單邊規格多品質特性製程能力指標CpuT的信賴下限

Abstract

製程能力指標已被廣泛用於單一產品品質特性的衡量。針對多品質特性的製程，我們考慮單邊規格製程能力指標CpuT。然而，CpuT的精確抽樣分配難以求得。為了對製程能力做統計推論，本篇研究引用CpuT的自然估計量 的近似常態分配，並透過模擬研究此近似常態分配在各個樣本數下的準確性。除此之外，根據這些樣本數，比較近似常態法和四種複式抽樣法所建構的95%信賴下界的績效，並以涵蓋率和信賴下限的平均值做為績效評比準則。最後，以一個實務上具有多品質特性之製程做為例子說明。一般而言，實驗結果顯示近似常態的方法較另外四種複試抽樣法可靠。

Process capability indices (PCIs) for processes with a single quality characteristic have been investigated extensively. For processes involved multiple characteristics, we consider the one-sided process capability index CpuT. However, the exact sampling distribution of CpuT is mathematically intractable. In this research, in order to make inferences on the process capability, we apply an asymptotic normal distribution for the natural estimator of CpuT and investigate the accuracy with the corresponding sample size by simulation. In addition, depending on the sample size, a performance comparison among the normal approximate method and four kinds of the bootstrap approach for 95% lower confidence bounds is conducted based on coverage rate and mean of the lower confidence bounds. Finally, an application from manufacturing process with multiple characteristics is presented. In general, the result indicates that the normal approximate technique is more reliable than the four bootstrap methods.