醫院工務部門在每年度都會預先編列下一年度的維護預算。如何根據醫院本身所累積的歷年維護費用資料，來發展一客觀且精確之維護費用預測模型是本研究的重要課題。灰色模型可以針對某個系統趨勢進行預測，而且用很少之歷史數據即可達到精確的預測精確度。本研究為提供醫院工務部門一客觀且精確的預測方法，有以下二目的：(1)探討醫院設施維護費用之分佈趨勢與特性；(2) 以四種灰預測模型（傳統灰模型、指數傳統灰模型、改良灰模型、及指數改良灰模型）進行醫院設施維護費用的預測，比較四種預測方法的精確度，及評估在預測下一年度醫院維護費用之適用性。

本研究以台北某一大型醫院之86年~95年歷史維護費用資料為對象進行：(1)以描述統計方法對醫院歷年維護費用進行分佈特性分析；(2)經由上述四種灰色模型之預測精確度來評估與比較四種灰色模型在預測下一年度醫院設施維護費用之適用性。

研究結果顯示：一、醫院設施總維護費用年均587元/m2．年，其歷年維護費用分佈之規律性小及離散程度大。各類維護費用佔總維護費用比例，以保養維護費用最多（41%），平均243元/m2．年；整建更新費用次之（34%），平均198元/m2．年；故障修理費用最少（25%），平均141元/m2．年。二、本研究使用之四種灰色模型在4年歷史費用建模~7年歷史數據建模、以及既有數據建模下，其預測之平均絕對殘差高達23.4%~35.2%，表示預測誤差大；而在8年歷史費用建模及9年歷史費用建模時，其平均絕對殘差只有0.01%~11.6%。顯示8年歷史費用建模及9年歷史費用建模時可得到較高之預測精確度。四種灰色模型在8年歷史費用及9年歷史費用下之平均絕對殘差比較下，「指數傳統灰模型」及「指數改良灰模型」之平均絕對殘差只有3.7%小於「傳統灰模型」及「改良灰模型」之平均絕對殘差6.0%。顯示「指數傳統灰模型」及「指數改良灰模型」在8年歷史數據建模及9年歷史數據建模時，較適合用於醫院預測下一年度維護費用預算。

Hospital facility management department will compile the maintenance budget of the next year in advance every year. The important subject of this research is how to use hospital maintenance costs to develop a impersonal and accurate maintenance cost prediction model. Gray model can predict the trend of the system, and can reach a accurate prediction with few historical data. In order to provide hospital facility management department a impersonal and accurate prediction model, this research have two purposes: (1) Probe the distribution trend and characteristic of hospital facility management cost; (2) Predict the hospital facility management cost by the four gray model (traditional gray model, traditional gray model combine with exponential smoothing method, improvement gray model, improvement gray model combine with exponential smoothing method). To compare with the result of the four gray model, and to estimate the applicability of predicting the next year cost of the hospital facility management.

This research is operated by the facility management cost data during 86 to 95 year of a large hospital in Taipei. (1)Analyze the distribution trend and characteristic of historical facility management cost data by statistics; (2)Compare with the result of the four gray mode, and to estimate the applicability of predicting the next year cost of the hospital facility management.

This study shows that: first, the distribution characteristic of hospital facility maintenance costs is NT 587/m2．year, and shows little regularity and large dispersion. The proportion of total maintenance costs of various types is that preventive maintenance costs is the hightest （41%）(NT 243/m2．year), and corrective maintenance costs is the second （34%） (NT 198/m2．Year), and breakdown maintenance costs is the fewest （25%） (NT 141/m2．year). Second, the four gray models can get high accuracy in 8 datas and 9 datas of history expense modeling, and the other modeling methods get low accuracy. The model of traditional gray model combine with exponential smoothing method and improvement gray model combine with exponential smoothing mothod in 8 datas and 9 datas of history expense modeling are the highest precision accuracy enough to suit to be the prediction model of hospital facility management budget of the next year.

