Proceedings of the 2006 Winter Simulation Conference L. F. Perrone, F. P. Wieland, J. Liu, B. G. Lawson, D. M. Nicol, and R. M. Fujimoto, eds. ABSTRACT Previous work has shown that the Cornish-Fisher expan- sion (CFE) can be used successfully in conjunction with discrete event simulation models of manufacturing systems to estimate cycle-time quantiles. However, the accuracy of the approach degrades when non-FIFO dispatching rules are employed for at least one workstation. This paper sug- gests a modification to the CFE-only approach which util- izes a power data transformation in conjunction with the CFE. An overview of the suggested approach is given, and results of the implemented approach are presented for a model of a non-volatile memory factory. Cycle-time quan- tiles for this system are estimated using the CFE with and without the data transformation, and results show a signifi- cant accuracy improvement in cycle-time quantile estima- tion when the transformation is used. Additionally, the technique is shown to be easy to implement, to require very low data storage, and to allow easy estimation of the entire cycle-time cumulative distribution function. 1 INTRODUCTION In today's business environment, with supply-chain com- plexity increasing, the ability to generate accurate customer delivery dates is crucial. Service-based industries with in- tricate supply-chains, such as the semiconductor manufac- turing industry, compete not only on traditional measures such as cost and product quality, but also on the timely de- livery of product to both end-product customers and inter- mediate parties in the supply-chain. Consequently, the ability to accurately and efficiently estimate customer de- livery dates are crucial. Estimates of mean cycle time are often readily available, but using them to generate esti- mates of delivery dates ignores variability in the cycle time distribution and can result in reduced on-time delivery. Es- timates of cycle time quantiles, on the other hand, provide a complete picture of the cycle time distribution for a given system and allow customer delivery dates to be quoted at a level of confidence acceptable to the decision maker. Unfortunately, obtaining estimates of cycle-time quan- tiles is substantially more difficult than obtaining estimates of the mean cycle-time, and currently available cycle-time quantile estimation techniques have several drawbacks, es- pecially when applied to non-FIFO systems. The most tra- ditional method for obtaining quantile estimates is to use order statistics. This technique requires all observations of the distribution to be stored, resulting in a large data stor- age requirement. Several techniques have been developed to reduce this data storage burden by modifying the basic order statistics approach (Jain and Chlamtac 1985, Heidel- berger and Lewis 1984). However, these approaches gen- erally have the drawbacks of becoming cumbersome to implement when estimates of multiple quantiles are desired and often requiring that the quantiles to be estimated are known in advance. More recently, Chen and Kelton (2006) developed an approach which accommodates esti- mation of multiple quantiles simultaneously and generates confidence intervals around the estimates, but their ap- proach has the drawback, albeit reduced when compared to order statistics, of requiring significant data storage. The approaches mentioned previously are direct, as they are all obtained by inverting an empirical cumulative distribution function (cdf). As described, these approaches have significant shortcomings. However, they also have the advantage of exhibiting quantile estimation accuracy that is independent of distributional shape. An indirect quantile estimation approach, alternatively, does not build an empirical cdf. Instead, it uses features of the distribu- tion to generate quantile estimates. Indirect techniques have the advantages of requiring low data storage, easily generating estimates of multiple quantiles, and not requir- ing that the quantiles to be estimated are known in ad- vance. On the other hand, their estimation accuracy is de- pendent on the shape of the distribution from which quantiles are to be estimated. INDIRECT CYCLE-TIME QUANTILE ESTIMATION FOR NON-FIFO DISPATCHING POLICIES Jennifer McNeill Bekki Gerald T. Mackulak John W. Fowler Industrial Engineering Department Arizona State University Tempe AZ 85287-5906, U.S.A. 1829 1-4244-0501-7/06/$20.00 ©2006 IEEE