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:اقتباس ازIntroduction to Statistical Quality Control, 5th edition

Douglas C. Montgomery

دکتر محمد صالح اولیاء دانشکده مهندسی صنایع دانشگاه یزد

کنترل کیفیت آماری

استنباط در مورد 3 کیفیت فرایند

Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 3

فهرست مطالب توزیعهای نمونه گیری

تخمین نقطه ای پارامترهای فرایند استنباط آماری بر اساس یک نمونه

استنباط آماری بر اساس دو یا چند نمونه

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Random Sample

Statistics

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Chi-square (χ2) Distribution

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t Distribution

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F Distribution

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•As n gets large the bias goes to zero

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Null HypothesisAlternative

Hypothesis

•In this example, H1 is a two-sided alternative hypothesis

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•H1 in equation 3-22 is a two-sided alternative hypothesis

•The procedure for testing this hypothesis is to:− take a random sample of n observations on the random variable x,− compute the test statistic, and − reject H0 if |Z0| > Zα/2, where Zα/2 is the upper α/2 percentage of the standard normal distribution.

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One-Sided Alternative Hypotheses

In some situations we may wish to reject H0 only if the true mean is larger than µ0

Thus, the one-sided alternative hypothesis is H1: µ>µ0, and we would reject H0: µ=µ0 only if Z0>Zα

If rejection is desired only when µ<µ0

Then the alternative hypothesis is H1: µ<µ0, and we reject H0 only if Z0<−Zα

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Confidence Intervals

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Confidence Interval on Mean, Variance Known

Furthermore, a 100(1 − α)% upper confidence bound on µ is

whereas a 100(1 − α)% lower confidence bound on µ is

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• For the two-sided alternative hypothesis, reject H0 if |t0| > tα/2,n-1, where tα/2,n-1, is the upper α/2 percentage of the t distribution with n − 1 degrees of freedom• For the one-sided alternative hypotheses,

• If H1: µ1 > µ0, reject H0 if t0 > tα,n − 1, and • If H1: µ1 < µ0, reject H0 if t0 < −tα,n − 1

• One could also compute the P-value for a t-test

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• Section 3-3.4 describes hypothesis testing and confidence intervals on the variance of a normal distribution

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• Section 3-4.3 describes hypothesis testing and confidence intervals on the variance of two normal distributions

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