Answered: The data represent individual…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

The data represent individual observations on bath concentration from a chemical process. The target value is 10 and the process standard deviation is given as o = 0.8. (a) Use k = 0.5 and h =5, built a tabular CUSUM to quickly detect a shift of about lo in the process mean. Based on the 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 mean shift started.

i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
xi
9.45
7.99
9.29
11.66
12.16
10.18
8.04
11.46
9.2
10.34
9.03
11.47
10.51
9.4
10.08
9.37
10.62
10.31
8.52
10.84
10.9
9.33
12.29
11.5
10.6
11.08
10.38
11.62
11.31
10.52

Q1. Download the dataset from Canvas. The data represent individual observations on bath concentration
from a chemical process. The target value is 10 and the process standard deviation is given as o=0.8.
(a) Use k = 0.5 and h=5, built a tabular CUSUM to quickly detect a shift of about 10 in the process mean.
Based on the 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 mean shift started.
(b) Estimate the magnitude of the mean shift and calculate the 8= μ₁ -μ/0.
(c) Calculate out-of-control ARL: (using the approximated formula) for the two-sided CUSUM.
Q2.
Use the same dataset as in Question 6. Mo = 10 and o=0.8 are the same as before.
(a) Using λ = 0.1 and L=3, please construct an EWMA chart, also please indicate at which sample the out-
of-control condition is detected.
(b) What are the steady state values of control limits for the EWMA chart in part (a).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution