在現今高度競爭產業時代，產品品質的好壞儼然成為企業生存的關鍵，在眾多評估產品品質績效的方法中，製程能力指標（Process Capability Indices, PCIs）為一個有效且方便的評估工具。但大多數的製程能力指標皆假設其品質特性來自常態分配，然而，在現實環境中，有些品質特性未必符合常態分配假設，例如:電子零件壽命常屬於指數分配、伽瑪（gamma）分配與韋伯（Weibull）分配等。為了衡量產品壽命之績效表現，壽命績效指標（lifetime performance index）因而被發展出來，由於產品壽命擁有望大型的品質特性，且要求所生產的產品之壽命至少大於L（壽命規格下限）單位時間。
驗收抽樣計畫（acceptance sampling plan）為另一個被業界廣為應用的品管工具，它可以在同時滿足生產者及消費者所要求的品質水準及保障雙方所能承受的風險下，提供買賣雙方是否該允收送驗貨批的決策準則。本研究主要目的為當產品壽命服從指數及伽瑪分配的情況下，利用完整樣本（complete data），基於壽命績效指標CL來建構出驗收抽樣計畫。接著，利用壽命績效指標估計量之精確抽樣分配，求算出計畫之允收機率函數及操作特性曲線。透過同時求解兩非線性允收機率函數，求得所需抽樣樣本數n及允收臨界值k之兩個計畫參數。此外，本研究更進一步比較分析採用壽命績效指標所發展驗收抽樣計畫與已存在常態近似方法之驗收抽樣計畫的數據結果。而為了實務上的方便使用，本研究求解及彙整出多種品質水準與風險組合之計畫參數表，因此使用者可透過計畫參數表得知所需抽樣樣本數及相對應之允收臨界值來進行送驗貨批之評判。最後，本研究透過實際案例來說明此驗收抽樣計畫之操作程序。

In today’s highly developed manufacturing industry, Process capability indices (PCIs) are effective means of measuring process performance. Most process capability indices have been developed under the assumption that the quality characteristics are normally distributed. However, the lifetime of electronic components generally may possess an exponential, gamma or Weibull distribution and so forth. A lifetime performance index CL was proposed and used as a means of measuring product lifetime performance. The lifetime of products is a larger-the-better type quality characteristic and is generally required to exceed L unit times.
Acceptance sampling plans provide the producer and the customer a general decision rule for lot sentencing that meets both of their quality and risk requirements. This thesis attempts to introduce two variables sampling plan for product acceptance determination based on the lifetime performance index. One is developed under the exponential complete data; the other sampling plan is developed under gamma complete data. The probability of acceptance, i.e., the operating characteristic function of the proposed sampling plan, is derived based on the exact sampling distribution of the estimator of the lifetime performance index. The required sample size n and the corresponding critical value k are determined by solving two non-linear equations simultaneously. Furthermore, a comparison study is also conducted to compare the proposed CL based sampling plan and the existing sampling plan. And for the practical purpose, this study tabulated the plan parameters for various combinations of acceptable and rejectable quality levels, producer’s risks and consumer’s risks. Thus, practitioners can easily understand the number of product items required for inspection and the corresponding critical value for making decisions on product acceptance determination. Finally, an application is given for illustration.

致謝 i
摘要 ii
Abstract iii
圖目錄 v
表目錄 vi
第一章 緒論 1
1.1研究背景與動機 1
1.2研究目的 3
1.3研究架構 4
第二章 文獻回顧與探討 5
2.1 驗收抽樣計畫 5
2.2製程能力指標 8
2.3 壽命績效指標 11
2.4 基於指數分配下之壽命績效指標 12
2.4.1 壽命績效指標與製程良率之關係 14
2.4.2 壽命績效指標之估計式 15
2.5 基於伽瑪分配下之壽命績效指標 16
2.5.1 壽命績效指標與製程良率之關係 17
2.5.2 壽命績效指標之估計式 18
第三章 產品壽命服從指數分配之驗收抽樣計畫 19
3.1 基於指數下藉由常態近似方法之驗收抽樣計畫 19
3.2 基於指數下藉由壽命績效指標之驗收抽樣計畫 26
3.2.1 計畫設計概念與操作程序 26
3.2.2 非線性規劃求解計畫參數 28
3.3比較與分析 37
第四章 產品壽命服從伽瑪分配之驗收抽樣計畫 39
4.1 計畫設計概念與操作程序 39
4.2非線性規劃求解計畫參數 42
4.3案例分析 50
第五章 結論與未來研究方向 54
5.1 結論 54
5.2 未來研究方向 55
參考文獻 56
附錄 59

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