【正文】 arm. A false alarm occurs when a decision is made that a shift in the process has occurred when, in fact, nothing has changed. False alarm is known as Alpha error.偏離均值 177。2 σ 是過程均值改變的警示。假警是指根據(jù)設定的規(guī)則確定過程均值已改變，而實際并未改變。 A false alarm rate is the area in the normal distribution curve that lies outside of the decision limits.假警率是正態(tài)分布曲線超出判定范圍部份的面積。54 Missed Detection 漏檢漏檢 Missed detection occurs when a decision is made that a shift in process average has not occurred when, in fact, it has. Missed detection is known as Beta error. 漏檢是指根據(jù)設定的規(guī)則確定過程均值并未改變，而實際已改變。55 　 What is the chance that the process with a target of will give values in the future less than our sign post value of ?右圖表明當過程設定為 而偏離為 2σ時，過程均值將低于 設定值的概率．　 The shaded area behind the sign post value of decision limits is missed detection probability.判定判定 范圍標示線后的陰影部范圍標示線后的陰影部份即為份即為 漏檢率漏檢率 ．The Balance Between False Alarm And Missed Detection假警率與漏檢率的關(guān)系56　 The Balance Between False Alarm And Missed Detection假警率與漏檢率的關(guān)系A two Sigma decision rule carries a 5% false alarm rate. If 3 Sigma decision rule is used for the same process to reduce false alarm rate, it will increase missed detection rate.右圖表明當采用 177。 2σ為判定規(guī)則時，假警率約 5%. 而當采用 177。 3σ時，假警率會降低，漏檢率則會增加．57　 The Balance Between False Alarm And Missed Detection假警率與漏檢率的關(guān)系The shaded area of the curve behind the one sigma post is only 16%. However, for a one sigma decision rule, the false alarm rate will be 32%而當采用 177。 1σ時，右圖標示線后的陰影部份僅為 16% 假警率則高達 32%.58Precision And Missed Detection Rate精密度與漏檢率的關(guān)系Precision helps us overe the effects of false alarm and missed detection probability errors and allows us to detect process average change more sensitively.精密度有助于克復假警率與漏檢率的影響，能使我們更敏感地發(fā)現(xiàn)過程均值的變化．59 Improve The Ability To Discriminate Between Changes In Process Averages提高識別過程均值變化的能力單值和均值在同單值和均值在同一過程中顯示不一過程中顯示不同的離散度同的離散度The sensibility and ability to discriminate changes in process averages can be improved through subgrouping a process and calculating the statistics with the data from subgroups.以分組方法取樣，并以以分組方法取樣，并以分組分組 均值，總均值，及均值，總均值，及由由 分組均值變異度算得分組均值變異度算得的標準偏差提高識別過的標準偏差提高識別過程均值變化的能力程均值變化的能力 ．．60Improve The Ability To Discriminate Between Changes In Process Averages提高識別過程均值變化的能力?　　 The subgroup averages vary less, thus, control limits will be tighter。 ?　　 The variability of subgroup averages is related to the variability of the individual values by the square rootof the subgroup size.　　 分組均值離散度與單值分組均值離散度與單值離散度的量值關(guān)系離散度的量值關(guān)系:　 均值均值 標準差標準差(standard error of the mean)61Example: Significant Change In Process Average例例 :過程均值的顯著變化過程均值的顯著變化 A channel sales manager wants to check the performance of a newly hired sales representative who has had two months practice with the old sales representative. The manager arranges the new person to run the business without the old person’s help, and then pare his sales volume with the old person’s historical sales record. 銷售經(jīng)理為了評測新招聘的銷售員 (已隨老銷售員見習二個月 ) 的業(yè)務能力 , 將其開始獨立運作的一周銷量與老銷售員的業(yè)績記錄作統(tǒng)計分析．左表為原銷售員前 25 周的銷量．該新手第一周的銷量為 1125 箱。假設不 存在特殊原因存在特殊原因 (special cause), 你會對你會對 該新手的銷售業(yè)績作何評價？Week Sales Week Sales１ 1500 14 1975２ 1450 15 1275３ 1750 16 1850４ 1890 17 1900５ 1450 18 1875６ 1760 19 1600７ 1890 20 1350８ 2023 21 1975９ 2100 22 167510　 1850 23 193011 1700 24 170012 1600 25 167513 1350 2662Example: Significant Change In Process Average例例 :過程均值的顯著變化過程均值的顯著變化1267 21781125最近 25 周的銷量 2σ　 ＋ 2σ63 Example: Significant Change In Process Average例例 : 過程均值的顯著變化過程均值的顯著變化　Calculate key pieces of data　計算出過程數(shù)據(jù)： 均值： = 樣本標準偏差： S = 2 σ = – = 1267 　　　　　　　 1125 箱明顯低于　　　　　　　　　　　　　　該新手的業(yè)績與原業(yè)務代表的該新手的業(yè)績與原業(yè)務代表的 銷售業(yè)績存在顯著差距，可以銷售業(yè)績存在顯著差距，可以認為其認為其 業(yè)務能力未能達標．業(yè)務能力未能達標．統(tǒng)計均值 – 2 σ64謝謝！謝謝！謝謝觀看 /歡迎下載BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES. BY FAITH I BY FAITH