(资料收集与分析)

1、Data Collection and Analysis(資料收集與分析),By C. L. Hsieh Department of Industrial Management Aletheia University,Data Collection and Analysis,2,Introduction (介紹),“You can observe a lot just by watching” (你可以只以視覺方式來觀察許多數據) Data gathering results a conceptual model of how the system operated (資料收集可以產生一個觀念

2、式模型來解釋系統是如何運作的) Data gathering should avoid ending up with lots of data but with very little useful information (資料收集應避免最後留下一堆資料但無太多有用的資訊),Data Collection and Analysis,3,Questions for Data Gathering(資料收集的可能問題),What is the best procedure to follow? (資料收集的最佳程序為何?) What types of data should be gathered

3、? (哪些資料種類應被收集?) What sources should be used ? (資料的來源為何?) What types of analyses should be performed on the data? (資料應進行何種分析?) How do you select the right probability distribution representing the data? (如何找出代表資料的分配?) How should data be documented? (資料如何文件化?),Data Collection and Analysis,4,Guidelines

4、 for Data Gathering (資料收集應注意事項),Identify triggering events: (了解啟動活動原因) identify the causes or conditions that trigger the activities，e.g. the causes of downtime: failure, idle, unavailability of stock (了解啟動活動的原因或狀況，如停機原因：機器故障、閒置、缺貨 ) Look for common grouping (分群以化簡資料) the solution is to reduce the d

5、ata to common behaviors and patterns (化簡資料至一般行為與樣式) Identify general categories (確定一般性分類),Data Collection and Analysis,5,Guidelines for Data Gathering (資料收集應注意事項),Focus on key impact factors (處理主要影響因子) Avoid little impact information (e.g. off-hour performance, extremely rare downtime, negligible mo

6、ve time.) (避免影響性小的因素，如加班特例、罕見的機器故障、可忽略的移動時間.) Separate input variables from response variables (區分輸入變數與回應變數) Input variables define how the system works (輸入變數決定系統運作) Response variables do not “drive” model behavior,Data Collection and Analysis,6,Guidelines for Data Gathering (資料收集應注意事項),Focus on ess

7、ence rather than substance Capture cause-effect relationships and ignore meaningless details (著重因果關係，忽略細節) Focus on the activity of using resources or the delay of entity flow (system abstraction) (重視系統抽象層面) Isolate actual activity times. (確定真正活動時間) Exclude any extra time waiting (排除額外等候時間),Data Col

8、lection and Analysis,7,Steps to Gathering Data (資料收集的步驟),Determine data requirements (決定資料需求) Identify data resources (確定資料來源) Collect the data (收集資料) Make assumptions (建立假設) Analyze the data (收集資料) Document and approve the data (資料文件化與驗證),Data Collection and Analysis,8,Determining Data Requirements

9、(決定資料需求),Structural data (結構型資料) All the objects in the system to be modeled (系統中被建模的所有物件) Describe the layout of the system (結構型資料描述系統的佈置情形) Identify the items to be processed (e.g. entities, resources, locations.) (結構型資料確定被處理的項目，如實體、資源、工作站等),Data Collection and Analysis,9,Determining Data Requirem

10、ents(決定資料需求),Operational Data (作業型資料) Explain how the system operates (解釋系統如何運作) When, where and how events (顯現相同趨勢之序列，如向上或向下走勢),Data Collection and Analysis,29,Test for Independency (檢定資料獨立性的方法),Types of runs tests: if there are too many or too few, the randomness of the series is rejected. (趨勢出現次數

11、過多，則應棄卻隨機性假設) Median Test (中位數檢定法): measure the number of runs (sequences of numbers) above and below the median Turning Point Test(轉折點檢定法): measure the number of times the series changes directions,Data Collection and Analysis,30,Test for Homogeneity(齊一性檢定),Test for Identically Distributed Data): T

12、est if data set come from the same distribution. (同一分配檢定) Examples of non-homogenous data set (非齊一分配資料項實例) Activity times that take longer or shorter depending on the type of entity being processed (活動時間隨實體改變) Inter-arrival times vary in length depending on the time of the day or week (到達間隔時間隨時間改變而改

13、變),Data Collection and Analysis,31,Test for Homogeneity(齊一性檢定),Visually inspect the distribution to see if it has more than one mode (眾數) (p.118 Fig. 5.9) (可以使用視覺觀察是否有一個以上的眾數) Analysis of variance (ANOVA) for normally distributed data (以變異數分析決定是否為常態分配資料) Two-Sample test, Chi-square multi-sample test

