Apply a general percentile method to evaluate process capability indices

Abstract

Several process capability indices (PCIs) such as C_p C_pk and C_pm have been used to evaluate process capability by monitoring whether the process tolerance is less than the allowable product tolerance interval. Using the traditional PCI assumes that the underlying distribution is a normal distribution and “six sigma” is adopted to be the process tolerance. However, this assumption may be too restrictive for some practical processes when an underlying probability distribution is skewed. The proposed method for calculating PCI uses a 3-parameters function expressed in terms of its cumulative probability function to approximate a quantile function for given data. Using this approach to derive the extreme percentiles PO.GGB65 and Pooom for a normal or skew process distribution is easy and accurate. The new percentile method is tested on several real data to verify its estimating capability.

摘要

製程能力分析用來評估當製程達到穏定狀態時，其製程離散量是否能符合所預設之產品規格內。目前所運用之多種製程能力指標，例如C{inp}、C{inpk}及C{inpm}等指標皆假設製程之品質特性資料爲常態分配，並設定製程離散量爲6σ。此項假設條件對某些具有單邊規格爲零之製程或其品質特性資料爲非常態分配之製程並不合適。因此在分析非常態分配之製程能力時，製程離散量須設定爲某一適合之反分配區間量。爲方便計算，通常設定非常態分配之製程離散量爲分配之99.85%百分位數與0.135%百分位數之差。本論文提出利用Shore通用分配公式來推導出一簡單公式，以便求出未知分配之99.85%百分位數與0.135%百分位數。本論文將舉實例說明與比較所提公式與其它方法之差異。

Key Words:

• process capability index
• Shore's general formula
• percentile

關鍵詞:

• 製程能力指標
• Shore通用分配公式
• 百分位數