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【正文】 SixSigma Training Book Dec 18 ,20231BPTL Confidential 6σ推行教材4 數(shù)據(jù)分布2BPTL Confidential 6σ推行教材4 NormalExponentialWeibullLognormaltc2fContinuous DistributionsSampling Distributions數(shù)據(jù)分布3BPTL Confidential 6σ推行教材The most widely used model for the distribution of continuous random variable.Arises in the study of numerous physical phenomena, such as the velocity of molecules.正態(tài)分布Plot is known as Probability Density Functionof X4BPTL Confidential 6σ推行教材4 Many natural 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。 Variance (?2)正態(tài)分布的一些特性Distribution OneDistribution TwoDistribution ThreeWhat is the difference between the 3 normal distributions?X ~ N(?, ?2)18BPTL Confidential 6σ推行教材A~Normal(?A,?A178。) B~Normal(?B,?B178。) A~Normal(?A,?A178。)B~Normal(?B,?B178。)A~Normal(?A,?A178。)B~Normal(?B,?B178。)What is the difference between process A B for each case?正態(tài)分布的一些特性9BPTL Confidential 6σ推行教材4 The mean, median and mode all coincide at the same value ?. There is perfect symmetry.181。+ 165。 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 midd
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