利用製程能力指標Spk構建製程良率之複式信賴區間

Abstract

良好的品質是產品不可或缺的一項競爭條件，企業通常應用統計製程管制(Statistical Process Control , SPC)來監控與改善產品或製程之品質，而管制圖及製程能力分析又是SPC的兩項重要工具。在作製程能力分析時，製程能力指標(process capability index , PCI)可用來量化一個製程能力的好壞，透過這些指標值可評估製程實際的績效與找出改善的方向。業界常用的指標有Cp、Cpk、Cpm 等等。當我們以抽樣的方式對製程能力指標進行點估計時，因無法保證其為原指標之不偏估計式，因此無法保證可代表真實製程能力，此外，因這些指標之估計式之機率分配太複雜不易求得，因此製程能力指標的區間估計公式亦不易取得。另外，製程能力指標與製程良率間有密不可分的關係，但是大部分指標都無法得到與製程良率一對一的關係，只有Boyles(1994)提出之新指標Spk與製程良率間有一對一的數學等式。由於良率比製程能力指標值更能直接顯示製程之好壞，故業界對製程之良率非常重視，因此本研究乃在製程為常態分配的假設下，以一種重複抽樣的複式模擬法(Bootstrap Simulation)透過Spk指標來構建製程良率的複式信賴區間，並將提出之製程良率構建流程發展成一套應用程序，用Visual Basic寫成簡易的視窗軟體，以供業界製程人員方便且快速的使用此應用軟體，準確的估計產品良率及有效的提昇企業的競爭力。

Quality is an essential factor to enhance product’s competitive capability in the market. Statistical process control (SPC) is broadly used in controlling and improving process capability in industry. Control chart and process capability analysis are two important tools for SPC. Process capability indices are employed to analyze the process capability. These indices can be used to evaluate the real process capability or improve the product/process. Among all developed process capability indices,Cp,Cpk,Cpm,Spk are widely used in industry. However, the probability distributions of the estimators of these indices are too complicated to derive, therefore, the confidence interval of the indices cannot be obtained. Furthermore, process yield has closely relationship with process capability index, but most process capability indices and the process yield aren't proportional. Boyles (1994) defined the new index,Spk, which has one-by-one relationship to process yield. This research will be based on repeating sampling, Bootstrap Simulation to construct the bootstrap confidence interval between the process yield, and an application procedure is developed. Finally, Visual Basic was used to create a simple windows interface for the application so that it could be used by industry to evaluate the precise process yield and improve the industry competitiveness.