考慮韋伯製程變異數發生變動下之製程能力調整

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。當製程之平均數發生微小偏移時，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。自從1980年代，Motorola公司提出6個標準差的觀念，許多統計學家質疑提倡6個標準差的學者，為什麼在衡量製程能力時需要對製程平均數做1.5被標準差的調整。Bothe (2002) 提出製程服從常態分配下之製程能力調整方法，他以統計的方法解釋了1.5倍標準差的調整之原因。但Bothe的研究是在製程服從常態分配的假設之下，而非常態分配製程在業界時常出現，過去的研究也針對了非常態分配的調整方法。事實上，製程標準差也是會改變的，因此本研究在變異數微小變動時，針對製程服從韋伯分配提出製程能力調整方法。在本研究的最後，以實例來說明如何在非常態的製程中，考慮製程變異數發生改變的情況下，調整製程能力指標 之計算。

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. The assumption that the process is stable (the process mean and variance are not change) must be made before PCIs are calculated. In practice, the process is dynamic. If the process mean has a small shift, and the control chart doesn’t detect, then the PCIs will overestimate the true process capability. For this reason, the PCIs have to be adjusted under those cases. Motorola, Inc. introduced its Six Sigma quality initiative to the world in the 1980s. Some quality practitioners questioned why the Six Sigma advocates claim it is necessary to add 1.5 . Bothe (2002) provided the adjustment method for normality processes. Bothe (2002) provided a statistical reason for including such a shift in the process average that is based on the chart’s subgroup size. Data in Bothe’ study was assumed to be approximately normally distribution, but the process output is usually not from approximately normally. Some research is about the PCIs adjustment for process output has a non-normal distribution. In fact, the process variance could also change. In this paper, we consider the variance change adjustments to compute reliable estimates for capability index Weibull distribution data. For illustration purpose, an application example is presented.