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    Monte Carlo Comparison of Weibull Two and Three Parameters in the Context of the Statistical Analysis of Rolling Bearings Fatigue Testing

    Published: 01 August 2012

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    This paper revisits the assumptions behind the use of the two versus the three parameter Weibull statistics in the evaluation of rolling bearings contact fatigue lives. This is done by performing parametric Monte Carlo (MC) dispersion simulations of bearing fatigue failures to assess the expected bias in the estimation of the L10, L50, and β of a given set of endurance test results. The simulations are extended to cover various situations related to bearing testing as number of failures, number of suspensions, and variation of the failure rate of the sample. The analysis includes the expected spread of results, i.e., the upper and lower bound of the confidence interval, to clarify, on factual statistical bases, the suitability of the use of a particular type of Weibull distribution. The results provided by the extended simulations show with clarity the role of the choice of the two versus the three parameter Weibull in the expected overall precision of reliability point estimations resulting from bearings endurance testing. It is found that for realistic test settings (the number of tested items for instance), the two parameter Weibull assumption provides significant benefits for the accuracy of the L10 and L50 estimation obtained from the computation of their confidence intervals, while the use of the three parameter Weibull distribution become evident only in case of a very large data set and for estimation of reliability higher than 90 %. However in this region the estimations are in general more difficult and significantly less accurate.


    Weibull, statistical estimation, endurance tests, Monte Carlo simulations, rolling bearing life, rolling contact fatigue

    Author Information:

    Blachère, Sébastien
    SKF ERC, Nieuwegein,

    Gabelli, Antonio
    SKF ERC, Nieuwegein,

    Committee/Subcommittee: A01.28

    DOI: 10.1520/STP104519