Two Probability Distributions of Interest in Balancing and Runout Problems

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Two Probability Distributions of Interest in Balancing and Runout Problems

Baddeley, Viv

The inability of the normal probability distribution to adequately model the residual (or “outgoing”) imbalance magnitude of an in-plant vehicle driveline balancing process is discussed. Based on the observation that the orthogonal components of the residual imbalance do appear to follow a normal distribution, the Rayleigh probability distribution is derived as a model of the residual imbalance magnitude, from first principles. The Rayleigh distribution is a special case of the Weibull distribution. Re-definitions of the standard process capability indicators, Cp and Cpk, to suit the Rayleigh distribution are proposed, and the results of the subject driveline balancing process presented.Another probability distribution is derived to describe the best-possible output for a balancing process using a given set of equally-spaced balance correction masses and mass placement options. This second distribution is named the “Shark Fin” distribution.