1.Boussabaine, A.H. and Kirkham, R.J. (2004), Simulation of maintenance costs in UK local authority sport centres. Construction Management and Economics, 22(10), 1011-1020.
2.Chen, Y.L. and Azzam, R. (2007). Creep fracture of sandstones. Theoretical and Applied Fracture Mechanics, 47, 57-67.
3.Edwards, D.J., Holt, G.D. and.Harris, F.C. (2000). A model for predicting plant maintenance costs. Construction Management and Economics, 18(1), 65-75.
4.Edwards, D.J., Holt, G.D. and.Harris, F.C. (2000). Estimating life cycle plant maintenance costs. Construction Management and Economics, 18(4), 427-435.
5.Edwards, D.J. and Holt, G..D. (2001). Predicting construction plant maintenance expenditure. Building Research & Information, 29(6), 417-427.
6.EI-Assaly, A., Ariaratnam, S.T., Ruwanpura, J. and Ng, H. (2006). Cost forecast model for sewer infrastructure. Proceedings of the institution of Civil Engineers, Municipal Engineer, 159(3), 155-160.
7.Hao, Y. et al. (2006). A gray system model for studying the response to climatic change: The Liulin karst springs, China. Journal of Hydrology, 328, 668-676.
8.Leephakpreeda, T. (2008). Grey prediction on indoor comfort temperature for HVAC systems. Expert Systems with Applications, 34, 2284-2289.
9.Liang, J. and Zuo, H.F. (2004). The predictive models of maintenance costs for a civil airplane. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 218(5), 347-351.
10.Lin, C.T. and Yang, S.Y. (2003). Forecast of the output value of Taiwan’s opto-electronics industry using the Grey forecasting model. Technological Forecasting & Social Change, 70, 177-186.
11.Lin, Y.F. (2001). A novel method of residual recognition to increase forecast precision of grey model. National Conference of Grey Theory And Applications, A-65-A-71.
12.Mao, M. and Chirwa, E.C. (2006). Application of grey model GM(1,1) to vehicle fatality risk estimation. Technological Forecasting & Social Change, 73, 588-605.
13. Wang, M.H. and Hung, C.P. (2003). Novel grey model for the prediction of trend of dissolved gases in oil-filled power apparatus. Electric Power Systems Research, 67, 53-58.
14.Wu, A.X. et al. (2007). Study on Grey Forecasting Model of Copper Extraction Rate with Bioleaching of Primary Sulfide Ore. Acta Metallurgica Sinica (English Letters), 20(2), 117-128.
15.Yao, W.L., Chi, S.C. and Chen, J.H. (2003). An improved Grey-based approach for electricity demand forecasting. Electric Power Systems Research, 67, 217-224.
16.日本醫療秘書教育全國協議會編，謝水林譯(2002)。醫院管理，國興出版社，新竹市。
17.王學萌、聶宏聲、李晉陵、雷錦霞(1989)。灰色系統模型在農村經濟中的應用，華中理工大學出版社，武漢。
18.王義鬧等人(2002)。一種逐步優化灰導數白化值的GM(1,1)建模方法。系統工程理論與實踐，第9期，pp.128-131。
19.田自力、陳碩珮(1996)。GM(1,1)模型之傅立葉級數殘差修正法。1996年第一屆灰色系統理論與應用研討會，pp.93-101。
20.田自力、劉碧發(1996)。灰色馬爾可夫鏈預測模型。1996年第一屆灰色系統理論與應用研討會，pp.157-162。
21.史玉峰、寧津生(2005)。指數平滑法改進灰色模型及在形變數據分析中的應用。煤炭學報，第30卷第2期，pp.206-209。
22.李秉展(2008)。創新灰色模型在營建工程應用之研究，國立台灣科技大學營建工程系博士論文。
23.吳漢雄、鄧聚龍、溫坤禮(1996)。灰色分析入門，高立圖書有限公司，台北市。
24.陳弘旭、張偉哲(2000)。GM(1,1)模型之指數級數殘差修正法。2000年第五屆灰色系統理論與應用研討會，pp.339-344。
25.陳亮、田德寶(2006)。GM(1,1)背景值重構模型在體育中的應用研究。首都體育學院學報，第18卷第6期，pp.127-128。
26.張真卿、李美燕（2007）。一看就懂編列預算。台灣廣廈出版集團，台北縣。
27.鄧聚龍、郭洪(1996)。灰預測原理與應用，全華科技圖書股份有限公司，台北市。
28.鄧聚龍著，淡江大學電機系校閱(2000)。灰色系統理論與應用，高立圖書有限公司，台北市。
29.鄭達才(2000)。設備維護管理─現在與未來。中國生產力中心，台北市。
30.鄭永勝(1992)。也談灰色GM(1,1)模型預測精度問題。地下水，第14卷第3期，pp.154-156。
31.鍾秋梅、任震(2006)。基于改進灰色模型的電力系統可靠性原始參數預測。中國高等學校電力系統及其自動化專業第二十二屆學術論文摘要集。
32.譚冠軍(2000)。GM(1,1)模型的背景值構造方法和應用(I)。系統工程理論與實踐，第4期，pp.98-103。
33.藍永超等人(2003)。黑河流域水資源動態變化及其趨勢的灰色Markov鏈預測。中國沙漠，第23卷第4期，pp.435-440。