ENBIS: European Network for Business and Industrial Statistics

ENBIS-8 in Athens

21 – 25 September 2008 Abstract submission: 14 March – 11 August 2008

The following abstracts have been accepted for this event:

• Poisson approximation for Consecutive Covering Arrays

Authors: F.S. Milienos, M.V. Koutras,A.P. Godbole
Affiliation: Department of Statistics and Actuarial Science,University of Piraeus, Greece; Department of Mathematics, East Tennessee State University, USA
Primary area of focus / application:
Keywords: t-covering arrays, consecutive covering arrays, Markov chains, random matrices, factorial designs
Submitted at 25-Jul-2008 11:31 by Fotios Milienos
Accepted (view paper)
22-Sep-2008 11:47 Poisson approximation for Consecutive Covering Arrays
A k×n array with entries from a q−letter alphabet is called a t−covering array if each
t×n submatrix contains amongst its columns each one of the qt different words of length
t that can be produced by the q letters (see e.g. Colbourn (2004), Godbole et al. (1996)
and Dalal and Mallows (1998)). In the present article we study a t-covering problem
where, instead of looking at all possible t × n submatrices, we consider only submatrices
of dimension t×n with its rows being consecutive rows of the original k ×n array. In the
present work, exploiting the celebrated Stein-Chen method (Barbour et al. (1992)), we
establish a Poisson approximation result for an enumerating random variable, that counts
the number of submatrices consisting of consecutive rows of the original k × n array, in
which, at least one word is missing. Finally, a potential application in the field of factorial
designs is also included.
Keywords. t-covering arrays, consecutive covering arrays, Markov chains, random matrices,
factorial designs
References
[1] Barbour, A.D., Holst, L. and Janson, S. (1992). Poisson Aproximation. Oxford Univ. Press.
[2] Colbourn C.J. (2004). Combinatorial aspects of covering arrays, Le Matematiche (Catania),
58, 121-167.
[3] Dalal S.R. and Mallows C.L. (1998). Factor-covering designs for testing software. Technometrics,
40, 234-243.
[4] Godbole A.P., Skipper D.E. and R.A. Sunley (1996). t-covering arrays: upper bounds and
Poisson approximations. Combinatorics, Probability and Computing, 5, 105-118.
• Design Schemes for the Xbar Control Chart

Authors: Marit Schoonhoven Muhammed Riaz Ronald J.M.M. Does
Affiliation: IBIS UvA
Primary area of focus / application:
Submitted at 25-Jul-2008 13:19 by Marit Schoonhoven
Accepted
23-Sep-2008 16:30 Design Schemes for the Xbar Control Chart
This paper studies several issues regarding the design of the Xbar control chart under normality. Different estimators of the standard deviation are considered and the effect of the estimator on the performance of the control chart is investigated. Furthermore, the choice of the factor used to get accurate control limits for moderate sample sizes, is addressed. The paper gives an overview on the performance of the charts by studying different characteristics of the run length distribution, both in the in-control and in the out-of-control situation.
• QED Queues: Quality- and Efficiency-Driven Call Centers

Authors: Avishai (Avi) Mandelbaum
Affiliation: Industrial Engineering & Management, Technion; http://ie.technion.ac.il/serveng
Primary area of focus / application:
Submitted at 10-Aug-2008 12:26 by Avi Mandelbaum
Accepted
23-Sep-2008 09:20 QED Queues: Quality- and Efficiency-Driven Call Centers
Through examples of Service Operations, with a focus on Telephone Call Centers, I review
empirical findings that motivate or are motivated by (or both) interesting research questions. These
findings give rise to features that are prerequisites for useful service models, for example customers’
(im)patience, time-varying demand, heterogeneity of customers and servers, over-dispersion in Poisson
arrivals, generally-distributed (as opposed to exponential) service- and patience-durations, and
more. Empirical analysis also enables validation of existing models and protocols, either supporting
or refuting their relevance and robustness.
The mathematical framework for my models is asymptotic queueing theory, where limits
are taken as the number of servers increases indefinitely, in a way that maintains a delicate balance
against the offered-load. Asymptotic analysis reveals an operational regime that achieves, under
already moderate scale, remarkably high levels of both service quality and efficiency. This is the
QED Regime, discovered by Erlang and characterized by Halfin & Whitt. (QED = Quality- and
Efficiency-Driven).
My main data-source is a unique repository of call-centers data, designed and maintained at
the Technion’s SEE Laboratory. (SEE = Service Enterprise Engineering). The data is unique in
that it is transaction-based: it details the individual operational history of all the calls handled by
the participating call centers. (For example, one source of data is a network of 4 call centers of a
U.S. bank, spanning 2.5 years and covering about 1000 agents; there are 218,047,488 telephone calls
overall, out of which 41,646,142 where served by agents, while the rest were handled by answering
machines.) To support data analysis, a universal data-structure and a friendly interface have been
developed, under the logo DataMOCCA = Data MOdels for Call Centers Analysis. (I shall have
with me DataMOCCA DVD’s for academic distribution.)
1. Gans, N., Koole, G., Mandelbaum, A. “Telephone Call Centers: Tutorial, Review and Research
Prospects.” Invited review paper by Manufacturing and Service Operations Management
(M&SOM), 5 (2), 79141, 2003.
http://iew3.technion.ac.il/serveng/References/Gans-Koole-Mandelbaum-CCReview.pdf
2. Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Zeltyn, S., Zhao, L. and Haipeng, S.
“Statistical Analysis of a Telephone Call Center : A Queueing-Science Perspective.” Journal
of the American Statistical Association (JASA), 100, 36-50, 2005.
http://iew3.technion.ac.il/serveng/References/JASA callcenter.pdf
• A New Response: An Approach to Handling Systematically Missing Data in a Designed Experiment

Authors: Ewan Polwart, Owen Lozman, Richard Williams
Affiliation: FUJIFILM Imaging Colorants
Primary area of focus / application:
Submitted at 11-Aug-2008 16:41 by Ewan Polwart
Accepted (view paper)
23-Sep-2008 11:10 A New Response: An Approach to Handling Systematically Missing Data in a Designed Experiment
Sometimes designed experiments don't run completely to plan. This poster will show a simple approach that, when applied to a series of responses, turned a nightmare collection of results with missing data in to a model that successfully described the outcome, can be used for prediction and was a guide for further work.
• Design of Six Sigma

Authors: Jonathan Smyth-Renshaw
Primary area of focus / application:
Keywords: Six Sigma
Submitted at 8-Sep-2008 09:43 by Jonathan Smyth-Renshaw
Accepted
23-Sep-2008 15:40 Design of Six Sigma
Last year I spoke about the use of DMAIC for traditional Six Sigma problem solving. This presentation will examine Design of Six Sigma, I wish to present the approach which I have been using and will discuss the merits and benefits of the approach. The approach will be demonstrated with a practical example, appropriate to the setting of the conference.