多重品質特性指數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

現在的科技業市場競爭激烈，人們對於產品品質的要求愈來愈嚴苛，耐用度是消費者在選購商品時，評估產品品質優劣的重要考量。在工業製程領域中，製程能力指標(Process capability indices, PCIs)是一個被廣泛運用在品質管制的工具，能夠以量化的方式，有效地衡量產品製程績效與潛在能力，評估該產品的品質特性是否合乎廠商所制定的規格界限，也符合消費者的需求。一般而言，消費者和廠商們都會希望產品使用壽命越長越好，代表該產品的品質越好，因此產品壽命是屬於望大型(Larger-the-better type)的品質特性。本論文主要的研究目的是考慮 d 條生產線上的產品壽命都服從單參數指數分配時，當規格下限L已知的條件下，提出綜合壽命績效指標C_T與相應的相等單一壽命績效指標 C_L之間的關係，使其為綜合製程良率之單調遞增函數。在逐步型I區間設限下，計算出綜合壽命績效指標C_T之最大概似估計量MLE(Maximum likelihood estimator)，求得其漸近分配。在給定綜合壽命績效指標目標值時，決定單一壽命績效指標之目標值，在顯著水準給定下，進行單一壽命績效指標之假設檢定程序，進而判別整體綜合製程是否具有能力。檢定程序的檢定力亦會列表和分析。最後，我們利用模擬資料與數值實例，說明如何使用本研究提出的檢定程序，判定d 條生產線的製程是否具有能力，管理人員可以運用此測試程序來評估綜合壽命績效指標是否達到要求的水準。

關鍵字

逐步型I區間設限樣本；指數分配；最大概似估計量；製程能力指標；檢定演算程序

並列摘要

In today's highly competitive technology market, the requirements of consumers for product quality are becoming more and more stringent. Durability is an important consideration for consumers to evaluate the quality of products when purchasing products. In the field of industrial processes, process capability indices (PCIs) are widely used in quality control tools to evaluate whether the quality characteristics of the product meet the specification limits set by the manufacturer and meet the needs of consumers. Overall speaking, the consumers hope to purchase products with long lifetime. Therefore, the lifetime of products is a quality characteristic of the larger-the-better type. The main research purpose of this paper is to consider the products produced on d production lines. When the lifetime of products on each production line has a one-parameter exponential distribution with known lower specification limit L, the overall lifetime performance index is proposed which is related to the corresponding d individual lifetime performance indices. The overall lifetime performance index is an increasing function of overall conforming rate. Under progressive type I interval censoring, the maximum likelihood estimator (MLE) of the overall lifetime performance index and the individual lifetime performance indices are obtained and their asymptotic distributions are also obtained. When the target value of the overall lifetime performance index is given, the target value of the individual lifetime performance index is determined, and the testing procedure algorithm is used to show whether the overall process has the capability under the given significance level. The corresponding test powers are also tabulated and analyzed. Finally, we use one simulation data and one numerical examples to illustrate how to use the testing algorithmic procedure proposed in this study to determine whether the processes of d production lines are capable, and managers can use this test procedure to assess whether the overall lifetime performance index meet the required level.