利用右型II設限樣本對雙參數指數分配之多重品質特性之整體績效評估

The evaluation of the performance index of multi-quality characteristic for the two-parameter exponential distribution based on the right type II censored sample.

林倩如(Chien-Ju Lin)

指導教授 ： 吳淑妃

淡江大學/管理學院/統計學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00163

摘要

假設一個產品具有t個望大型品質特性(如壽命時間)和s個望小型品質特性(如處理時間、維修時間)之多重品質特性。CL和CU是分別用來衡量望大型和望小型品質特性的製程能力指標。在壽命檢測的試驗中，試驗者可能無法同時觀測到所有n個產品的壽命時間，假設只觀測到前面k個最短的壽命時間資料，則收集到的資料稱為右型II設限樣本。本文假設每個品質特性皆服從雙參數指數分配，針對產品的多重品質特性為互相獨立和相依兩種情況，我們分別提出一個多重績效指標(Multi-process performance index, MPPI) CT 。

利用第i個望大型品質特性之右型II設限樣本和第j個望小型品質特性之右型II設限樣本，i=1,...,t, j=1,...,s，我們可推導出CT的最大概似估計量。在給定整體良品率下，可求得CT之目標值，我們欲檢定多重績效指標值是否大於CT之目標值。在顯著水準alpha下，產品的多重品質特性為互相獨立和相依兩種情況時，分別發展出一個檢定演算程序。此外，六標準差的概念也會應用於本文中。最後，本文使用兩個數值實例來示範本文提出的檢定演算程序，以評估產品的整體績效是否達到所要求的水準。

關鍵字

右型II設限樣本 ； 雙參數指數分配 ； 最大概似估計量 ； 製程能力指標 ； 多重績效指標 ； 檢定演算程序 ； 六標準差

並列摘要

Suppose that a product has multiple quality characteristic with t larger-the-better type quality characteristics (such as lifetime ) and s smaller-the-better type quality characteristics (such as processing time and repairing time). The process capability index CL and CU are used to measure the larger-the-better and the smaller-the-better type quality characteristics respectively. In lifetime experiment, the experimenter may not obtain the lifetimes of n items on test. Assuming that there are only the k smallest lifetimes are observed, the type II right censored sample is collected. We assume that each quality characteristic follows a two-parameter exponential distribution. For the case of independent quality characteristics and the case of dependent quality characteristics, we propose a multi-process performance index (MPPI) CT respectively.

Based on the type II right censored samples from the ith larger-the-better type quality characteristic and the jth smaller-the-better type quality characteristic, i=1,...,t, j=1,...,s, we derive the maximum likelihood estimator for CT. Given the specified overall conforming rate, we can find the target value for CT. To test if CT is greater than the target value, a testing algorithm is developed at level alpha for the case of independent quality characteristics and the case of dependent quality characteristics respectively. The concept of Six sigma is also applied in this paper. At last, two numerical examples are used to illustrate the proposed testing procedure to assess if the multi-processes reach the required level.

並列關鍵字

Type II right censored sample ； Two-parameter exponential distribution ； Maximum likelihood estimator ； Process capability indices ； Multi-process performance index (MPPI) ； Testing algorithmic procedure ； Six sigma

參考文獻

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