩應力水準階段應力加速壽命試驗(two-level step-stress ALT , SSALT) 之最佳化問題, 並比較兩最佳化試驗之優劣。在型一設限下, 可由數值結果看出最佳SSALT 在三個準則下皆優於最佳CSALT ; 在無設限下, 我們証明了兩最佳化試驗可得到相同的估計精確度。另外我們以最佳CSALT 作為基準試驗進行SSALT 之等效試驗計畫, 探討在三個準則下之成本效益, 並以實際例子說明, SSALT 只需較少的樣本數或可以縮短試驗的時間。

摘要(英)

Accelerated life testing (ALT) is a process of testing products by subjecting it to strict
conditions, in order to observe more failure data in a short time period. In this thesis,
we consider the ALT of series system, each consists of two components whose life time
distributions follow independent exponential distributions. Optimal designs on the sample
allocation for the two-level constant-stress ALT(CSALT) and on the time for changing stress
levels for the two-level step-stress ALT(SSALT) are considered based on V-optimality, D-
optimality and A-optimality, respectively. Under Type-I censoring, it shows, by numerical
results, that the optimal SSALT is better than the optimal CSALT in terms of the resulting
objective functions. We also prove that the two optimal ALTs are indeed equivalent without
censoring. In addition, we use the optimal CSALT as the baseline ALT to obtain an equivalent
SSALT plan. A real data is analyzed to demonstrate the performance of both ALT plans
under the three optimality criteria as well as the equivalent test plans.

關鍵字(中)

★ 串聯系統
★ 指數分配
★ 階段應力加速壽命試驗
★ 恆定應力加速壽命試驗
★ 型一設限
★ V-準則
★ D-準則
★ A-準則
★ 等效試驗計畫

關鍵字(英)

★ series system
★ exponential distribution
★ step-stress ALT
★ constant-stress ALT
★ Type-I censoring
★ V-optimality
★ D-optimality
★ A-optimality
★ equvalent plan

論文目次

目錄
摘要i
Abstract ii
誌謝iii
目錄v
圖目次viii
表目次ix
第一章緒論1
1.1 研究背景............. . 1
1.2 文獻探討............. . 3
1.3 研究方法............. . 4
第二章最佳化恆定應力加速壽命試驗7
2.1 模型假設.............7
2.2 最大概似推論............9
2.3 最佳化準則............. 12
2.3.1 V-最佳化準則..........12
2.3.2 D-最佳化準則..........14
2.3.3 A-最佳化準則..........15
2.4 二維最佳化設計.......... . . 6
第三章最佳化階段應力加速壽命試驗17
3.1 最大概似推論............17
3.2 最佳化準則............. 21
3.2.1 V-最佳化準則..........21
3.2.2 D-最佳化準則..........22
3.2.3 A-最佳化準則..........24
第四章型一設限下最佳CSALT 和SSALT 之比較26
4.1 加速效應斜率相等之最佳試驗.......26
4.1.1 V-最佳化準則.......... . . 26
4.1.2 D-最佳化準則.......... . . 28
4.1.3 A-最佳化準則.......... . . 29
4.2 一般參數下兩最佳試驗之比較....... 31
4.3 等效試驗計畫............34
第五章實例分析46
5.1 資料說明............. . 46
5.2 V-最佳化準則............48
5.3 D-最佳化準則............50
5.4 A-最佳化準則............51
第六章結論與展望52
參考文獻53
附錄56

參考文獻

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2013-7-17

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