Pareto分配產品在逐步型I區間設限下之壽命績效指標之最佳實驗設計

許多科技產品蓬勃發展的時代，人們為了追求便利的生活，對於產品的技術要求精益求精，廠商希望在限制的時間內、有限成本下，提高品質追求利潤；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，在多種需求下，製程能力是否被有效評估，成為生產產品非常重要的關鍵因素。本研究假設產品的壽命服從Pareto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，並使用此估計量作為檢定統計量進行假設檢定程序，同時在逐步型I區間設限下決定最佳實驗設計以達到最小的總實驗成本，並以表格形式列出相關值供實際使用，本篇研究最後也利用兩個實際數據的例子來為整個研究做出驗證。

關鍵字

設限樣本； Pareto分配；最大概似估計量；製程能力指標；檢定程序；實驗設計

並列摘要

Many technological products are booming in the era. In order to pursue a convenient life, people keep improving the technical requirements of products. Manufacturers hope to improve quality and pursue profits within a limited time and limited cost. Consumers expect to be able to purchase products with long life and low failure rate. In practice, process capability indices (PCIs) are widely used to evaluate the performance of process. Under various requirements, evaluating the process capability has become a very important key factor in the production of products. This study assumes that the lifetime of the product obeys Pareto distribution. The maximum likelihood estimator of the lifetime performance index is calculated and used as the testing statistic for the hypothesis verification procedure under progressive type I interval censoring. To achieve the minimum total experimental cost, the optimal experimental design is determined and the relevant values for the experimental design are listed in tables for practical use. At the end of this study, two numerical examples are used to verify the entire study.