後山，也就是花蓮臺東地區，被稱為臺灣的最後一塊淨土。相對來說，交通並不是那麼的方便，西部有兩條高速公路、一條高速鐵路以及多條省道。但東部僅有兩條省道，因此火車成為東部重要的交通工具，然而在班次量不足以及班次分佈不均的情況下，一位難求的情況十分常見。本論文將分析衡量載客比率的統計量-客座利用率(Efficiency of Seat Utilization，簡稱為ESU)，此統計量可分析特定班次在某些時段以及平日假日的客座利用率變動狀況。事實上列車會因為車種(車型)、時段、行駛區間、停靠站的不同，造成訂票難度亦不相同。在此研究中，我們探討臺鐵屏東線(高雄-枋寮)、南迴線(枋寮-臺東)、以及臺東線(臺東-花蓮)所有對號列車(limited express)之客座利用率變動狀況。並根據不同車種、不同停靠站等諸多因素進行集群分析(Cluster Analysis)，將某路線上的班次做分類。而本論文也將對於不同類型的連續假期，探討加班車之安排是否妥適之相關議題，根據特定列車的變動曲線，使用縱斷面分析(ProfileAnalysis)來判斷加班車是否有效，可給予臺鐵日後加開班車之參考，避免發生尖峰時段車次大爆滿，加班車卻幾乎空車的現象發生。

The east coast of Taiwan between Hualien and Taitung has been called the last paradise of Taiwan. Comparing to the west, the traffic is the east obviously is short of convenience. As we know in the west, there are two national highways, one provincial highway, one high speed rail, and many other high roads, while there is only one provincial highway in the east. Therefore train is very important transportation in the east of Taiwan. However, the number of trains is insufficient and the distribution of train schedule is not uniformly arranged as needed. It is hard for people to buy tickets with reserved seats especially during the holidays. This study is based on the Efficiency of Seat Utilization(ESU) aiming at finding the corresponding trends and variations of ESU in some time intervals and between the weekday and holiday. In fact, booking success rates are influenced by train types, time intervals, and train stops. In this work we discuss ESU for all limited express in three lines of Taiwan Railways Administration(TRA): Pingtung Line(Kaohsiung-Fangliao),
South Link Line(Fangliao-Taitung), Taitung Line(Taitung-Hualien). According to different train types, train stops and many other factors, we use cluster analysis to do classification of all trains in the three lines. For different types of long holidays, we explore relevant issues of timetable arrangement for addition trains whether they are appropriate or not. According to the profile of a particular train,the profile analysis has been used to determine whether the ”addition train” is effective in reducing the overbooking situations. Through this study we would like to provide some useful guidelines on the train scheduling for the TRA. It is hoped that it may help to avoid situations that there is no seat available for trains in the peak hours, but the addition trains are almost empty.

論文審定書　i
誌謝　ii
摘要　vi
Abstract 　vii
1 研究動機與目的　1
2 客座利用率資料介紹　2
　2.1 行駛路線以及車種介紹　2
　2.2 鐵路統計名詞介紹　3
　2.3 資料型態　4
　2.4 客座利用率計算　5
　2.5 缺值判斷以及處理　9
3 實證分析　15
　3.1 改點前後檢定　15
　3.2 各列車經各車站的客座利用率波動檢定　17
　3.3 加班車效果檢定　19
4 結論與討論　22
　4.1 結論　22
　4.2 討論　22
　　4.2.1 客座利用率的優缺點　22
　　4.2.2 客座利用率於不賣站票之列車討論　24
5 參考文獻　27
6 附錄A 　28
　6.1 統計理論與方法　28
　　6.1.1 雙樣本縱斷面分析　28
　　6.1.2 多樣本縱斷面分析　31
　　6.1.3 集群分析　34
　6.2 實例　35
　　6.2.1 改點前後檢定　35
　　6.2.2 各列車經各車站的利用率波動檢定　38
7 附錄B 　41
　7.1 南迴臺東線各車站營業里程表　41
　7.2 改點前後檢定所有班次(含起訖站時刻表) 　42
　　7.2.1 改點前後所有班次-縱斷面圖比較　42
　　7.2.2 改點前後所有班次-檢定結果　51
7.3 各列車經各車站的利用率波動(含主要車站時刻表) 　57
　　7.3.1 所有班次經各車站-縱斷面圖比較　57
　　7.3.2 所有班次經各車站-檢定結果　75
　　7.3.3 臨時加班車案例(莒光5703次、莒光5722次) 　81

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Statistical Learning with Applications in R. Springer-Verlag. New York.
[2] Rencher, A. C. (2002). Methods of Multivariate Analysis, 2nd edition. Wiley, New
York.
[3] 鍾志成、李治綱、賴勇成、盧麗嵩、黃笙玹、張仕龍、張恩輔、林志偉、林蓁、蘇振維、劉昭榮(2013)。2013年臺灣鐵道容量手冊，交通部運輸研究所。
[4] 交通部臺灣鐵路管理局-北迴線自強號利用率http://www.railway.gov.tw/tw/CP.aspx?sn=7461.
[5] 交通部運輸研究所http://www.iot.gov.tw/.