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DS impl
VDM-SL
SM spec
VDM-SL
SM impl
VDM-SL
PM spec
VDM-SL
PM impl
VDM-SL
CG spec
VDM-SL
CG impl
VDM-SL
SS spec
VDM-SL
SS impl
Implicit time line
56
IFAD
IFAD
European Industrial use of FM
European Academia
FME Profile
The ESPRIT Programme
European Tool Support
Example Industrial Projects
Concluding Remarks
57
IFAD
IFAD
Concluding Remarks
Strong European FM supplier side
Industrial FM usage outside critical
domains started
USA still strongest on model checking
for hardware
Hopefully Japanese industrial use of
FM will increase
UTRECHT UNIVERSITY
DEPARTMENT OF MATHEMATICS
IN PARTIAL FULFILMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF MASTER OF SCIENCE
IN
MATHEMATICAL SCIENCES
STATISTICAL ANALYSIS AND FORECASTING
OF KLM ROYAL DUTCH AIRLINES GROUND
HANDLING PROCESS DURATIONS
Author:
Evrim AKAR
Supervisors
Dr. Eduard BELITSER
Department of Mathematics,
UU
Marc PAELINCK
Department of Decision -
Support, KLM
May 31, 2009
Abstract
It is crucial for organizations of all sizes to make future forecasts in order to decrease
the uncertainty of the environment and to take the advantage of opportunities
available to the organization. As each data set has its specific properties, not every
method results in accurate forecasts for a given data set. Therefore, a variety of
techniques have been developed for effective and efficient predictions.
In this study, the analysis of random processes and time-series are examined. Moreover,
a brief description about the major forecasting methods are given and a nonparametric
curve estimation method is introduced for future predictions. In order to
increase the forecast accuracy, ”comparison and combination method” is applied.
We focus on the quantile values of Royal Dutch Airlines (KLM) Ground Handling
Process Times Data.
Contents
Abstract 1
Contents 2
List of Tables 4
List of Figures 5
1 INTRODUCTION 7
2 EMPIRICAL ANALYSIS 15
2.1 DISTRIBUTION ANALYSIS OF THE DATA . . . . . . . . . . . 15
2.2 QUANTILES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 ESTIMATION OF THE DISTRIBUTION : AN
OPTIMIZATION APPROACH . . . . . . . . . . . . . . . . . . . 22
2.4 DISTRIBUTION ANALYSIS: WEIBULL DISTRIBUTION . . . 27
3 FORECASTING 31
3.1 METHODOLOGICAL TOOLS FOR ANALYZING TIME-SERIES
DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.1 Plotting the Data . . . . . . . . . . . . . . . . . . . . . . 32
3.1.2 The Autocorrelation Coefficient . . . . . . . . . . . . . . 32
3.1.3 The Periodogram and Spectral Analysis . . . . . . . . . . 33
3.1.4 The Partial Autocorrelation Coefficient . . . . . . . . . . 34
2
3.1.5 Examining Stationarity and Seasonality in a Time-Series . 34
3.2 APPLICATIONS WITH KLM GROUND HANDLING PROCESS
TIMES DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 BASIC FORECASTING METHODS . . . . . . . . . . . . . . . 40
3.3.1 Regression Analysis . . . . . . . . . . . . . . . . . . . . 40
3.3.2 Exponential Smoothing . . . . . . . . . . . . . . . . . . . 41
3.3.3 Box Jenkins Method . . . . . . . . . . . . . . . . . . . . 42
3.4 FORECAST ACCURACY . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 Standard Statistical Measures . . . . . . . . . . . . . . . 43
3.4.2 Relative Measures . . . . . . . . . . . . . . . . . . . . . 44
3.5 NONPARAMETRIC CURVE ESTIMATION . . . . . . . . . . . 45
3.5.1 A Recursive Estimator . . . . . . . . . . . . . . . . . . . 47
3.5.2 Estimation of
n . . . . . . . . . . . . . . . . . . . . . . 57
3.5.3 Improvement of the Model Paramters . . . . . . . . . . . 57
3.6 EVALUATION OF FORECAST RESULTS . . . . . . . . . . . . 57
3.7 COMPARISON AND COMBINATION OF FORECAST METHODS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
BIBLIOGRAPHY 58
A BACKGROUND 60
A.1 GAMMA DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . 60
A.2 WEIBULL DISTRIBUTION (2-parameter) . . . . . . . . . . . . 61
A.3 MAXIMUM LIKELIHOOD ESTIMATION . . . . . . . . . . . . 61
A.3.1 Maximum Likelihood Estimator for Gamma Distribution . 63
A.3.2 Maximum Likelihood Estimator for Weibull Distribution . 64
A.3.3 Asymptotical Convergence of MLE . . . . . . . . . . . . 65
A.4 CHI-SQUARE GOODNESS OF FIT TEST . . . . . . . . . . . . 66
B APPLICATIONS WITH DIFFERENT TYPES OF KLM GROUND
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