破壞性加速衰變試驗之適合度檢定

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姓名

童昱翔(YU-HSIANG TONG) 查詢紙本館藏

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統計研究所

論文名稱

破壞性加速衰變試驗之適合度檢定
(Goodness of Fit Test for Accelerated Destructive Degradation Tests)

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摘要(中)

破壞性加速衰變試驗 (accelerated degradation test) 常用來推估高可靠度產品之相關可靠度資訊，試驗中欲量測產品壽命相關的品質特徵值(quality characteristic)，必須破壞產品才能取得，故產品一經測試後即無法再次量測使用，因此在破壞性衰變試驗中，各測試產品只有一次量測時間點所產生的一筆衰變數據。在過去的文獻中，僅考慮具產品間差異性隨機效應之混合效應模型卻忽略量測誤差，並只著重以產品間差異性對模型適合度進行探討。本文首先將量測誤差加入破壞性加速衰變模型中，以近似衰變分析方法驗證破壞性加速衰變模型所得產品壽命分配之適合性，利用所有資料估計虛擬失效時間 (pseudo failure time)，且以統計假設檢定驗證，以確保其估計的合理性。最後，輔以五組實際資料說明所提簡易流程之優點，當產品間差異性之變異占破壞性加速衰變模型總變異之比例較高時，由適合度檢定得到的結論會傾向於模型配適良好。

摘要(英)

The accelerated destructive degradation tests (ADDTs) are widely used to assess reliability information for highly reliable products whose quality characteristics degrade over time and can be measured only once from one tested unit. For most ADDT models in literature, only unit-to-unit variability is considered in the mixed-effect models without measurement errors. The issue of model checking is assessed on unit heterogeneity only. In this thesis, we first incorporate the measurement errors into the ADDT models. The use of an approximate degradation method is presented to evaluate the validity of the ADDT model, in addition to providing a statistical justification to the estimation of pseudo failure time. Five case studies show the flexibility and applicability of the proposed approach. When the proportion of the heterogeneity in the total variation is larger for the ADDT model, the performance of the goodness-of-fit test would be more satisfactory.

關鍵字(中)

★ 破壞性加速衰變試驗
★ 適合度檢定
★ 虛擬失效時間

關鍵字(英)

★ accelerated destructive degradation test
★ goodness of fit test
★ pseudo failure time

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 v
圖目錄 vii
表目錄 ix
第一章緒論 1
1.1 研究動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻探討 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 本文架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章破壞性衰變模型 5
2.1 破壞性衰變模型之一般模型 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 具量測誤差之模型 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 具批次效應之模型 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 可辨別性驗證 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 產品壽命分配 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
第三章破壞性衰變模型之適合度檢定 10
3.1 虛擬失效時間之估計 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 最加線性不偏預測 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 虛擬失效時間之適合度檢定 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
第四章破壞性衰變資料實例分析 17
4.1 分析步驟 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 破壞性衰變模型實例分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 破壞性加速衰變模型實例分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3.1 黏著劑 B 黏力資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3.2 黏著劑 K 黏力資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.3 聚合物拉力比例資料分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.4 具批次效應之破壞性加速衰變模型實例分析 . . . . . . . . . . . . . . . . . . . . . 34
第五章結論與未來展望 43
附錄：模型之可辨別性驗證 44
參考文獻 51

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指導教授

樊采虹、彭健育(Tsai-Hung Fan Chien-Yu Peng)

審核日期

2017-7-21

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