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