Answered: The visibility standard index (VSI) is…

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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The visibility standard index (VSI) is a measure of Denver air pollution that is reported each dayto theDenver Post. The index ranges from 0 (excellent air quality) to 200 (very bad air quality).During the winter months, when air pollution is higher, the index has a mean of about 90 (rated as fair) with a standard deviation of approximately 30.

Suppose that for 15 days (during the winter), the following VSI measures were recorded each day.

Day	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
VSI	80	115	100	90	15	10	53	75	80	110	165	160	120	140	195

a) Make a control chart for the VSI, and plot the above data on the control chart. Besure to include the horizontal lines on the control chart

b) identify all out-of-control signals (above or below the mean) that you find in the control chart by type (Type I, II, or III)

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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