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1、工程方法sigma概率分布演示文稿1MPT Confidential1页，共81页，星期一。优选工程方法sigma概率分布2MPT Confidential2页，共81页，星期一。Learning ObjectivesLearning Objectives学习目的学习目的学习目的学习目的What is a Probability Distribution? 什么是概率分布什么是概率分布?Experiment, Sample Space, Event 实验,样本空间,事件Random Variable, Probability Functions (pmf, pdf, cdf)随机变量,概率函数
2、Discrete Distributions离散分布离散分布Binomial Distribution 二项式分布Poisson Distribution 泊松分布.Hypergeometric distribution 超几何分布Continuous Distributions连续分布连续分布Normal Distribution 正态分布Uniform distribution 均匀分布Exponential distribution 指数分布Logarithmic normal distribution 对数正态分布Weibull distribution 威布尔分布Sampling D
3、istributions样本分布样本分布Z Distribution Z 分布t Distribution t 分布2 Distribution 2 分布F Distribution F 分布3MPT Confidential3页，共81页，星期一。As we progress from description of data towards inference of data, an important concept is the idea of a probability distribution.当我们从描述性数据进步到推论性数据时,一个重要的内容就是概率分布的概念.To apprec
4、iate the notion of a probability distribution, we need to review various fundamental concepts related to it:为了解概率分布的概念, 我们需要复习各种基本相关概念:Experiment, Sample Space, Event实验,样本空间,事件Random Variable 随机变量.What is a Probability Distribution?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?Wh
5、at do we mean by inference of data?4MPT Confidential4页，共81页，星期一。Experiment实验实验An experiment is any activity that generates a set of data, which may be numerical or not numerical.实验是产生一系列数据的行为,数据有可能是数字的或非数字的.1, 2, ., 6(a)Throwing a dice掷骰子Experiment generates numerical / discrete dataPinsStainsReject
6、Accept(b)Inspecting for stain marks检检查污点印记查污点印记Experiment generates attribute dataPins(c)Measuring shaft 测量 轴径10.53 mm10.49 mm10.22 mm10.29 mm11.20 mmExperiment generates continuous dataWhat is a Probability Distribution?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?实验产生数字实验产生数字/
7、离散数据离散数据实验产生计数性数据实验产生计数性数据实验产生连续性数据实验产生连续性数据5MPT Confidential5页，共81页，星期一。Random Experiment 随机实验随机实验If we throw the dice again and again, or produce many shafts from the same process, the outcomes will generally be different, and cannot be predicted in advance with total certainty.如果我们掷子一次由一次,或从相同工序生
8、产许多轴,结果会是不同的.不能完全提前预测.An experiment which can result in different outcomes, even though it is repeated in the same manner every time, is called a random experiment.一个实验导致不同的结果,即使它是每次以相同方式,这叫做随机实验What is a Probability Distribution?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?6MPT
9、 Confidential6页，共81页，星期一。Sample Space样本空间样本空间The collection of all possible outcomes of an experiment is called its sample space.收集实验的所有可能结果称为样本空间Event事件事件An outcome, or a set of outcomes, from a random experiment is called an event, i.e. it is a subset of the sample space.一个结果,或一套结果,从一个随机实验出来的称为事件,
10、也就是样本空间的子集What is a Probability Distribution?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?7MPT Confidential7页，共81页，星期一。Event事件事件Example例 1: Some events from tossing of a dice.从掷骰子的一些事件.Event 事件1: the outcome is an odd number 结果是奇数Event事件 2: the outcome is a number 4 大于4的结果Exampl
11、e例 2: Some events from measuring shaft :从测量轴径的一些事件Event事件 1: the outcome is a diameter mean直径大于平均值Event 事件2: the outcome is a part failing specs.未通过规格的结果. E2 = x USL E2 = 5, 6 E1 = 1, 3, 5 E1= x What is a Probability Distribution?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?8MPT
12、 Confidential8页，共81页，星期一。Random Variable随机变量随机变量From a same experiment, different events can be derived depending on which aspects of the experiment we consider important.从一个相同的实验, 由于我们认为重要的实验方面不同而产生不同的结果In many cases, it is useful and convenient to define the aspect of the experiment we are interes
13、ted in by denoting the event of interest with a symbol (usually an uppercase letter), e.g.: 许多方面,它是很有用和方便的定义我们感兴趣的实验方面, 通过一个大写的字母表示.举例说明:Let X be the event “the number of a dice is odd”.用X代表事件”骰子的数字是奇数”Let W be the event “the shaft is within specs.”.用W代表事件”轴径尺寸在规格内”What is a Probability Distribution
14、?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?9MPT Confidential9页，共81页，星期一。Random Variable随机变量随机变量We have defined a function that assigns a real number to an experimental outcome within the sample space of the random experiment.我们定义了一个函数,其代表了一个在随机实验的样本空间的一个真实实验数字This function (X
15、 or W in our examples) is called a random variable because: 函数(例子中的X 或W )称为随机变量,是因为:The outcomes of the same event are clearly uncertain and are variable from one outcome to another一个事件的发生结果是明显不定的,是同另一个结果相异的.Each outcome has an equal chance of being selected.每一个结果有相同被选择的机会.PinsMeasuring shaft X = Pa
16、rts out of specs.(LSL = 8 mm,USL = 10 mm)0.,7.99998, 7.99999, 8, 8,00001,9.99999, 10, 10.00001, 10.00002, LSLUSLWhat is a Probability Distribution?What is a Probability Distribution?什么是概率分布什么是概率分布什么是概率分布什么是概率分布? ?10MPT Confidential10页，共81页，星期一。Probability概率概率To quantify how likely a particular outcome of a random variable can occur, we typically assign a numerical value between 0 and 1 (or 0 to 100%).为量化一个随机变量的指定结果发生的可能性,我们指定一个数字介于0和1之间(或0100%)This numerical value is called the probability of th
