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. One equation, designed to predict the hardness of a weld, is X = 0 + 2N + (2/3)C, where X is the oxygen equivalence, and O, N, and C are the amounts of oxygen, nitrogen, and carbon, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, μO = 0.1668, μN = 0.0255, μC = 0.0247, σO= 0.0340, σN = 0.0194. and σC = 0.0131.

a. Find μx

b. Suppose the weight percents of O, N, and C are independent. Find σx.

Step 1</p>

The equation which used to predict the hardness of a weld is X= 0+ 2N+ (2/3) C , where X is the oxygen equivalence , O, N, C are the amounts of oxygen, nitrogen and carbon.

We have to find

if the weight percentage of O, N, and C are independent.Step 2</p>

It is given that the weight of oxygen, nitrogen and carbon for wields of a certain type are

0.1668 , , , , 0.0194 and .

The expected amount of oxygen equivalence :

The given equation X = O + 2 N + (2/3) C

Since E(ax + b ) = a E(x) + b

E(x) = E(O) + 2 E(N) + (2/3) E(C)

= 0.1668 + 2 (0.0255) + (2/3)

= 0.2342

Therefore the expected amount of oxygen equivalence , = 0.2342 .