Independent Competing Risks in Common Shape-Parameter Weibull Systems, With Application to Rolling Bearing Service Life

This article re-evaluates, formalizes, and extends a previously proposed methodology for enhancing the specificity of bearing life analysis based on field failure data. The central research problem is demonstrated to relate to characterizing validity, accuracy, and precision for a given statistical estimator, and subsequently a transformed version thereof, in the context of independent competing risks affecting a common shape-parameter Weibull system. Validity of the initial estimator is demonstrated for a single population, and the result then extended to encompass multiple populations of different ages. Under certain nonstringent conditions, both the single- and multipopulation initial estimators are proved to be unbiased. An analytical approach to determining confidence intervals for these quantities is also proposed, and shown to provide highly accurate characterizations of estimator precision. The transformed estimator is then considered, with some amount of bias shown to occur. However, the levels of bias are found to decay rapidly as the failure dataset increases in size. Delta method confidence intervals are constructed and shown to provide excellent characterizations of estimator deviations. Application of these concepts to enhance rolling bearing service life analyses is demonstrated, including consideration of methodological limitations. The advances made regarding independent competing risks in common shape-parameter Weibull systems hold in general, hence, are expected to have broader reliability applications.