為了預測高可靠度產品在市場上的保固期失效率 (failure rate)，廠商通常會在產品上市前，於實驗室進行相關測試，並利用測試結果推論新產品在市場上之壽命。但傳統的實驗室實驗大多屬於加速壽命試驗 (accelerated lifetime test, ALT)，此種試驗的原理為加速產品的劣化肇因，使測試樣品在短時間內失效。當實驗室的測試不屬於壽命試驗，而是強度測試 (stress test) 時，例如以摔落、翻轉等方式進行試驗，再以失效樣品所能承受的強度，做為產品的可靠度指標，如何將這些與壽命相關的可靠度指標，也納入預測產品壽命的分析中，是此論文欲研究的議題。當廠商除了新產品的實驗室資料，還有許多同質性產品的歷史資料時，如何善用這些資料，是另一個研究重點。另一方面，現代的產品多為高可靠度產品，其在保固期內的失效率通常相當地低，因此當我們使用常見的機率分佈來描述產品在市場上的失效率時，往往得到不盡理想的結果。有鑑於此，本論文提出一個聯合模型 (joint model)，以整合數個產品的實驗室資料及市場資料，且允許實驗室測試不為壽命試驗，並以成長曲線 (growth curve) 描述市場資料，而非一般的機率分佈。透過貝氏分析 (Bayesian analysis) 之技巧估計參數，並依上市時間動態地更新失效率預測。在實例分析中，採用模擬資料，透過本論文提供的方法，評估保固期失效率之動態預測表現。

For predicting the field failure rate, the manufacturer usually performs laboratory quality or stress tests before products being in the market. When the product is highly reliable and its use cycle is relatively short, lab tests related to early-stage reliability are sufficiently informative on failure rate prediction in the warranty period. Taking the smartphone as an example, drop and tumble tests are performed for the product strength under which the stress level that a specimen can withstand is treated as a reliability index. This thesis aims to incorporate these lab reliability indices to improve the warranty failures prediction. But, due to high reliability of modern products, most of testing units are passed in the lab stress test leading to very few failures or even no failures, which raises challenges for estimating the reliability index precisely. To overcome this issue, this thesis suggests a hierarchical model structure to integrate all available historical lab data from other homogeneous products to further improve the estimation precision for the reliability index when sparse lab failures are encountered in practice. Another contribution of this thesis is to perform on-line predictions for the warranty failure rates using a Bayesian framework based on a joint modeling of lab data and field data. The performance and the advantages of the proposed methodology are demonstrated by a case study with simulated data.

第一章 緒論 1
第二章 實驗室及市場資料之聯合模型 5
第三章 貝氏推論 15
第四章 實例分析 21
第五章 結論與後續分析 35

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