無 / In this article, a two-step process is considered to investigate the effects of measurement errors on EWMA and cause-selecting EWMA control charts. At the end of current process, a pair of imprecise measurements of in-coming quality and out-going quality is randomly taken with individual units. The linear relationship between in-coming quality and out-going quality is assumed and four possible states of the process are defined with respective distributions of in-coming and out-going qualities derived. The EWMA control chart with measurement error is then constructed to monitor small-scale shift in mean for the previous process while the cause-selecting control chart, or EWMA control chart based on residuals, including measurement error, is proposed to diagnose the state of current process. Based on sensitivity analysis, the presence of imprecise measurement diminishes the power of both the EWMA and the proposed control charts and affects the detectability of process disturbances. Further, applications of proposed control charts are demonstrated through a numerical example to show some possible misuses of control charts. If the process mean shifts in a small scale when a single assignable cause occurs on each step, the proposed cause-selecting control chart is more sensitive than other control charts. The Hotelling T^2 control chart is also compared to illustrate the diagnostic advantage outweighed by proposed cause-selecting control chart.

Most products are produced by several process steps and have more than one interested quality characteristics. If each step of the process is independent, and the observations taken from the process are also independent then we may use Shewhart control chart at each step. However, in many processes, most production steps are dependent and the observations taken from the process are correlated. In this research, we consider the process has two dependent steps and the observations taken from the process are correlated over time. We construct the individual residual control chart to monitor the previous process and the cause-selecting control chart to monitor the current process. Then simulate all the states occur in the process and present the individual residual control chart and the cause-selecting control chart of the simulations. Furthermore compare the proposed control charts with the Hotelling T2 control chart. At last, we give an example to illustrate how to construct the proposed control From the proposed control charts, we can determine which step of the process is out of control easily. If there is a signal in the individual residual control chart, it means the previous process is out of control. If there is a signal in the cause-selecting control chart, it means the current process is out of control. The Hotelling T2 control chart only indicate the process is out of control but does not detect which step of the process is out of control.

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Today, most products are produced by several dependent subprocesses. This paper considers the economic-statistical process control for two dependent subprocesses with two assignable causes following Weibull shock distributions. We construct the individual X control chart to monitor the in-coming quality produced by previous process, and use the cause-selecting control chart to monitor the specific quality produced by current process. By using the charts, we can effectively and economically distinguish which subprocess is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and the successive quadratic programming algorithm and a finite difference gradient method in the Fortran IMSL subroutine (dnconf) is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts. Furthermore, the sensitivity analysis illustrates the effects of cost and process parameters on the optimal design parameters and the minimal expected cost per unit time for the proposed control charts.

在子製程相關下所產生的品質特性資料使Shewhart管制圖無法對各別的製程狀態加以解釋，而選控圖可診斷前後製程的責任歸屬。本文提出有n個子製程時，建立選控圖的方法及在製程上之應用，以追蹤製程變異之發生，明確地劃分出子製程的責任歸屬。文中並以模擬資料和實際例證說明，在相關品質特性的資料中，選控圖的建立及診斷效果。在實務上，若產品是由許多相關的子製程共同製造而成時，對於受到前製程影響的品質特性，即可用選控圖進行管制，以獲得正確的製程狀態訊息，並進一步採取正確的管制行動。

由近期的研究中發現變動所有參數的管制圖在偵測小幅度偏移時的速度比起傳統的舒華特管制圖來的快，許多文獻也討論到利用調適性管制技術同時監控製程的平均數和變異數。而在這份研究中，為了改善現有管制圖的偵測效率，依序提出了U-V管制圖以及Max-M管制圖來偵測單一製程與兩相依製程的平均數和變異數。採用AATS及ANOS來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。透過兩階段的範例來介紹所提出的管制圖的應用方法並將VP U-V管制圖、VP Max-M管制圖與FP Z(X-bar)-Z(Sx^2)管制圖加以比較。從所研究的數值分析中發現VP Max-M管制圖比另兩種管制圖的表現來的好，再加上只需要單一管制圖在使用上對工程師來說也較為簡便，因此建議Max-M管制圖値得在實務上被使用。 / Recent studies have shown that the variable parameters (VP) charts detect small process shifts faster than the traditional Shewhart charts. There have been many papers discussed adaptive control schemes to monitor process mean and variance simultaneously. In the study, to improve the efficiency and performance of the existing control charts, the U-V control charts and Max-M control charts are respectively proposed to monitor the process mean and variance for a single process and two dependent process steps. The performance of the proposed control charts is measured by using adjusted average time to signal (AATS) and average number of observations to signal (ANOS). The calculation of AATS and ANOS is derived by Markov chain approach. The application of the proposed control charts is illustrated by a numerical example for two dependent process steps, and the performance of VP U-V control charts, VP Max-M control charts and FP Z(X-bar)-Z(Sx^2) control charts is compared. From the results of data analyses, it shows that the VP Max-M control charts have better performance than VP U-V control charts and FP Z(X-bar)-Z(Sx^2) control charts. Furthermore, using a single chart to monitor a process is easier than using two charts for engineers. Hence, Max-M control charts are recommended in real industrial process.