An article in Lubrication Engr. ("Accelerated Testing of Solid Film Lubricants," 1972: 365-372) reported on an investigation of wear life (y, in hr) for solid film lubricant. Three sets of journal bearing tests were run on a Mil-L-8937-type film at each combination of three speeds (x1, in rpm), and three loads (x2, in 1000s of hr). The values of x1 for the resulting 27 observations were 20, 20, ... , 20, 60, ... , 60, 100, ... , 100, and the values of x2 were 3, 3, 3, 6, 6, 6, 10, 10, 10, 3, 3, 3, ... , 10, 10, 10. The corresponding values of y = wear life (hr) were 300.2, 310.8, 333.0, 99.6, 136.2, 142.4, 20.2, 28.2, 102.7, 67.3, 77.9, 93.9, 43.0, 44.5, 65.9, 10.7, 34.1, 39.1, 26.5, 22.3, 34.8, 32.8, 25.6, 32.7, 2.3, 4.4, and 5.8.
The investigators commented that a lognormal distribution is appropriate for Y because ln(Y) is known to follow a normal law, and then proposed the multiplicative power regression model

a. Estimate the model parameters.
b. Interpret R2 for the transformed model, and then carry out a model utility test.
c. Does it appear that both predictors provide useful information about wear life?
d. Predict wear life when speed is 50 and load is 5 in a way that conveys information about precision and reliability.

Transcribed Image Text:

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