模擬輸出分析下的不完全批次效應

Incomplete Batch Effects in Simulation Output Analysis

黃鈴琇(Ling-Hsiu Huang)

指導教授 ： 葉英傑 ； 陳家祥

元智大學/管理學院/企業管理學系/碩士(2004年)

摘要

本研究針對模擬輸出分析中的批次法，探究不完全批次效應。一般來說，在處理具有相關性的樣本資料時，最常用的方法即批次法（batching method）。批次法的原理乃是透過分組之概念將原始資料的相關關係呈現在組內，而組間彼此獨立，以求樣本符合獨立且具相同分配的特性（iid），繼而能以初級的統計方法計算。但從過去批次法的探討裡，卻發現研究的假設前提為資料可以完全均勻分配至每一組批次裡，此點與現實情形不符，實際處理上常存在最後一組不完全批次（Incomplete batch）；試想之，當該組不完全批次內所含的資訊量逼近一個完全批次，或當各筆資訊得來不易時，不完全批次是否會棄之可惜或造成關鍵性的影響是令人存疑的。
因此本研究修正該假設，以不完全批次存在為前提，針對「考量不完全批次與否」分成兩種情境，重新進行樣本平均變異數的估計式推導，進而驗證估計式是否合乎統計不偏特性，並推算變異數。經由研究結果發現，利用布朗運動和漸進變異數的相關研究，推導出估計式修正係數，再以此為基礎進行運算，得知估計式可轉換為卡方分配的型態，並利用卡方分配與期望值的關係，證實估計式符合不偏特性，具備好的統計特性，由最終量化效果的整理，得知當我們透過處理，將不完全批次賦予適當的權重時，可有效的降低誤差比例，得到較精準的結果，同時從均方誤差和信賴區間均可發現考量不完全批次有其必要性。總結而言，本研究站在合乎現實的資料分組情況下，推導新估計式，作為協助系統效能評判的標準，提供更準確的分析數值，使得具有相關性的資料，如等候線賦予更有意義的解讀，使企業資源做更有效之規劃應用。

關鍵字

蒙地卡羅模擬 ； 標準誤差 ； 批次法

並列摘要

This research addresses the issue of the incomplete batch arising from estimating the quality of the sample mean from a stochastic simulation experiment by batching method. Batching method is a conceptually straightforward approach, which divides observations in groups in a way that each batch contains the correlation structure of an output process. Incomplete batch is a practical situation in which number of observations in the last batch is different from those in previous batches. However, researches in batching method often ignore the existence of incomplete batch for analytic simplicity.
Our study revises the assumption that the incomplete batch does not exist. We construct two new estimators of variance of the sample mean: one discarding the observations contained in the incomplete batch and the other considering all of the observation contained in that with a proper weight. We use large sample theory to derive distributions of new variance estimator. We show that both of our new estimators are asymptotically unbiased and the variance of the estimator considering observations contained in the incomplete batch is smaller than that of the estimator discarding observations contained in the incomplete batch. Moreover, we study analytically to quantify the effect of incomplete batch for confidence-interval estimation by using these two estimators.

並列關鍵字

Monte Carlo Simulation ； Standard Error ； Batching Estimator

參考文獻

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