Potential of Reduced Experimental Designs in Object-Oriented Modeling of a Manufacturing
Department for Film Production
From Proceeding of European Simulation Multiconference,ESS94, Barcelona, June 1-3 1994
Agostino G.Bruzzone
THE EXPERIMENTAL CAMPAIGN
To avoid the excessive duration of the experimental campaign, it was decided to design a reduced experiment by means of
two alternative methods and to evaluate the possible performances.
There, we will consider the set of independent variables studied which, in their entirety, include the following:
Machine 05 nominal productivity
Machine 05 retooling time
Machine 05 setting time
Machine 020 nominal productivity
Machine 020 retooling time
Machine 020 setting time
Average speed of transports
Personnel distribution index
Number of highly qualified operators
To obtain information with general validity within ranges which are industrially pertinent for this situation, an
experimental campaign must be carried out that is capable of estimating the influence of each factor and of producing the
meta-models necessary to evaluate and optimize the production process.
If reference were made to an experimental design based on the base two Central Composite Design (CCD), the following
number of experimental tests would be necessary:
512 Factorial Points (29)
18 Star Points (2 9)
20 Central Points
Everything would correspond to a duration of more than one month of experimentation on a personal computer, and
obviously this time period is much too long and so much so that in the operating situation, this period would tend to
become even longer due to practical problems (breakdowns, input file debugging, experimentation flexibility, etc.).
In practice, to supply the information required on the model while remaining within acceptable time periods, it was
decided to develop a reduced experimental campaign and thus implement two alternatives: fractional composite designs
and Small composite design.
Both techniques generate interesting experimental results requiring a limited number of tests and, above all, they clearly
indicate the level of aliasing induced by the lack of information on the data obtained.
However, it order to provide a highly-accurate tool, the study in question proposed the objective of obtaining a meta-model
of the system as a combination of those polynomials supplied by these two techniques. This choice was dictated by the
confirmation that the runs needed by the two base methods used are common for about 50% of the total (and specifically
all the star points and central points plus a certain number of factorial points).
Thus, it is possible to guarantee improved experimental accuracy, while the number of tests remains limited to 96 runs
(less than those required by a higher order fractional); obviously, to achieve this result, it was necessary to choose the
minimum aberration 2(9-4) type designs with the greater number of factorial tests which are also common to the Small
Composite Design.
The first experimental campaign developed was based on the fractional composite design: fractioning the CCD reduces the
number of required tests while the effect of several variables is confusing with that of others. To reduce the rate of aliasing,
reference was made to the minimum aberration method
susceptible to optimization and analytical analyses.
The author has developed a software package designed to determine the minimum aberration designs from among generic
2(k-p) types using numerical calculation techniques. In this case, through fourth order fractioning based on a minimum
aberration, the number of tests is reduced to 66 runs (25 + 2 9 + 16), i.e. the equivalent of "only" 4 machine simulation
days.
An alternative to this method was determined based on the use of a design derived from the generalization of Westlake's
Small Composite Design presented by Draper. This technique is based on the calculation, starting from Plackett and
Burmann's tables, of the runs needed (the minimum possible number) to obtain a second order polynomial regression
from the experimental campaign.
Instead, this second design required 71 runs (37 + 2 9 + 16) and therefore the duration
is comparable to the previous one; the proper choice of the type of fractional from among all those which verify the
conditions imposed by the theorems on minimum aberration have made it possible to obtain 41 tests in common with the
fractional (18 star points, 16 central point, 7 factorial points).
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