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Ch3 Inference About Process Quality

Ch3 Inference About Process Quality. Sampling from a Normal distribution Sampling from a Bernoulli distribution Sampling from a Poisson distribution Estimation of process parameter 5. Hypothesis testing. （ a ） Point estimator （ b ） Interval estimation （ confidence interval ）.

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Ch3 Inference About Process Quality

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  1. Ch3 Inference About Process Quality • Sampling from a Normal distribution • Sampling from a Bernoulli distribution • Sampling from a Poisson distribution • Estimation of process parameter 5. Hypothesis testing （a）Point estimator （b）Interval estimation（confidence interval）

  2. 假設 ，則 ～ ～ ～ , 其中 ～ （ with ，當 時， ） 1. Sampling from a Normal distribution

  3. e.g.～ 其中 is the sample var. of i.i.d. is the sample var. of i.i.d. 其中U and V indep.～ and 回上頁

  4. 假設 i.i.d. Bernoulli with success prob.= p 令 ～ B（n , p） a discrete r.v. with range space 2. Sampling from a Bernoulli distribution 回上頁

  5. 假設 i.i.d. a discrete r.v. with taking values ～ 3. Sampling from a Poisson distribution

  6. 令 indep. （e.g. A unit of product can have m different types of defect, each modeled with a Poisson distribution with parameter ） 此稱為 demerit procedure, 若不全為1, 則L一般未必為Poisson分佈。 回上頁

  7. In general, and are unbiased estimators of the population mean and variance, respectively. 但S則一般並非 population standard deviation 的 unbiased estimator. e.g. Poisson ， Binomial 4. Estimation of process parameter （a）Point estimation： Important properties of an estimation （1）Unbiased （2）Minimum variance 回上頁

  8. [L,U]稱為 的 two sided confidence interval. 稱為 的 one sided confidence interval. （b）Interval estimation：

  9. Two sided C.I. e.g. i.i.d. 當variance unknown, 則以 取代 ， S 取代 。 two-sided C.I. On the variance or Lower C.I. Upper C.I. 回上頁

  10. 1. C.I. on the difference in two means （a）Variance known （b）Variance unknown 2. C.I. on the ratio of the variance of two Normal distribution

  11. （a）If n is large, and , use Normal. C.I. on the difference of two binomial parameter and . 3. C.I. on Binomial parameter （b）If n is small, then use Binomial distribution. （c）If n is large, p is small, then use Poisson.

  12. Hypotheses Testing • Null hypotheses • Alternative hypotheses • Test statistic • Rejection region（or critical region）

  13. =P(Type II error)=P(fail to reject | is false) Power=1- =P(Type II error)=P( reject | is false) Specify and design a test procedure maximize the power （ minimize , a function of sample size.） p-value = The smallest level of significance that would lead to rejection of the null hypotheses. =P(Type I error)=P(reject | is true) （在Q.C. work, 有時亦可稱為produce’s risk. ） （consumes’s risk）

  14. v.s. or 1. Test on means of normal distribution, variance known Test statistic

  15. Tests on Means with Known Variance

  16. 2. Test Means of Normal Distribution, Variance Unknown

  17. v.s. if v.s. if Test on Binomial Parameter Test on Poisson parameter

  18. v.s. Probability of Type II error

  19. Operating characteristic (O.C.) curve

  20. ～ Tests Means of Normal Distribution, Variance Unknown 3. Paired Data

  21. Test on variance of Normal distribution

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