Answered: Day Impurity (%) Day Impurity (%) 1…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a manufacturing process, the impurity level of the product is measured on a daily basis. When the pro-cess is operating normally, the impurity level is approx-imately normally distributed with a mean value of 0.800% and a standard deviation of 0.021%. The laboratory measurements for a period of eight consecutive days are shown below. From an SPC perspective, is there strong evidence to believe that the mean value of the impurity has shifted? Justify your answer.develop CUSUM and EWMA charts. Do these charts indicate an “abnor-mal situation”? Justify your answer. For the CUSUM chart, use K=0.5s and H=5s where s is the sample standard deviation. For the EWMA chart, use λ=0.25.

Day
Impurity (%)
Day
Impurity (%)
1
0.812
5
0.799
2
0.791
0.833
3
0.841
7
0.815
4
0.814
8
0.807

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 + ...

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