Pareto分配產品的壽命績效指標在逐步型I區間設限下之檢定程序的檢定力分析

The power analysis of the testing procedure for the lifetime performance index of products with Pareto distribution under progressive type I interval censoring

林其儒(Chi-Ju Lin)

指導教授 ： 吳淑妃

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2019年)

https://doi.org/10.6846/TKU.2019.00013

摘要

當科技加速進步，人們對於產品的要求也日益嚴苛，不僅廠商希望在限制的時間、成本下，提高品質以追求利潤；消費者更是期望能購買到高壽命、低故障率的產品。在實務上，製程能力指標(process capability indices, PCIs)被廣泛用來評估製程，在雙方的需求下，製程能力能否被有效評估，成為非常重要的關鍵因素。
因此，本研究假設產品壽命服從柏拉圖分配時，在逐步型I區間設限下，計算出壽命績效指標C_L之最大概似估計量並求得其漸近分配。在規格下限L已知的情形下，使用此估計量及兩種拔靴法發展三個檢定程序以評估壽命績效是否達到預定的水準；接著對三種檢定程序計算其模擬檢定力，並進行三種檢定程序之比較分析。最後，利用一個模擬資料與一個實務資料，說明如何利用本研究提出的檢定程序評估產品績效指標是否達到要求水平。

關鍵字

製程能力指標 ； 逐步型I區間設限 ； 柏拉圖分配 ； 最大概似估計量 ； 拔靴法 ； 檢定程序

並列摘要

As the science and technology make progress day by day, people are in the pursuit of more stringent product quality requirements. Not only manufacturers hope to improve quality and pursue profits under limited time and cost; but also consumers are expecting to purchase products with high life expectancy and low failure rate. In practice, process capability indices (PCIs) are widely used to evaluate the capabilities of manufacturing processes. Under the highly demand of both parties, whether the process capability can be effectively evaluated becomes a very important key factor.

In this thesis, the lifetime of products is assumed to have Pareto distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample and its asymptotic distribution is also derived. The MLE and two kinds of Bootstrap methods are developed to construct three testing procedures about the lifetime performance index. The comparisons of power analysis of three methods are done and analyzed. Finally, one simulate example and one practical example are given to illustrate the use of these three testing algorithmic procedure to determine whether the process is capable.

並列關鍵字

process capability index ； progressive type I interval censoring ； Pareto distribution ； maximum likelihood estimator ； bootstrap ； testing procedure

參考文獻

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