Modeling the Reliability of Ball Bearings

Abstract

A data set containing n = 210 observations and published by Lieblein and Zelen (1956) provides a useful example of multiple linear regression applied to an engineering problem. It relates percentiles of the failure time distribution for ball bearings to characteristics of the bearings (load, ball diameter, number of balls) in a theoretically derived equation that can be put into linear form. The analysis requires testing the equality of regression coefficients between manufacturers and between types of ball bearing within manufacturer to see if the same equation applies across the industry. Furthermore, there is special interest in confirming an accepted value for one of these coefficients. The original analysis employed weighted least squares, although this may have been unnecessary. In addition to the regression aspects of the problem, the example is useful for the extensive data manipulation required.

• Failure times
• Multiple linear regression
• Percentiles
• Weighted least squares