14、, Kruskal-Wallis non-parametric test. (無母數分析法),Data Collection and Analysis,32,Test for Homogeneity(齊一性檢定),One type of nonhomogenous data occurs when the distribution changes over time Example of time-changing distribution (隨時間而變之分配) Learning Curve (學習曲線) Non-stationary or time variant (據時間變異性 Arriv

15、al rate of customers to a service facility (顧客到率),Data Collection and Analysis,33,Approaches for Stationary Data (穩定性測試),Non-stationary data can be detected by plotting subgroups of data that occur within successive time intervals (Fig 5.10) (非穩定性可以依連續時間區間描點資料子群組來觀察) Run Stat:Fit and see what distri

16、bution best fits each data set. If the same distribution fits both, the same population is assumed (執行Stat:Fit 檢查何種分配適合資料集),Data Collection and Analysis,34,Distribution Fitting (分配配對),Three ways of Data Representation (資料表示法) Original data record (原始資料) The data set is usually not large enough Empir

17、ical distribution (characterize data) (次數分配) Continuous frequency distribution (次數分配): the percentage of values that fall within given intervals (數值落在特定區間之比例),Data Collection and Analysis,35,Distribution Fitting (分配配對),Empirical distribution (characterize data) Discrete frequency distribution: the p

18、ercentage of times a particular value occurs. (特定值出現之次數的比例) Drawbacks (缺點) Insufficient sample size may create artificial bias (樣本數太少) Fail to capture rare extreme values that may exist in the population from which they were sampled (無法解釋少數臨界值),Data Collection and Analysis,36,Distribution Fitting (分

19、配配對),Theoretical distribution (理論分配) Fitting theoretical distribution to the data (找出一個適當的理論分配) Random variates (generated from the probability distribution provide the simulated random values. (由亂數產生程式產生隨機變量),Data Collection and Analysis,37,Distribution Fitting (分配配對),Theoretical distribution (理論分配

20、) Fitting a theoretical distribution to sample data smoothes artificial irregularities (理論分配緩和資料不規則行為) Ensure extreme values are includes (不排除臨界點) Most simulation software provide utilities for fitting distributions to numerical data (大多數模擬軟體提供公用程式來配對數值資料),Data Collection and Analysis,38,Theoretical

21、 Distribution (理論分配),Uniform Distribution (均一分配) (see p. 124) XU(a,b) with EX=(a+b)/2, VarX=(b-a)2/12 Used as a “first” model that is felt to be randomly varying between a time to complete a task in a PERT (可用於設備不良率，PERT中完成某工作之時間),Data Collection and Analysis,44,Theoretical Distribution (理論分配),Beta

22、Distribution (貝他分配) XBeta(1,2) Used as a rough model in the absence of data (可用於資料缺乏時的粗操模式上) Distribution of a random proportion, e.g. the proportion of defective items in a shipment; time to complete a task in a PERT (可用於設備不良率，PERT中完成某工作之時間),Data Collection and Analysis,45,Theoretical Distribution

23、(理論分配),Weibull Distribution (韋伯分配) XWeibull(,) Exp()=Weibull(1,) Used as time to complete some task or time to failure of a piece of equipements (完成工作時間、設備持續至故障的時間) Distribution of a random proportion, e.g. the proportion of defective items in a shipment; time to complete a task in a PERT (可用於設備不良率，

24、PERT中完成某工作之時間),Data Collection and Analysis,46,Fitting Theoretical Distribution (理論分配配對),Stat:Fit does a reasonable job of data fitting which ranks distribution. (Stat:Fit 可以提供一些合理的資料配對的排名分配 (p.127) Trial and Error Process (試誤法) Goodness of fit test evaluates each fitted distribution to ascertain th

25、e relative goodness of fit. (適合度檢定評估每個配對的分配來確定相關的適合度,Data Collection and Analysis,47,Fitting Theoretical Distribution (理論分配配對),Two common goodness of fit tests: 2 and Kolmogorov-Smirnov tests (兩種常見的適合度檢定： 2 檢定與 Kolmogorov-Smirnov 檢定) If little data are available, goodness of fit test is unlikely to

26、reject any candidate distribution (資料不足時，適合度檢定無法拒絕任何分配) Good idea to look at graphical display in a histogram (直方圖) before making decisions (作決定前，先看看直方圖視個好辦法),Data Collection and Analysis,48,Data Absence (缺乏資料),Most likely or Mean Value (最可能資料或平均值) About 10 customers arrivals per hour Approximately 20 mi