製程能力指標Cpk之近似不偏估計量

Abstract

製程能力指標是被廣泛地用來評估製程產出的產品是否符合品質要求的重要工具，不僅能提供品質保證，也是提供品質改善的一個方針。其中，雙邊規格Cpk指標是在製造業中使用最多的指標之一，其用來量測極低不良率製程。但Cpk的估計量並非為不偏估計量，為了能更正確且精準的估計製程能力，本篇論文利用Matlab軟體之curve fitting tool去計算並得到Cpk的估計量的校正因子。然而又在實際應用上，因為母體參數μ 和 σ 為未知，校正因子中的參數ξ=|μ-m|/σ也同樣無法得知。因此我們以複式抽樣法求出參數ξ。如此，將此估計量帶入校正因子計算後，即可求得Cpk之近似不偏估計量。

Process capability indices (PCIs) are very important tools in quality control activities. They can provide measures on the process performances and can provide plans for improving the process quality. Among those indices, Cpk is the most popularly used index in the manufacturing industry, which often used to deal with measuring the process performance with very low fraction of defectives. However, the estimator of Cpk is unbiased. In order to accurately infer to Cpk via its estimator, we apply the mathematical equation fitting to obtain a correction factor to the estimator. Since the process parameters μ and σ are unknown, then the distribution characteristic parameter ξ=|μ-m|/σ of the correction factor is also unknown, we further use bootstrap method to obtain the estimator of the parameter ξ . Afterwards, we can obtain the modified index of Cpk , which is approximately unbiased.