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【正文】 tural phenomena and manmade processes are observed to have normal distributions, or can be closely represented as normally distributed.4 For example, the length of a machined part is observed to vary about its mean due to:– temperature drift, humidity change, vibrations, cutting angle variations, cutting tool wear, bearing wear, rotational speed variations, fixturing variations, raw material changes and contamination level changes4 If these sources of variation are small, independent and equally likely to be positive or negative, the length will closely approximate a normal distribution.正態(tài)分布5BPTL Confidential 6σ推行教材4 First introduced by French mathematician Abraham DeMoivre in 1733.4 Made famous in 1809 by German mathematician . Gauss when he also developed a normal distribution independently and used it in his study of astronomy.4 As a result, it is also known as the Gaussian distribution.4 During mid to late nieenth century, many statisticians believed that it was “normal” for most wellbehaved data to follow this curve.正態(tài)分布 歷程表Karl Friedrich Gauss6BPTL Confidential 6σ推行教材4 正態(tài)分布易于理解 , 具有特性 , 統(tǒng)計(jì)學(xué)提供了許多基于正態(tài)分布的強(qiáng)有力的分析方法來幫助人們做決定 .4 因此 , 我們通常會(huì)試圖用正態(tài)分布去近似模擬其它分布 (如可能 ) 或轉(zhuǎn)化數(shù)據(jù)以 “使 ”它遵從正態(tài)分布 .4 它是分析過程能力的首選分布形式 .正態(tài)分布7BPTL Confidential 6σ推行教材4 A normal distribution can be pletely described by knowing only the:216。 Mean (?)216。) B~Normal(?B,?B178。)B~Normal(?B,?B178。)B~Normal(?B,?B178。+ 165。 MeanMedianMode2The mean represents the arithmetic average of all observations in a data set.If a set of observations is arranged in an increasing order of magnitude (ranked data), the middle value is called the median.l If the number of observations is odd, the median is the value of the middle number.l If the number of observations is even, there are 2 middle numbers, and the median is the average of the 2 values.The mode is the observation that occurs most frequently in the sample.正態(tài)分布的一些特性10BPTL Confidential 6σ推行教材4 The area under sections of the curve can be used to estimate the cumulative probability of a certain “event” occurring:181。 165。 165。 165。 165。 Probability Distributions 240。 意即工序運(yùn)作處于 統(tǒng)計(jì)控制狀態(tài) , 換言 之 ,普遍的原因是變化的僅有來源 .216。 過程的跟蹤表現(xiàn)來証實(shí)它是否建立了長(zhǎng)時(shí)間穩(wěn)定的數(shù)據(jù)分布表現(xiàn) ,典型地 , 用帶有 “僅從工序中的數(shù)據(jù)計(jì)算出的 ”控制圖表 . 216。 “好處 ” 是工序能力可被度量216。 度量一個(gè)穩(wěn)定的工序狀態(tài) (受控制 )在多大程度上能滿足客戶的規(guī)格 .30BPTL Confidential 6σ推行教材變化的類型固有的或定值的變化4許多微小又不可避免的原因?qū)е碌睦鄯e效果4只有微小的機(jī)會(huì)導(dǎo)致變化的運(yùn)作工序稱為 “統(tǒng)計(jì)控制 ” 31BPTL Confidential 6σ推行教材變化的類型特定或確定的變化4 可能由于 a) 不正確的調(diào)機(jī) b) 操作者錯(cuò)誤 c) 有缺陷的原材料4 一個(gè)工序如果出現(xiàn)上面的變化則稱為 “失控 ” .32BPTL Confidential 6σ推行教材工序能力工序能力 研究能 : 4顯示工序輸出的恒定性4顯示輸出符合規(guī)格的程度4用于和另一工序或競(jìng)爭(zhēng)對(duì)手比較33BPTL Confidential 6σ推行教材工序能力與規(guī)格極限a) b)c)a) 工序能力高b)工序能力能夠滿足c)工序能力不足夠34BPTL Confidential 6σ推行教材三種極限類型 規(guī)格極限 (LSL and USL) 4 created by design engineering in response to customer
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