The Hypergeometric Distribution N number of units in
The Hypergeometric Distribution N = number of units in the lot (population) n = number of units in the sample D = number of noncomforming units in the lot x = number of noncomforming units in the sample 1
The Hypergeometric Distribution 1. It is the appropriate probability model for sampling from an finite number of lot of N items) population). )เปนตวแบบการกระจายความนาจะเปนท ใชสำหรบการสมตวอยางจา กลอตททราบขนาดปร ะชากร). 2
The Hypergeometric Distribution (P. 3) A lot of 9 thermostats located in a container has 3 nonconforming units. What is the probability of drawing(ความนาจะเปนในการสมหยบ ) 1 nonconforming unit in a random sample of 4? Lot Sample sampling Conforming Unit N=9 D=3 n=4 x=1 Nonconforming unit 3
The Hypergeometric Distribution (P. 4) If a lot contains 100 items, 5 of which do not conform to requirements. If 10 items are selected at random without replacement, what is the probability of finding one or fewer nonconforming items in the sample )หาความนาจะเปนทจะพบของเสยหนงชนหรอนอยกวานน ( 4
The Poisson distribution λ = average count or average number of events (or nonconforming products) per unit x = count or number of events (nonconforming products) per unitp is the proportion (fraction) or fraction nonconforming in population 5 e = 2. 718281
The Poisson Distribution Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 7
Estimation of the Binomial distribution using the Poisson distribution 1. the Poisson distribution can be derived as a limiting form of the binomial distribution if the number in a sample (n) is very large and the proportion (fraction) or fraction of nonconforming (p) is very small 10
Estimation of the Binomial distribution using the Poisson distribution Consider the binomial distribution Let = np so that p = /n. We may now write the binomial distribution as if n→ ∞ and p → 0, the terms and → 1 11
Estimation of the Binomial distribution using the Poisson distribution 12
Estimation of the Binomial distribution using the Poisson distribution (P. 7) ถาโรงงานผลตหลอดไฟพบวามหลอดเสยอย 100 หลอดจงหาความนาจะเปนทจะมหลอดเสย 3% ถาสมหลอดไฟ 5 หลอด (in this case p = 0. 03, and n =100; we can assume that n is large and p is very small or n→ ∞ and p → 0 so that we can apply the Poisson distribution for this case. First we have to find which equal to np. Second calculate the population using ) 13
The Normal distribution 14
The Normal distribution 1. In quality engineering, this model is used for attributes data or measurable data )ใชกบ คาขอมลทตอเนอง (variables data) ขอมลเหลานไดมาจากการวด คาความหนาของชนงาน ). เชน 2. Under certain condition the normal probability distribution will approximate the Binomial and Poisson probability distribution )ในบางกรณการแจกแจงแบบปกตสามารถน ำมาใชประมาณคาการแจกแจงทวนามได. ( 15
The Normal distribution -3 -2 - + +2 +3 16
The Normal distribution Standard normal distribution = การแจกแจงปกตมาตรฐาน Standard normal random variable = ตวแปรสมปกตมาตรฐาน 17
The Normal distribution Normal Distribution, x~( =40, =2) P(X 35) P(Z -2. 5) Standard Normal distribution, z~( =0, =1) 18
The normal standard distribution table 19
The normal standard distribution table 20
Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 21
The Normal distribution (Ex) 22
The Normal distribution (Ex) 23
The Normal distribution (Ex) 24
The Normal distribution fg 0319 26
The Normal distribution (EX) Chapter 3 Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 27 27
The Normal distribution 28
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