### STP771: Analysis of Sets of Two-Parameter Weibull Data Arising in Rolling Contact Endurance Testing

McCool, JI

*Research scientist, SKF Industries, Inc., King of Prussia, Pa.*

Pages: 27 Published: Jan 1982

**Abstract**

Frequently in conducting rolling contact endurance tests, several small samples are subjected to some kind of “treatment.” It is shown herein that if the treatment affects the rating life but not the Weibull shape parameter the data can be analyzed as a set rather than as individual samples, with considerable improvement in the precision with which the rating lives can be estimated.

Methods and supporting tables are given for the detailed analysis of sets of such data under the assumption that they represent censored data samples drawn from two-parameter Weibull populations.

The complete analysis consists of the following: (*a*) a test for the equality of shape parameters among the populations, and, when a common shape parameter is found to be plausible, (*b*) two tests for the equality of scale parameters or any fixed percentile, (*c*) an interval and bias-corrected point estimation of the common shape parameter and the tenth percentiles of the individual groups, and (*d*) a procedure for assessing which of the populations differ in their scale parameter and, hence, any percentile values.

The numerical values of key percentage points of the relevant distributions required for carrying out the analyses cover the range from *k* = 2 samples of size *n* = 5, censored at the third (*r* = 3) failure, to *k* = 5 and *n* = *r* = 30. As an illustration, the analyses are applied to two sets of rolling contact endurance data obtained with various steel materials fabricated into cylindrical rod and ball test specimens.

Two procedures for the selection of sample size are discussed, and illustrative examples are given of their use.

**Keywords:**

one-way classification, maximum likelihood estimation, likelihood ratio, multiple comparisons, rolling contact fatigue, bearing steels

**Paper ID:** STP36146S

**Committee/Subcommittee:** A01.28

**DOI:** 10.1520/STP36146S

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