1. 1 Ch3 Inference About Process Quality 1.Sampling from a Normal distributionSampling from a Normal distribution 2.Sampling from a Bernoulli distributionSampling from a Bernoulli distribution 3.Sampling from a Poisson distributionSampling from a Poisson distribution 4.Estimation of process parameterEstimation of process parameter 5. Hypothesis testing （ a ） Point estimator Point estimator （ b ） Interval estimation （ confidence interval ） Interval estimation （ confidence interval ）

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

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

4. 4 回上頁 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

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

6. 6 令 indep. 回上頁 （ 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。

7. 7 （ a ） Point estimation ： Important properties of an estimation （ 1 ） Unbiased （ 2 ） Minimum variance 回上頁 4. Estimation of process parameter 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

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

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

10. 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. 11 3. C.I. on Binomial parameter （ c ） If n is large, p is small, then use Poisson. （ b ） If n is small, then use Binomial distribution. C.I. on the difference of two binomial parameter and. （ a ） If n is large, and, use Normal.

12. 12 Hypotheses Testing 1.Null hypotheses 2.Alternative hypotheses 3.Test statistic 4.Rejection region （ or critical region ）

13. 13 =P(Type I error)=P(reject | is true) （在 Q.C. work, 有時亦可稱為 produce’s risk. ） =P(Type II error)=P(fail to reject | is false) （ consumes’s risk ） 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.

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

15. 15 Tests on Means with Known Variance

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

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

18. 18 Probability of Type II error v.s.

19. 19 Operating characteristic (O.C.) curve

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

21. 21 Test on variance of Normal distribution