製程能力指標Cpk近似不偏估計量的績效分析

Performance Analysis of the Approximately Unbiased Estimator of Process Capability Index Cpk

楊育穎(Yu-Ying Yang)

指導教授 ： 彭文理

國立交通大學/管理學院/工業工程與管理系所/碩士(2018年)

摘要

製程能力指標Cpk被視為高科技產業中用來衡量製程或產品品質最普遍的指標之一。主要解決製造產業之製程能力量測與評估等問題並進行處理與分析，進而提升產品品質以達到極低不良率之品質要求。對於製程能力之衡量與評估，指標Cpk提供了製程良率的信賴下界之重要訊息，因此被業界廣泛應用且被認為是一個可信度極高的尺度標準。本研究分為兩大部分，由於指標Cpk的近似不偏估計式裡含有未知參數ξ，第一部分是將未知參數ξ利用估計方法以及乘上校正因子後的ξ ̃_n做取代，經由偏差(Bias)、平均絕對離差(MAD)以及方均根差(RMSE)來做績效分析。當經由第一部分的績效分析確定指標Cpk的近似不偏估計式是可行的，再進行第二部分的模擬分析。第二部分是利用數學分析方法、有母數複式抽樣方法來做模擬，並透過各模擬方法來計算信賴下界，經由信賴下界再求出各方法的覆蓋率，藉由這些模擬後的數值之比較做出可靠之模擬決策。

關鍵字

製程能力指標 ； 近似不偏估計式 ； 信賴下界 ； 數學分析方法 ； 有母數複式抽樣方法

並列摘要

Process capability index Cpk has been the most popular index used in the manufacturing industry dealing with problems of measuring reproduction capability of process to enhance product development with very low fraction of defectives (in Parts Per Million; PPM). The index Cpk provides a lower bound on the process yield, a widely recognized criterion for measuring process capability. This thesis can be divided into two main parts, owing to the unknown parameter ξ in the unbiased estimator of process capability index Cpk, the first part of the thesis replaces the unknown parameter ξ with ξ ̃_n , which is an estimated parameter with correction factor from simulation. By way of analyzing the performance of bias, mean absolute deviation (MAD), and root mean square error (RMSE), we can confirm that the approximately unbiased estimator of process capability index Cpk is reliable and can undertake the second part. The second part utilizes the analytical method and parametric bootstrap method to calculate the lower confidence bound and coverage rate. The computational results are useful for reliable decision making.

並列關鍵字

process capability index ； approximately unbiased estimator ； lower confidence bound ； analytical method ； parametric bootstrap method

參考文獻

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