Modeling spare part demand data using transmuted or exponentiated Poisson distribution
R. Jiang and Z.Chen
https://doi.org/10.19124/ima.2018.001.11
Abstract
Traditionally, it is assumed that the lead time spare part demand follows the Poisson or normal distribution. It is well-known that the mean of Poisson distribution equals to its variance, which is called Poisson dispersion. Actual demand data scarcely meet the Poisson dispersion. To overcome this problem, several two-parameter variants (e.g., zero-inflated Poisson and hurdle shifted Poisson) of the Poisson distribution have been used for modelling irregular spare part demand data. In this paper, we propose two new two-parameter alternatives, which are transmuted and exponentiated Poisson distributions. The proposed distributions can be over- or under-Poisson dispersive, and hence provide better flexibility without losing the simplicity of the Poisson distribution too much. The appropriateness of the proposed models is illustrated through three real-world examples. Based on the idea that a fitted distribution should provide a good goodness-of-fit to the right tail of the empirical demand distribution so as to achieve good inventory performance, a weighted least square method is also proposed to estimate the model parameters. The appropriateness of the proposed approach is also illustrated.
Keywords. Spare parts demand, transmuted Poisson distribution, exponentiated Poisson distribution, weighted least square method