以複式模擬法構建單一非對稱規格區間之C"pmk指標的信賴下限

Abstract

產業界常使用製程能力指標來分析製程能力的好壞。在製程呈常態分配且製程是在管制的狀態時，可以此指標來判斷製程能力或產品的品質。Cp及Cpk為最早期發展出來的製程能力指標，也是目前產業界最常使用的製程能力指標，後來發展之新指標Cpm加入了田口損失函數期望值的概念，考慮了製程平均偏離目標值的情形，而Cpmk指標則又結合了Cpk與Cpm的優點。由於實務上非對稱規格區間的製程例子有逐漸增加的趨勢，所以，近年來學者在傳統的指標中考慮了目標值不等於規格中心的影響而發展出非對稱規格之製程能力指標 、 和 等，而 更反映出製程平均偏離目標值對製程能力的影響。由於 之估計式 的機率分配過於複雜，至目前為止，學者僅能推導出其近似的機率分配，故 相關的假說檢定與信賴區間的研究迄今尚未被發展出，因而導致 無法被業界廣為使用。 因此，本研究之主要目的是針對 指標，以一種藉由重複抽樣的複式模擬法(bootstrap simulation)來推導單一指標的信賴下限，以此信賴下限來判斷真實製程能力的範圍並衡量製程能力的好壞。本研究並將構建信賴下限過程寫成完整的應用流程，可供業界製程品管人員快速的構建出 之信賴下限，以正確的判斷製程之狀況。

Process capability index(PCI) is extensively adopted to assess a manufacturing process that is in control. Although conventionally used PCIs, Cp and Cpk can not accurately reflect the process capability when the process mean deviates from the center of the specifications or the target value. As widely assumed, Cpmk incorporates the above two factors. Additionally, C"pk, C"pm and C"pmk are more efficient than conventional PCIs with asymmetric tolerance. Although C"pmk is assumed to be a more superior index than C"pk and C"pm, C"pmk is seldom applied in industry owing to its complex probability distribution, thus making it impossible to derive the exact test statistics when testing the null hypotheses that C"pmk equals a specific value. This study adopts bootstrap simulation to construct a lower confidence limit for C"pmk with a single asymmetric tolerance. The lower confidence limit is used to evaluate process capability. A detailed procedure is then written so that process engineers can construct the lower confidence limit for C"pmk flexibly and efficiently.