# HW7 - ) (b) Fill in the blank in the table based on your...

This preview shows pages 1–3. Sign up to view the full content.

Page 1 of 3 Problem 1: Textbook 9.4 (Hint for b: use MR chart to estimate sigma. Compare whether the estimated sigma is close to the assumed sigma). Problem 2: Textbook 9.6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Page 2 of 3 Problem 3: The following data present individual observations on a certain process. The mean value of the molecular weight is 28, and process standard deviation is known to be 2. A CUSUM chart is built as shown in the following table. Obs, i x i C i + N + C i - N - 1 26.40 0 0 1.1 1 2 25.30 0 0 3.3 2 3 31.80 3.3 1 0 0 4 27.10 1.9 2 0.4 1 5 28.50 ?? 3 0 0 6 20.20 0 0 7.3 1 7 19.30 0 0 ?? 2 8 22.70 0 0 20.3 3 9 20.40 0 0 27.4 4 10 19.50 0 0 35.4 5 11 21.70 0 0 41.2 6 12 24 0 0 44.7 7 (a) Based on the data in the CUSUM chart, what is the slack value K? (You cannot assume k=1/2. You should find K base on the data in the table using the CUSUM statistic formula. You need to show your steps
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) (b) Fill in the blank in the table based on your obtained K in (a).( Show your steps) (c) Based on this tabular CUSUM, please conclude whether the process has a mean shift using h=5, If the process has a mean shift, please indicate at which sample this process was last in control, and estimate the magnitude of this mean shift. Page 3 of 3 Problem 4: Textbook 9.19 (Table 9E.2, miu=8.02, sigma=0.05) Problem 5: extra credit point: for normally distributed data ) , ( ~ 2 N X i t X is the sample average at time t with the sample size n Define EWMA monitoring statistic as Please prove Var (Z t ) = 2 n 2 ( ) 1 (1 ) 2t You are required to write out each step assumption. 1 ) 1 ( ) 1 ( t j t t j j t X Z...
View Full Document

## This note was uploaded on 03/16/2012 for the course IEOR 466 taught by Professor Richard during the Spring '12 term at Columbia.

### Page1 / 3

HW7 - ) (b) Fill in the blank in the table based on your...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online