Two Probability Distributions of Interest in Balancing and Runout Problems

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, C_p and C_pk, 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.