自Duncan提出管制圖的經濟設計以來，陸續有學者提出各種不同型態經濟管制圖的設計。這些文章中，只考慮到特殊原因發生的時間服從期望值為1/Lambda的指數分配，由於指數分配具有固定的失敗率(Hazard Rate)，但實務上很多零組件的壽命卻隨著時間的遞增而增加，若只考慮到指數分配的層面似乎有其欠妥的地方，因此，Hu提出韋伯模式下X-bar經濟管制圖的設計，由於Hu所提出的韋伯模式只考慮到固定抽樣間隔時間的情況，於是Banerjee and Rahim在1987年提出韋伯模式下經濟X-bar管制圖的設計在兩種抽樣方式（變動與固定抽樣間隔時間）下，對單位時間平均成本的影響。上述所提出的韋伯模式下X-bar經濟管制圖，皆未將描點的連串檢定列入考慮，Jaehn的區域管制圖不但可以解決管制圖沒將描點的連串檢定列入考慮的缺失，在操作上亦比管制圖加上連串檢定方便。 於是，本研究提出韋伯模式下X-bar & S-square區域管制圖的經濟設計，並考慮變動與固定抽樣間隔時間下，對單位時間平均成本的影響。另外，我們根據Saniga提出經濟統計管制圖的概念，建立韋伯模式下X-bar & S-square區域管制圖的經濟統計設計，即在統計表現的基本要求下，找出符合此統計表現下使成本最小的最適設計參數值。雖然X-bar & S-square區域管制圖之經濟統計設計的最小成本會稍大於X-bar & S-square區域管制圖之經濟設計的成本，但經濟統計設計的統計表現則符合我們所設定的要求。另外，固定抽樣間隔時間下所得到的最小成本亦會明顯地大於變動抽樣間隔時間下所得到的最小成本。因此，考慮變動抽樣間隔時間的區域管制圖是較好的。

參考Yue等論文，我們延續探討在通訊網路中對於非及時Available Bit Rate(ABR)資料與及時Variable Bit Rate(VBR)資料共同使用一條傳輸的等候模型。假設及時VBR資料傳輸較非及時ABR資料傳輸有優先權，我們建立與分析資料在離開過程之模型。本論文研究在非強制性優先權策略下之一般等候模型，藉由ABR資料的等候區域設立檢查點來控制流入量，在離開過程中推導VBR資料與ABR資料的離去時間的數學關係式，以及調查他們的數值模擬的表現。在此數學推導中需要藉MMBP關係，從ABR資料的等候區域觀點製造Markov矩陣算出穩定狀態下的機率分量、生成函數以及閒置時間的函數。結果發現檢查點影響兩者的離去時間並不顯著，但是VBR資料流入的速度卻會造成影響。 / Following the work by Yue et al., this thesis considers the departure of a multi-traffic network system for a popular communication network where a transmission link is shared by an Available Bit Rate (ABR) application for non-real time traffic and a Variable Bit Rate (VBR) application for real time traffic. It is assumed that the VBR traffic has a higher transmission priority than the ABR traffic. In this thesis, we establish a tractable analytical model of departure processes for such a system. The departure process is characterized by a general queueing model with a non-preemption policy for which the inter-departure times of VBR and ABR are derived, respectively. Since the VBR traffic is only affected when ABR is in service, the analysis is given to describe the departures of ABR, and VBR traffics. Numerical results are conducted to illustrate the system performance with input control of ABR traffic.

