Indirect Cycle-time Quantile Estimation Using the Cornish-fisher Expansion

This paper proposes a technique for estimating steady-state quantiles from discrete-event simulation models, with particular attention paid to cycle-time quantiles of manufacturing systems. The technique is justified through an extensive empirical study and supported with mathematical analysis. The Cornish-Fisher expansion is used as a basis for this estimation, and it is shown that for an M/M/1 system, a system of 5 tandem M/M/1 queues, and a full factory simulation model, the technique provides precise, accurate estimates for the most commonly estimated quantiles with minimal data storage. The performance of the Cornish-Fisher expansion is compared to both traditional direct quantile estimation using order statistics and indirect quantile estimates obtained from four-parameter distributions. Based on these evaluations, the Cornish-Fisher expansion is found to be the most appealing quantile estimation technique of the three approaches because it provides accurate results for a variety of systems and has the advantages of being easy to implement and having extremely low data-storage requirements. It also provides the capability for estimating all quantiles of a given random variable from a single set of multiple replications at a given design point, negating the need to know in advance which quantile estimates are desired.