近幾年來，有一些研究提出了只用單一一個管制圖即可同時偵測平均數和變異數。根據此目的，我們提出了加權平均損失管制圖，此管制圖是利用加權平均損失所建立的，在一個製成的目標值和平均數不一定相等時，它可同時監控一個製成的平均數和變異數。此加權平均損失統計量是應用一個加權因子，去調整製程平均和目標值的平方差和變異數的損失比重，所以此管制圖的效能比未經由加權因子調整過的管制圖還好。我們不只建立了固定管制參數(FP)加權平均損失管制圖，也建立了適應性加權平均損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)；我們利用平均連串長度(ARL)來衡量固定管制參數管制圖的偵測績效，利用馬可夫鏈的方法計算偵測出異常訊息所需的平均時間(ATS)來衡量適應性管制圖的績效，並且做比較，我們發現適應性管制圖比固定管制參數管制圖的效能還要好。我們也利用最佳化技術建立最加適應性管制圖，當製成失控時，此最佳化管制圖能使ATS1最小。此外，當平均數和變異數的偏移幅度很小時，我們利用指數加權移動平均法(EWMA)建立EWMA加權平均損失管制圖，使其有較好的偵測力。這些我們所提出的管制圖，是只根據單一一個統計量所建立的，和X bar-S管制圖相比，有較好的效能，且和使用兩個管制圖同時偵測平均數和變異數相比，比較輕易理解且容易執行。 / In recent years, a few researchers had proposed different types of single charts that jointly monitor the process mean and the variation. In this project, we use the weighted average loss (WL) to construct WL control charts for monitoring the process mean and variance simultaneously while the target value may be different from the in-control mean. This statistic WL applied a weighted factor to adjust the weights of the loss due to the square of the deviation of the process mean from the target and the variance change. So the WL charts are more effective than unadjusted loss function charts. We not only construct the fixed parameters (FP) WL chart but also the adaptive WL charts which included variable sampling interval (VSI) WL chart, variable sample size and sampling interval (VSSI) WL chart and variable parameters (VP) WL chart. We calculate the average run length (ARL) for FP WL chart and using Markov chain approach to calculate the average time to signal (ATS) for adaptive WL charts to measure the performance and compare each other. From the comparison, we find the adaptive WL charts are more effective than the FP WL chart. We also proposed the optimal adaptive WL charts using an optimization technique to minimize ATS1 (ARL1) when the process was out-of-control. In addition, in order to detect the small shifts of the process mean and variance effectively, we construct the WL charts using the EWMA scheme. The proposed charts are based on only one statistic and are more effective than the X bar-S chart. And the WL charts are easy to understand and apply than using two charts for detecting the mean and variance shifts simultaneously.

傳統的二項累積和(CUSUM)管制圖是監測不合格率變化的有效工具。在本文中，我們考慮了俱有機率管制界線的二項CUSUM管制圖的設計，旨在控制每一期的條件誤報率達到所需的值。與固定的管制界線相比，機率管制界線將會是動態的，且更一般化、更能適應各種複雜的實際情況。在本文中，我們著重在機率管制界線的決定。藉由積分方程式法的發展，以促成動態二項加權CUSUM管制圖的設計與分析。俱有機率管制界線或固定管制界線的二項加權CUSUM管制圖與是否俱有快速起始反應特性的管制圖皆進行了比較。此外，在高良率的情境下，我們互相比較俱有機率管制界線與固定管制界線的二項加權CUSUM管制圖在製程失控時的偵測力表現。舉了一個例子來說明該如何應用所提出的管制圖。比較的結果顯示，動態界線的管制圖優於固定管制界線的管制圖，且在高良率的情況下，若樣本數越大，對動態管制界線的管制圖越有利。 / The conventional binomial CUSUM chart is an efficient tool for monitoring changes in fraction nonconforming. In this paper, we consider the design of Binomial CUSUM charts with probability control limits aimed at controlling the condi- tional false alarm rate at the desired value at each time step. The resulting control limits would be dynamic, which are more general and capable of accommodating more complex situations in practice as compared to the use of a constant control limit. In this paper, We focus on the determination of the probability control limits. An integral equation approach is developed to facilitate the design and analysis of the binomial WCUSUM control chart with probability control limits. The performance of the binomial WCUSUM charts with probability and constant control limits and the binomial WCUSUM charts with and without the fast initial response feature are compared. Besides, we compared the out-of-control detection perfromance of the binomial WCUSUM charts with probability and constant control limits for high yield process. An example is used to illustrate the application of the proposed control chart. Our comparisons show that the binomial WCUSUM chart with probability control limits generally outperforms the WCUSUM chart with constant control limits, and the conventional binomial CUSUM control chart with a constant control limit for high yield process when the sample size is large.