《精品》工程方法_6 sigma_13.概率分布.ppt

Event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,也就是样本空间的子 集
E1 = {1, 3, 5}
➢ Event事件 2: the outcome is a number > 4 大于4的结果
E2 = {5, 6}
• Example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
E1= {x > m}
➢ Event 事件2: the outcome is a part failing specs.未通过规格的结果.
E2 = {x < LSL, x > USL}
0.0
Page 7
What is a Probability Distribution? 什么是概率分布?
Random Variable随机变量 • From a same experiment, different events can be derived depending on which
• 为了解概率分布的概念, 我们需要复习各种基本相关概念: What do we mean by
➢ Experiment, Sample Space, Event
inference of data?
➢ 实验,样本空间,事件
➢ Random Variable 随机变量.
0.0
Page 3
What is a Probability Distribution? 什么是概率分布?
0.0
Page 6
What is a Probability Distribution? 什么是概率分布?
Event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
• 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
Measuring shaft Pins
X = Parts out of specs.
(LSL = 8 mm, USL = 10 mm)
LSL
0..,7.99998, 7.99999, 8, 8,00001,…, 9.99999, 10, 10.00001, 10.00002, …
• 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 appreciate the notion of a probability distribution, we need to review various
fundamental concepts related to it:
• Discrete Distributions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
➢ Normal Distribution
实验产生数字/离散数据
Experiment generates numerical / discrete
data
实验产生计数性数据
Experiment generates attribute data
实验产生连续性数据
Experiment generates continuous data
0.0
Page 4
➢ Z Distribution
Z 分布
➢ t Distribution
t 分布
➢ c2 Distribution
c2 分布
➢ F Distribution
F 分布
0.0
Page 2
What is a Probability Distribution? 什么是概率分布?
• As we progress from description of data towards inference of data, an important concept is the idea of a probability distribution.
(a) a dice
掷骰子
Inspecting for
(b)
Байду номын сангаас
stain marks检 查污点印记
Pins
Measuring
(c) shaft
测量 轴径 Pins
{1, 2, .., 6}
Stains
Accept
Reject
10.53 mm 10.49 mm 10.22 mm 10.29 mm 11.20 mm ……
0.0
Page 9
What is a Probability Distribution? 什么是概率分布?
Probability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
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
• 有几种方式解释概率.一般的方式是解释概率为在许多相同实验重复后发生的分数 (或比例)次数 ➢ This method is the relative frequency approach or frequentist approach to interpreting probability. ➢ 这种方法概率解释的相对频率模拟或单位频率模拟
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 Distributions样本分布
➢ 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”
0.0
Page 8
What is a Probability Distribution? 什么是概率分布?
we are interested 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:
0.0
Page 5
What is a Probability Distribution? 什么是概率分布?
Sample Space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
Probability Distributions 概率分布
0.0
Page 1
Learning Objectives学习目的
• What is a Probability Distribution? 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
0~100%) ➢ This numerical value is called the probability of the outcome. ➢ 这个数字称为结果的概率
• There are a few ways of interpreting probability. A common way is to interpret probability as a fraction (or proportion) of times the outcome occurs in many repetitions of the same random experiment.
Random Variable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.
USL
• This function (X 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.
Tossing a dice摇骰子
{1, 2, 3, … 6}
Inspecting for stain marks 污点痕迹检查
Measuring shaft f轴径测量
{Pass, Fail}通过,不通过
{All values between 0 and max. possible f, say, 10mm} 所有值在0和最大值,可能的轴径,例如:10mm
Experiment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.
Throwing
What is a Probability Distribution? 什么是概率分布?
Random Experiment 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
page22cumulativedistributionfunction累计分布函数dxnormaldistributionprobabilitydensityfunction概率密度函数normaldistributionnormaldistribution正态分布正态分布page23probabilitymassfunctioncumulativedistributionfunctioncumulativedistributionfunction累计分布函数累计分布函数cumulativedistributionfunction累计分布函数page24commonprobabilitydistributionscommonprobabilitydistributions常用概率分布常用概率分布discretedistributions离散分布uniform均匀分布binomial二项式分布geometric几何分布hypergeometric超几何分布poisson泊松分布continuousdistributions连续分布uniform均匀分布normal正态分布exponential指数分布weibull威布尔分布erlanggammalognormal对数正态分布theoreticallyderiveddistributionsusingcertainrandomexperimentsfrequentlyarise理论上讲分布是随机实验大量应用得来的modeloutcomesphysicalsystemsbehavesimilarlyrandomexperimentsused通常自然系统模型输出近似于随机实验page25importantimportantdiscretedistributionsdiscretedistributionsbinomialdistribution二项式分布poissondistribution泊松分布page26binomialdistributionbinomialdistribution二项式分布二项式分布page27binomialexperiment二项式实验assumingwehavehistoricallyknownrejectrate