Competing Risk and Multiple Comparison Analysis for Bearing Fatigue Tests

Abstract

New developments in statistical inference for the two parameter Weibull distribution are explained in the terminology of bearing endurance testing.

Specifically the developments are:

1.	Procedures for conducting an exact test of whether the Weibull shape parameter and a percentile, such as the L10 life, differs significantly among κ (2≤κ≤10) groups of censored life test results. These procedures have application in the very common circumstance wherein one wishes to evaluate the effect of several levels of a design or environmental variable upon fatigue life. Given the results of a censored life test conducted at each level of the variable, it is necessary to decide whether the observed differences in life are real or are explainable by random variation.
2.	Procedures for setting confidence limits on the shape parameter and the L10 life of a Weibull distributed failure mode when observations are censored through the failure of the bearing by means of another competing failure mode. These procedures have application, for example when one component; e.g. the inner ring, is made of experimental material while the outer ring and ball complement are of standard make. One needs to use the results of a life test in which inners, outers, and balls have failed, to infer the fatigue behavior of the experimental material.
3.	A new, highly accurate closed form approximation is given for the tabular values needed in setting confidence limits for a Weibull shape parameter from the results of a censored life test. This approximation is useful for the automatic computation of confidence limits for the shape parameter within a computer program that calculates maximum likelihood estimates of the Weibull parameters.

Numerical examples and necessary tabular data are included to illustrate and facilitate the implementation of these techniques by bearing test engineers.

Presented at the 32nd Annual Meeting in Montreal, Quebec, Canada, May 9–12, 1977

Notes

Presented at the 32nd Annual Meeting in Montreal, Quebec, Canada, May 9–12, 1977