量測誤差是工業製程中影響產品值常見的因素。大的量測誤差會使得產品的量測值偏離實際值，並引導監控者至錯誤的結論。本文提出一種新的捲積管制圖。提出指數分配形式的時間間隔型資料，並加上量測誤差的考量，應用在指數加權移動平均管制圖上。此外，假設量測誤差為常態或是指數分配。研究顯示出，在兩種不同分配的量測誤差之下，管制圖的表現都會顯著的受到影響。 / Measurement error is an important factor in industry that influences the outcome of a process. Large measurement error would cause the observation measure deviate from the true value and consequently lead to a wrong decision. In this project, we propose a convolution control chart. We then design the EWMA ‘time between events’ (TBE) control chart with the measurement error, with the assumption that the observations are exponentially distributed. In addition, we assumed the measurement error follows a normal distribution or an exponential distribution. We showed that, in two cases of the measurement error, the performance of the proposed chart monitoring the process mean is greatly affected.

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.