製程變異的降低在製造業的管理扮演一關鍵的角色。許多文獻指出品質系統設計及品質技術使用是降低製程變異的重要工具，然而品質計畫中量測精確度(precision)對於品質系統良窳有著舉足輕重的地位。量測系統通常使用重複性及重現性(Repeatability & Reproducibility, R&R)統計量以確認量測系統之精確度。重複性及重現性之評估通常透過標準的指導方針與作業程序以有效地確保量測資料之可靠度，並有助於製程變異監測及品質改善方案的執行。目前國際標準對於計量值量測系統精確度評估有一套標準作法與作業程序，相關之學術研究也相當完整且豐富，但對於計數值量測系統精確度評估之標準作法與作業程序則較為不足，相關研究亦較為匱乏。
本研究針對一般之離散值量測資料，整合不完全資料之E-M (Expectation Maximization)法則與完全資料之廣義線性模式(generalized linear models, GLMs)、疊代加權最小平方法(iterative weighted least square, IWLS )等方法，估計量測參數之最大概似估計量(maximum likelihood estimator, MLE )，以連絡函數之線性預估量與重複性建立重複性變異估計公式。為分析量測系統間變異成分，本研究亦以數學方法推導出一套估計量測系統間變異之法則，再以重現性定義推算重現性變異。最後以精確度評估準則，構建一套計數值量測系統之精確度評估模式。
研究結果顯示，單變量離散值資料可以GLM建立指數家族分配之統計量及本體連絡函數之線性預估量，再以IWLS估計量測參數，然而單變量離散值資料因隨機衝擊所產生零值膨脹(zero-inflated)之不完全資料問題，則以E-M法則之E步驟建立量測參數對數概似估計量之期望值，M步驟找出E步驟之最大值，以得到量測參數MLE。雙變量離散值資料可以GLM建立雙變量指數家族分配之統計量及本體連絡函數之線性預估量，再以IWLS估計量測參數，然而由於高附加價值製程及量測精密度不足所造成資料群聚效應，可以GLM建立卜瓦松分配-卜瓦松分配之統計量及本體連絡函數之線性預估量，再以IWLS估計量測參數。本研究亦透過實證研究以驗證所提出量測系統精確度評估模式，以提供產業評估量測品質與量測系統發展之參考。

Reducing the process variability plays an important role in many manufacturing organizations. Therefore, it is essential to develop a quality system and to utilize quality techniques in order to reduce the process variability as shown in the literature. Quality programs, which are corresponding to the degree of measurement precision, are fundamental to the quality system. The common program assessing the precision of measurement system is the repeatability and reproducibility (R&R) study. The R&R study program is a highly effective means of adopting standard guidelines to ensure reliability of measurement data. Such accurate data can be applied when monitoring process variability and implementing quality improvement initiatives. The general scheme for assessing variable measurement system precision has guidelines and procedures in international standards, and has been studied in extensively academia. However, the R&R study for attribute data has not been thoroughly investigated and requires guidelines.
This research presents statistical methods to evaluate precision for the attribute measurement system. Meanwhile, the E-M (Expectation Maximization) algorithm, generalized linear models (GLM), and iterative weighted least square (IWLS) method are applied to estimate maximum likelihood estimators (MLE) of measurement parameters that can be adopted to calculate the repeatability variance, and the proposed mathematical model is used to compute the variance between measurement systems. According to the above-mentioned variance and the definition of reproducibility variance, this study proposes a novel method to evaluate the precision of general attribute measurement system.
This study shows that uni-variate discrete data can use GLM to get the statistics of exponentially family of distributions, linear predictor of identity link function and then IWLS is adopted to estimate measurement parameters. However, uni-variate discrete data subject to random shocks with incomplete-data problem of zero-inflation can utilize the E-step of E-M algorithm to calculate the expectation of complete-data log likelihood function for measurement parameters. The M-step requires the maximization of E-step with respect to measurement parameters over the parameter space. The bivariate discrete data can use GLM to get the statistics of bivariate exponentially family of distributions, linear predictor of identity link function and then IWLS is adopted to estimate measurement parameters. Due to high value-added processes and poor measurement capability, the bivariate discrete data has clustered effect and can utilized GLM to generate the statistics of Poisson-Poisson, linear predictor of identity link function and then IWLS is adopted to estimate measurement parameters. Based on the proposed methodology, this investigation can meet the practical measurement results and manufacturing cases can be utilized to demonstrate the process and potential of this proposed model. This research can be viewed as the reference model for the evaluation of measurement systems with attribute data. Moreover, the analysis results are also insightful for the quality practitioners to improve their measurement systems effectively.

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