You are analyzing the behavior of two machines used to drill metal parts. Each hole derived by the machine needs to have an average diameter around 7mm accepting a variation of ±0.3mm, and to check how the machine is behaving, you took 100 holes from each machine making your choices. The values found are found in Tables 1 and 2. Table 1 - Measurement of holes performed by Machine 1. 6,92 6,78 7,09 6,98 7,02 7,01 7,25 6,84 6,61 6,82 6,81 6,57 6,93 7,01 6,99 7,19 6,55 6,93 6,97 6,83 6,82 6,59 6,83 7,03 7,11 7,09 7,02 6,71 6,95 6,91 6,60 7,00 7,04 6,96 6,48 6,55 6,77 6,72 7,32 6,77 6,66 6,74 6,39 6,98 7,28 6,70 6,67 6,52 7,25 6,81 Table 2 - Measurement of holes executed by Machine 2. 7,05 7,73 6,25 6,17 7,29 6,40 6,67 6,85 6,83 7,15 7,18 7,15 6,06 7,19 7,23 7,04 6,77 7,46 7,87 6,61 6,54 6,22 7,49 7,08 7,34 7,28 7,88 7,94 7,14 6,79 7,52 7,26 6,80 6,79 8,05 6,64 6,12 7,24 7,08 6,56 6,13 6,50 6,27 7,32 7,30 6,82 5,94 5,72 6,66 6,42 With the data from the tables, use Excel a) Obtain descriptive statistics for each machine, comparing the mean, maximum values and deviations and standard deviation found for each data set. Also build a histogram for each dataset to observe the behavior of the data. Check for the presence of moderate outliers, excluding them if any. Do not eliminate out-of-spec points for this analysis. b) Analyze the entire data set and find the percentage of holes outside the specifications on each machine, which machine has the lowest percentage of failures.

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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You are analyzing the behavior of two machines used to drill metal parts. Each hole derived by the machine needs to have an average diameter around 7mm accepting a variation of ±0.3mm, and to check how the machine is behaving, you took 100 holes from each machine making your choices.

The values found are found in Tables 1 and 2.

Table 1 - Measurement of holes performed by Machine 1.

6,92 6,78 7,09 6,98 7,02 7,01 7,25
6,84 6,61 6,82 6,81 6,57 6,93 7,01
6,99 7,19 6,55 6,93 6,97 6,83 6,82
6,59 6,83 7,03 7,11 7,09 7,02 6,71
6,95 6,91 6,60 7,00 7,04 6,96 6,48
6,55 6,77 6,72 7,32 6,77 6,66 6,74
6,39 6,98 7,28 6,70 6,67 6,52 7,25
6,81

Table 2 - Measurement of holes executed by Machine 2.

7,05 7,73 6,25 6,17 7,29 6,40 6,67
6,85 6,83 7,15 7,18 7,15 6,06 7,19
7,23 7,04 6,77 7,46 7,87 6,61 6,54
6,22 7,49 7,08 7,34 7,28 7,88 7,94
7,14 6,79 7,52 7,26 6,80 6,79 8,05
6,64 6,12 7,24 7,08 6,56 6,13 6,50
6,27 7,32 7,30 6,82 5,94 5,72 6,66
6,42

With the data from the tables, use Excel

a) Obtain descriptive statistics for each machine, comparing the mean, maximum values and deviations and standard deviation found for each data set. Also build a histogram for each dataset to observe the behavior of the data. Check for the presence of moderate outliers, excluding them if any. Do not eliminate out-of-spec points for this analysis.

b) Analyze the entire data set and find the percentage of holes outside the specifications on each machine, which machine has the lowest percentage of failures.

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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