在生產製造的過程中，製程能力指標(Process Capability Index)通常是用來衡量產品或製程品質是否具有符合工程規格的能力。一般而言，多維切割製程之規格區域為位置容差之特殊規格。過去幾十年來已有多位學者致力於多維切割製程能力指標之研究，但彼等的研究大多假設製程服從多變量常態下制定。然而實務上，許多製造過程，如奈米切割製程產出的分佈常出現不服從常態分配的情況。因此，本研究之目的主要係希望提出能正確反映製程良率之非常態多維切割製程能力指標。
我們首先利用Scaled Weighted Variance (SWV)方法對Pan和Li (2014)之NPC_p與 NPC_pk指標進行修正，並據此推導出非常態多維切割製程能力指標RNPC_p與RNPC_pk。接著，我們以數值計算的方式比較在不同參數組合之非常態分配下，各多維切割製程能力指標之表現。結果發現本研究所提出之RNPC_p與RNPC_pk指標均能正確反映非常態多維切割製程之表現。
最後，我們以一筆奈米切割製程之實際資料進行數值實例的探討及驗證，說明本研究所提出之新指標可正確的評估非常態多維切割製程的風險。

Process capability index (PCI) is commonly used to measure the capability of a manufacturing process and evaluate whether it can meet the engineering specifications in industries. Generally speaking, the multidimensional machining process has a specific specification called the positional tolerance. In the past decades, many scholars including Krishamoorthi (1990), Davis et al. (1992), Pan and Li (2014), etc. have devoted themselves to developing capability indices for multidimensional machining processes based on the assumption of normality. However, in practical applications, many manufacturing processes, such as nano-cutting process may not follow normal distribution. Thus, by relieving the normality assumption, this paper aims to propose new non-normal capability indices that can correctly reflect the true nonconforming rate for multidimensional machining processes.
We first use Scaled Weighted Variance (SWV) method to revise NPC_p and NPC_pk indices proposed by Pan and Li (2014). Then, the two new indices RNPC_p and RNPC_pk can be derived accordingly. In the numerical calculation studies, we compare the performance among various multidimensional machining process capability indices under different parameter combinations for non-normal distributions. The numerical calculation results show that our proposed indices can properly reflect the actual performance for non-normal multidimensional machining processes.
Finally, a nano-cutting example is used to demonstrate that the proposed indices are suitable to assess the risk of non-normal multidimensional machining processes.

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