Confidence Intervals for Multivariate Process Capability Indices using Bootstrap

陳 欽雨, Fu-Kwun Wang

Research output: Contribution to journalJournal Article peer-review

Abstract

  多變量製程能力指標數值已被廣泛用為評估具多重特性之製程。由於區間估比點估計較能完解釋指數值的影響程度,因此經常被研究者採用。然而,多變量製程能力指標數值之統計分配通常極為複雜,故欲建立這些指標數值之信賴區間頗為困難。可行辦法之一是採用複式抽樣法(bootstrap),此法根據實證之機率分配函數,運用重複抽樣方式收集資料。本研究採用四種複式抽樣法:標準,百分位數,矯正百分位數,及加速矯正百分位數,進行資料蒐集以建立各指標數值之信賴區間。研究結果顯示:若以標準及百分位數抽樣資料分析時,本研究所採用三種多變量製程能力指標數值,Cpm,MCpm及MCp其信賴區間有較高比例含蓋原指標數值。但是若針對其它兩種取樣方法之資料分析時,信賴區間所含蓋比例在不同製程能力指標數值之間,差異相當大。
  Multivariate process capability indices have recently been developed for assessing the capability of processes with multiple characteristics. In many situations, confidence intervals are more useful than point estimates, because an interval estimate enables a practitioner to see both how small and how large an effect may be. Unfortunately, the statistical distributions of multivariate process capability indices are complicated, and hence it can be difficult to construct confidence intervals no these indices. As an alternative, bootstrap sampling, which is equivalent to sampling with replacement from an empirical probability distribution function, can be used to construct confidence intervals on these indices. In this paper, four different types of Bootstrap methods-standard, percentile, bias-corrected percentile, and accelerated bias-corrected percentile are used to construct confidence intervals. Two real examples are given to show the application of the proposed method. The confidence intervals of three leading multivariate process capability indices, Cpm, MCpm AND MCp, are obtained using the standard and percentile bootstrap methods and the coverage proportions for these indices are close to the nominal values. When the bias-corrected percentile and accelerated bias-corrected percentile methods are used, coverage proportions are sensitive to the choice of index.
Original languageAmerican English
Pages (from-to)429-438
Journal工業工程學刊
Volume15
Issue number5
StatePublished - 1998

Keywords

  • Bootstrap
  • confidence interval
  • multivariate process capability index

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