考慮韋伯製程平均發生偏移下之製程能力調整

Abstract

製程能力指標被用來衡量製程製造產品符合規格的能力，不僅是提供品質保證的工具，也是在品質改善方面的一個方針。計算製程能力指標需服從製程為穩態的前提假設，也就是在生產過程中平均數和標準差不會改變，但是在實務上製程為動態。當製程發生平均數微小偏移時，有些管制圖可能無法偵測到，造成製程能力指標高估製程良率，因此必須將製程能力指標進行調整。Bothe (2002) 提出製程服從常態分配下之製程能力調整方法。事實上，非常態分配製程在業界也時常出現，因此本研究將針對製程服從韋伯分配提出其製程能力調整方法。由於調整量的大小與管制圖檢定力息息相關，故本研究先比較三種不同的韋伯管制圖在相同平均偏移量下之檢定力。再選定檢定力最高的管制圖計算在韋伯分配下應調整的偏移量，並針對非常態適用的Cpk指標做調整。在本研究的最後，我們用一個實例來說明如何在製程服從韋伯分配並考慮製程平均會發生變動，如何調整製程能力指標Cpk。

Process capability indices (PCIs) have been proposed in the manufacturing industry to provide numerical measures on process reproduction capability, which are effective tools for quality assurance and guidance for process improvement. PCIs are calculated under the assumption that the process is stable (the process mean and variation are not change), but in practice, the process is dynamic. If the process mean has a small shift, the control chart doesn’t detect obviously so that the PCIs will overestimate the true process capability. For this reason, the PCIs have to be adjusted. Bothe (2002) provided the adjustment method for normality processes. In this paper, we provide capability adjustment method for Weibull processes. The magnitudes of adjustment is correlated with the detection power of control chart, so we first compare the detection powers of three Weibull control chart under the same mean shift distances, and choose the best powerful Weibull control chart to calculate the mean shift adjustments for Weibull processes. At the end, we add the adjustment to capability index Cpk of non-normal processes. For illustration purpose, an application example is presented.