「世代」是一個是父死子繼的過程，亦是一個家庭生命歷程的交換、更新與取代，要產生人口「替代」（replace），就必須有人口「再生產」或「繁殖」（reproduction），才會有所謂的替代過程發生。本文以繁殖率（reproduction rate）為基礎，計算世代長度（mean length of generation）。並以臺灣總生育率的變化作為切入點，從其半世紀以來的整體趨勢，去看生育率變化與世代長度變遷之關連性；而代間間隔時間之變遷必然影響臺灣家庭世代的共存結構，使得家庭結構產生改變。本文從女性觀點著手，納入初婚年齡中位數與平均餘命的概念，討論半世紀以來臺灣家庭世代共存結構變遷。世代變遷之所以重要在於其不只是對家庭產生意義，也同時影響個人生命及其生活之樣貌。 在1979年以前，臺灣世代長度變化與總生育率變化的趨勢大抵一致，在1979年以前，世代長度隨著總生育率下滑，到了1979年，總生育率還是不斷減少，但世代長度卻已停止下降，向上攀升。 從家庭可能產生之人口數量說明臺灣五十餘年之家庭世代共存結構變化： 1) 50年代--三代共存：此時期的家庭人口相當多，可能同時包括雙親、七個子女、七個媳婦，八至十個孫子三代，家庭裡共存人數可能多到40人以上，此時期家庭最大的特色在於叔姪同齡、「長兄如父、長嫂如母」的特殊現象。 2) 60年代--四代共存：從人口層面推論，四代同堂最有可能發生在70年代，主要在於此時期的平均餘命延長，讓親代有足夠的生命等待曾孫子女的來臨，同時也有足夠的生命看著所有的子女長大結婚生子。 3) 70年代--四代共存：此時期的家中共存人數較前期減少許多，約莫在30人左右，主要原因是此時期的總生育率已下降至1.9人。 4) 80年代--四代共存：和70年代相同的是，此時期也可能是個四代同堂的家庭型態，不同的是，由於總生育率下降，家庭共存人口比起70年代數量驟減，約莫10-15人。 5) 90年代--三代共存：此時期的家庭結構將再度回到三代共存的情形，與50年代三代共存不同的是，此時期由四代共存回到三代共存原因在於遲育現象，而家庭人口組成也愈趨簡單。 6) 21世紀--兩代共存：此時期的家庭結構將產生很大的變化，結婚年齡延後加上所生育的子女數銳減，使得家庭人口數將更少，可能出現僅有兩代共存的情形，勢必造成親代與子代的鍊結更深，意味著所有雙親照顧的責任可能全落在一個子女身上。 世代變遷影響下的家庭世代共存結構改變，改變了家庭人口的規模與組成，進而影響了家庭成員的生活模式及型態；現今家庭所生育子女數僅1人餘，因此獨生子女現象造成一人需負擔兩人的照顧問題，無論是在經濟或心理上都將是一種沈重的負擔。 關鍵字：世代、代間間隔時間、女性生命週期、家庭世代共存結構 / The languid flow of one generation to the next symbolizes the constant reweaving of our social fabric: As daughters assume the roles their mothers left in death, the life of the family is renewed and perpetuated, but also is steered onto a unique path. The motivating force behind this familiar familial story is the reproduction of human life, without which the replacement of human populations, of mothers with daughters and fathers with sons, cannot occur. Naturally, reproduction rates form the crux of my research, as I use it to calculate mean generation lengths over the last fifty years. The trends and trajectories of the past half-century are integral to examining the interconnectivity of changes in the total fertility rate and changes in mean generation lengths; moreover, changes in mean generation lengths impact significantly the structure of intergenerational coexistence in particular and the entire family structure in general. My research also approaches the topic through a yoni-centric perspective: I employ statistics concerning the median age of first marriage and average life expectancy of women to discuss the evolution of the structure of intergenerational coexistence in Taiwan over the past half-century, as women, stereotypically speaking, exhibit more predictable and stable life patterns than men. Ultimately, generation replacement is important not only because it fosters meaning within the family, but also because it weighs heavily on the very content that forms the lives that individual family members lead. Prior to 1979, the mean generation length and total fertility rate in Taiwan exhibited similar fluctuation patterns: Mean generation lengths shortened in accordance with total fertility rate’s steady decline. However, by 1979, the total fertility rate continued to fall, while mean generation lengths leveled off and even began to rise. Through my research, I discovered that potential family size serves as an effective analytical window to study the evolution of the structure of intergenerational coexistence in Taiwan over the last fifty odd years: 1) 1950s (three generations coexisting): The family size during this decade was very large, and can include parents, seven children, seven daughter-in-laws, and eight to ten grandchildren all living under the same roof. Total family size sometimes exceeds forty persons. There were two unique characteristics of families during this decade. First, family members of two generations may be of the same age (i.e. an uncle is the same age as his nephew). Second, traditional practice dictated that upon the death of the parents, the eldest son assumes the role of the father (head of the house) and his wife assumes the role of the mother. 2) 1960s (four generations coexisting): According to population studies, the phenomenon of four generations living under the same roof was mostly likely to occur during the 1970s, since average life expectancies increased significantly during this decade, allowing parents to witness grandchildren marry and sire great-grandchildren. 