多變量製程能力指標在評估空氣品質上之比較研究－以台灣地區空氣污染資料為例

A Comparative Study on Evaluating Air Quality of Taiwan Using Various Multivariate Process Capability Indices

潘浙楠(Jeh-Nan Pan) ； 賴盛振(Sheng-Chen Lai) ； 李俊毅(Chun-Yi Lee)

《品質學報》 16卷1期 (2009/02) Pp. 1-13

摘要

地球生態環境在人類文明高度發展下，各種空氣、水源及土地污染所衍生的問題，導致全球性的危機。環境污染會對生態系統造成直接及間接的危害，如溫室效應、人體呼吸系統功能受損、影響植物的生長等。爲善盡地球環境保護的責任，以期達到全球永續發展 (global sustainability)，各國皆訂定相關的罰則以防止環境污染更進一步的惡化。因此如何有效監控環境品質並進行事前防範等措施，已成爲重要的研究課題。一般多變量製程能力指標如Niverthi and Dey (2000)均假設資料服從常態分配。然而空氣污染之資料並不一定服從常態性假設。因此，本研究以百分位數估計法結合田口二次損失函數的觀念，提出一個新多變量製程能力指標RND (Revised ND index)，再利用涵蓋率(coverage probability)進行各種多變量製程能力指標在反映空氣品質現況能力之比較及評估，研究結果顯示RND指標較其他學者所提出之多變量製程能力指標，更能正確反映空氣品質之現況。最後，本研究利用R程式撰寫一個應用程式來簡化RND指標的計算，並透過數值實例進一步說明我們提出之RND指標可及早偵出台灣地區空氣污染之狀況。

關鍵字

涵蓋率 ； 多變量製程能力指標 ； 百分位數估計法 ； 田口損失函數

並列摘要

With the advent of high-technology era, the problems of the air, water and land pollution have led to the crisis of global ecosystems, e.g., greenhouse effect, human respiratory system damage and plants damage. In order to further prevent the deterioration of environmental system and achieve global sustainability, major organizations and corporations around the world are starting to systematically review the environmental performance of their supplies based on the regulations stipulated by Environmental Protection Agency of each country. Therefore, how to monitor environmental performance becomes an important research issue. The multivariate process capability index established by Niverthi and Dey (2000) is based on the assumption of normality. However, the air pollution data may not follow normal distribution. In this paper, a novel RND index using percentile estimation as well as Taguchi's quadratic loss function is developed to relieve the normal assumption. Applying the concept of coverage probability, the results of our comparative study indicate that RND index can correctly reflect the actual air quality. Finally, a computer program using R language is developed to simplify the calculation of the RND index, and a numerical example further demonstrates that our proposed RND index can facilitate the early detection of air pollution in Taiwan.

並列關鍵字

multivariate process capability indices ； coverage probability ； percentile estimation ； Taguchi's quadratic loss function

參考文獻

潘浙楠、陳業統(2003)。雙變量製程能力指標在評估環境風險上之研究。中國統計學報。41(3)，321-350。

Andrews, D. F.,Gnanadesikan, R.,Warner, J. L.(1971).Transformations of multivariate data.Biometrics.27,825-840.

Box, G. E. P.,Cox, D. R.(1964).An analysis of transformations.Journal of the Royal Statistical Society, Series B.26(2),211-252.

Chan, L. K.,Cheng, S. W.,Spiring, F. A.(1988).A new measure of process capability: Cpm.Journal of Quality Technology.20(3),162-175.

Juran, J. M.(1974).Quality Control Handbook.New York:McGraw-Hill.