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研究生: 張家淇
Chang, Chia-Chi
論文名稱: 考量 Wiener 退化過程設計逐步壓力加速退化測試抽樣計畫
Designing a Step-stress Accelerated Degradation Test Acceptance Sampling Plan based on Wiener Process
指導教授: 胡政宏
Hu, Cheng-Hung
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業與資訊管理學系
Department of Industrial and Information Management
論文出版年: 2023
畢業學年度: 111
語文別: 中文
論文頁數: 45
中文關鍵詞: 驗收抽樣計畫Wiener 退化過程Step-stress加速退化測試
外文關鍵詞: Acceptance Sampling plan, Wiener degradation process, Step-stress accelerated degradation test
相關次數: 點閱:173下載:6
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  • 隨著科技的快速發展,產品的可靠性大幅的提升,然而,傳統的壽命測試所能夠在短時間內收集到的資訊非常有限,因此需要更有效率的方法來獲得關於產品壽命的資訊。如果產品存在一個品質特徵與其壽命有關,且會隨時間的增加而漸漸退化,並使用更嚴苛的測試條件加速產品失效,利用此退化路徑來估計產品之壽命資訊,稱為加速退化試驗,此外,過去學者提出了將壓力水平從最低到最高逐步提升的Step-stress 加速退化測試(SSADT),能夠用於縮短測持續時間和減少所需樣本量。
    當買方向生產者訂購了一批產品時,生產者需要透過檢驗的方式來判斷產品的好壞,以確定是否符合買方所指定的可靠性要求。然而,如果採取全部檢驗的方式,將會耗費大量的時間和成本,因此採用隨機抽取一定比例的樣本的驗收抽樣方式,將會是更有效率的方法。但由於產品的更新速度非常快,無論是生產者還是消費者都無法忍受長時間的驗收抽樣。因此,建構一個在較為嚴苛環境條件下的加速退化抽樣計畫是非常必要的。
    由於Wiener退化過程已被廣泛應用於退化建模和可靠性分析,因此本研究建立一個假設產品退化路徑服從Wiener過程的Step-stress退化測試抽樣計畫,以最小化允收標準檢定統計量的漸進變異數為目標,在滿足預算下求得最佳的樣本量及測量次數,並同時考量消費者風險與生產者風險,訂定允收標準判定是否允收貨批,最後利用操作特性(OC)曲線,來探討其最佳SSADT抽樣計畫的判別能力。

    With the rapid development of technology, the reliability of products has been greatly improved. However, the information that can be collected in a short period of time by traditional life testing is very limited. In the past, scholars proposed a Step-stress accelerated degradation test that gradually increases the stress level from the lowest to the highest, which can be used to shorten the test duration and reduce the required sample size.
    When the buyer orders a batch of products from the manufacturer, the manufacturer needs to judge whether the product meets the reliability requirements specified by the buyer through inspection. However, it will consume a lot of time and cost if the method of all inspections is adopted, so it will be more efficient to adopt the method of acceptance sampling.
    Therefore, this study establishes a Step-stress degradation test sampling plan assuming that the product degradation path obeys the Wiener process, with the goal of minimizing the asymptotic variation of the acceptance standard test statistics, and obtaining the optimal sample size and Measure the number of times, and consider consumer risk and producer risk at the same time, set acceptance criteria to determine whether to accept the batch, and finally use the operating characteristic curve to explore the discriminant ability of the best SSADT sampling plan.

    摘要 I 致謝 IX 表目錄 XII 圖目錄 XIII 第一章 緒論 1 1.1 研究背景 1 1.2 研究動機與目的 2 1.3 研究架構 3 第二章 文獻探討 4 2.1 驗收抽樣計畫 4 2.1.1 計數型抽樣計畫 4 2.1.2 計量型抽樣計畫 4 2.2 加速壽命測試抽樣計畫 5 2.2.1 型一設限(Time-censored) 6 2.2.2 型二設限(Failure-censored) 6 2.3 退化試驗 7 2.3.1 退化路徑 7 2.3.2 加速退化試驗 9 2.3.3 退化測試抽樣計畫 11 第三章 Wiener模型的SSADT抽樣計畫 13 3.1 問題描述 13 3.2 參數符號設定 14 3.3 模型建立 15 3.3.1 服從Wiener過程之 SSADT模型 15 3.3.2 試驗之成本 19 3.3.3 允收抽樣計畫 19 3.4 模型求解 21 3.5 小結 30 第四章 模型驗證與分析 31 4.1 個案說明 31 4.2 個案結果分析 32 4.3.1 實驗結果 32 4.3.2 敏感度分析 34 4.3 3階應力水平SSADT抽樣計畫 38 4.4 小結 39 第五章 結論與未來展望 40 5.1 研究結論 40 5.2 未來方向 41 參考文獻 42

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