3) 1970s (four generations coexisting): Due to total fertility rates declining to 1.9, family size during this decade decreased significantly, consisting of at most about thirty persons. 4) 1980s (four generations coexisting): Like the 1970s, it was also possible for four generations to live under one roof during this decade. Unlike the 1970s, family size shrunk to about ten to fifteen persons in accordance with steady declines in the total fertility rate. 5) 1990s (three generations coexisting): Family structures returned to three generations living under the same roof during this decade. Unlike the 1950s, however, the cause of this decline was the fact that women began bearing their first child at an older age, which resulted in simpler organization of family members. 6) Present (two generations coexisting): Family structures are undergoing dramatic changes in the 21st century. People are marrying later in life and having fewer children, which leads to considerable decline in family size and only two generations living under the same roof. This, however, has also precipitated closer ties between parents and their children, and the responsibility of caring for both parents in their old age is likely to fall on a single son or daughter. The structure of intergenerational coexistence has evolved over the past half-century under the influence of changes in the process of generation replacement. As a result, the roles of individual family members and the particular burdens they bear have also undergone considerable change. Today, families often have only one child, which results in the problem of a single child having to care for two aging parents. This is a mighty burden in terms of both economic and emotional sacrifice. Keyword: Generation、Mean Length of Generation、Life Course of Female 、Structure of Intergenerational Coexistence

共變數的值會隨著時間而改變時，我們稱之為時間相依之共變數。時間相依之共變數往往具有重複測量的特性，也是長期資料裡最常見到的一種共變數形態；在對時間相依之共變數進行重複測量時，可以考慮每次測量的間隔時間相同或是間隔時間不同兩種情形。在間隔時間相同的情形下，我們可以忽略間隔時間所產生的效應，利用分組的Cox模式或是合併的羅吉斯迴歸模式來分析，而合併的羅吉斯迴歸是一種把資料視為“對象 時間單位”形態的分析方法；此外，分組的Cox模式和合併的羅吉斯迴歸模式也都可以用來預測存活機率。在某些條件滿足下，D’Agostino等六人在1990年已經證明出這兩個模式所得到的結果會很接近。 當間隔時間為不同時，我們可以用計數過程下的Cox模式來分析，在計數過程下的Cox模式中，資料是以“對象 區間”的形態來分析。2001年Bruijne等人則是建議把間隔時間也視為一個時間相依之共變數，並將其以B-spline函數加至模式中分析；在我們論文的實證分析裡也顯示間隔時間在延伸的Cox模式中的確是個很顯著的時間相依之共變數。延伸的Cox模式為間隔時間不同下的時間相依之共變數提供了另一個分析方法。至於在時間相依之共變數的預測方面，我們是以指數趨勢平滑法來預測其未來時間點的數值；利用預測出來的時間相依之共變數值再搭配延伸的Cox模式即可預測未來的存活機率。 / It is so called “time-dependent covariates” that the values of covariates change over time. Time-dependent covariates are measured repeatedly and often appear in the longitudinal data. Time-dependent covariates can be regularly or irregularly measured. In the regular case, we can ignore the TEL(time elapsed since last observation) effect and the grouped Cox model or the pooled logistic regression model is employed to anlalyze. The pooled logistic regression is an analytic method using the“person-period”approach. The grouped Cox model and the pooled logistic regression model also can be used to predict survival probablity. D’Agostino et al. (1990) had proved that pooled logistic regression model is asymptotically equivalent to the grouped Cox model. If time-dependent covariates are observed irregularly, Cox model under counting process may be taken into account. Before making the prediction we must turn the original data into“person-interval”form, and this data form is also suitable for the prediction of grouped Cox model in regular measurements. de Bruijne et al.(2001) first considered TEL as a time-dependent covariate and used B-spline function to model it in their proposed extended Cox model. We also show that TEL is a very significant time-dependent covariate in our paper. The extended Cox model provided an alternative for the irregularly measured time-dependent covariates. On the other hand, we use exponential smoothing with trend to predict the future value of time-dependent covariates. Using the predicted values with the extended Cox model then we can predict survival probablity.