製程能力指標應用於低不良率製程的工具汰換問題

Abstract

在產品製造過程中，工具磨損之監控是一個非常重要的議題。由於機具設備持續運轉製造產品，工具將逐漸產生磨損的現象。通常工具磨損發生於生產過程中，包含有銑床、鑽床、車床等製程。由於此種磨損是無法避免的，因此必須對工具作有效的監控以維持產品品質。在工具管理上，其中一個很重要的議題就是工具汰換策略。過早做工具汰換會增加生產之成本，相對地，太晚作工具汰換則會導致不良的生產品質。因此如何找出最佳工具汰換時機，儼然成為一個重要的課題。製程能力分析是對製程的產出績效提供一個數值的衡量方法，根據這些數值，生產者可作為衡量製程能力好壞及製程是否達到對產品品質要求的重要標準。實際上；無論是消費者訂購產品或是工程師製造生產時，都會事先預設一個製程能力指標的最小值。若因嚴重的工具磨損而無法達到預設之製程能力的最小值，則會認為製程能力是不夠的並且開始作工具的汰換。由於製程能力分析可以被應用在決定汰換工具的最佳時間點，而且此方法對於在低不良率的製程下維護低生產成本和高品質產品而言是特別有效的。然而，必須要注意到的是，在計算製程能力時應該考慮到可歸屬原因的影響。工具磨損正是製程裡一個非常普遍的可歸屬原因之一，當我們在進行製程能力的運算時應該將此項因素考量進來，否則所得到的製程能力值可能會產生嚴重的偏差，所以希望能透過修正後的製程能力指標之運用，讓我們正確的估算製程能力並且找出合適的工具汰換時機。因此，在本文中，我們首先提出一個透過 Cpk (被視為良率基礎的指標)來找出工具汰換的最佳時間點之方法。接著對於單邊規格製程，也提出單邊指標 CPU 和 CPL 的應用去找出最佳工具汰換的時間點。因為 Cpmk 指標結合三個基本的指標 Cp , Cpk 和 Cpm 的優點。所以，我們也提出以 Cpmk 找出最佳工具汰換時間點的分析方法。在考慮製程能力為動態地改變時，我們將探討這些製程能力指標之估計式及推導出各個指標的統計抽樣分配。此外；並提供在低不良率要求下之生產製程，如何尋找出工具汰換最佳時間點之程序。因此操作人員將可以根據所提出的方法來判斷他們的製程是否達到所設定的製程能力水準，而作出正確的工具汰換決策。最後為說明其應用，我們將會列舉三個例子以完整地說明整個工具汰換之作業程序。

Tool wear control is an important component to many manufacturing factories for producing quality products. As the manufacturing activities keep on going, the tool wears gradually. Tool wear occurs in production process involving milling machines, drilling machines, lathes, etc. While such wear is unavoidable, tool wear must be controlled to maintain product quality and efficient tool utilization. One important issue for tool wear control is the tool replacement policy. Early tool replacement increases the production cost. Overtime tool replacement, however, results in poor production quality. Consequently, detecting suitable time for tool replacement operation becomes essential. Process capability analysis is to provide numerical measures for determining whether a process is capable and meets the required quality standards. In practice, a minimal capability requirement would be preset by the customers/engineers. If the prescribed minimum capability fails to be met due to severe tool wear, one would conclude that the process is incapable and a tool replacement activity must be initiated. Process capability analysis is applied to determine the optimal tool replacement time. The proposed approach is useful, particularly, for low fraction defective processes requiring low production cost and stringent quality standards. Process capability can be calculated accurately if the data contains no assignable cause variation. Tool wear, however, is a dominant and irremovable component in many machining processes, which is a systematic assignable cause. The ordinary measures of process capability are inaccurate because the process data is contaminated by the assignable cause variation. In order to determine the optimal tool replacement time to maintain minimal product quality, conventional capability calculation must be modified. In this dissertation, we first proposed a method based on capability index Cpk, a yield-based index, to find the appropriate time for tool replacement. For unilateral processes, a procedure for finding the appropriate tool replacement time based on the one-sided process capability index CPU (or CPL) is obtained. The index Cpmk combines the merits of the three basic indices Cp , Cpk and Cpm. Therefore, we also present an analytical approach using Cpmk to find optimal tool replacement time. Considering process capability changes dynamically, the estimators of these indices are investigated. Closed form of the exact sampling distribution is derived. An effective tool management procedure for finding optimal tool replacement time is presented for processes with low fraction defective to meet manufacturing requirement. The practitioners can use the proposed method to determine whether their process meets the preset capability requirement, and make reliable decisions regarding the tool replacement time. For illustration purpose, three application examples involving tool wear are presented.