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Solved: The oxygen equivalence number of a weld is a

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 30E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 30E

The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article "Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds" (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s) presents several equations for computing the oxygen equivalence number of a weld. An equation designed to predict the strength of a weld is X = 1.12C + 2.69N + O − 0.21 Fe, where X is the oxygen equivalence, and C, N, O, and Fe are the amounts of carbon, nitrogen, oxygen, and iron, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, μc = 0.0247, μN = 0.0255, μ0 = 0.1668,  ,μFe = 0.0597, σc = 0.0131, σN = 0.0194, σO = 0.0340, and σFe = 0.0413.  Furthermore assume that correlations are given by ρC,N = -0.44, ρC,O = 0.58, ρC,Fe = 0.39, ρN,O = -0.32, ρN,Fe = 0.09, and ρO,Fe = -0.35.

a. Find μX.

b. Find Cov(C, N), Cov(C, O), Cov(C, Fe), Cov(N, O), Cov(N, Fe), and Cov(O, Fe).

c. Find σX.

Step-by-Step Solution:

Step 1 of 4:

Here an equation designed to measure the strength of a weld is given.

The equation is X=1.12C+2.69N+O-0.21Fe, where X is the oxygen equivalence,C stands for amount of carbon,N stands for amount of nitrogen, O stands for amount of oxygen,Fe stands for amount of iron.

Also,the means of the amounts of C,N,O and Fe are given.

=0.0255

=0.0597

Standard deviations of C,N,O and Fe are

=0.0131

=0.0194

=0.0340

=0.0413

The correlations between C,N,O and Fe are also given as

=-0.44

=0.58

=0.39

=-0.32

=0.09

=-0.35

Using these given values we have to find the required values.


Step 2 of 4

Chapter 2.6, Problem 30E is Solved
Step 3 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 30E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article "Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds" (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s) presents several equations for computing the oxygen equivalence number of a weld. An equation designed to predict the strength of a weld is X = 1.12C + 2.69N + O ? 0.21 Fe, where X is the oxygen equivalence, and C, N, O, and Fe are the amounts of carbon, nitrogen, oxygen, and iron, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, ?c = 0.0247, ?N = 0.0255, ?0 = 0.1668, ,?Fe = 0.0597, ?c = 0.0131, ?N = 0.0194, ?O = 0.0340, and ?Fe = 0.0413. Furthermore assume that correlations are given by ?C,N = -0.44, ?C,O = 0.58, ?C,Fe = 0.39, ?N,O = -0.32, ?N,Fe = 0.09, and ?O,Fe = -0.35.a. Find ?X.________________b. Find Cov(C, N), Cov(C, O), Cov(C, Fe), Cov(N, O), Cov(N, Fe), and Cov(O, Fe).________________c. Find ?X.” is broken down into a number of easy to follow steps, and 186 words. This full solution covers the following key subjects: cov, oxygen, equivalence, weld, Find. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 30E from 2.6 chapter was answered, more than 782 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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Solved: The oxygen equivalence number of a weld is a