Download Presentation
Ch3 Inference About Process Quality

Loading in 2 Seconds...

1 / 21

# Ch3 Inference About Process Quality - PowerPoint PPT Presentation

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 ）.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## Ch3 Inference About Process Quality

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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）

, 其中

（ with ，當 時， ）

1. Sampling from a Normal distribution

e.g.～

is the sample var. of i.i.d.

a discrete r.v. with range space

2. Sampling from a Bernoulli distribution

a discrete r.v. with taking values

3. Sampling from a Poisson distribution

（e.g. A unit of product can have m different types of

defect, each modeled with a Poisson distribution

with parameter ）

In general, and are unbiased estimators of the

population mean and variance, respectively.

unbiased estimator.

e.g. Poisson ， Binomial

4. Estimation of process parameter

（a）Point estimation：

Important properties of an estimation

（1）Unbiased

（2）Minimum variance

（b）Interval estimation：

Two sided C.I.

e.g.

i.i.d.

S 取代 。

two-sided C.I. On the variance

or

Lower C.I.

Upper C.I.

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

（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.

Hypotheses Testing

• Null hypotheses
• Alternative hypotheses
• Test statistic
• Rejection region（or critical region）

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）

v.s.

or

1. Test on means of normal distribution, variance known

Test statistic

v.s.

if

v.s.

if

Test on Binomial Parameter

Test on Poisson parameter

v.s.

Probability of Type II error

Tests Means of Normal Distribution, Variance Unknown

3. Paired Data