Case Studies in Data Analysis

269 Pages·1994·11.582 MB·English

by  John D. Kalbfleisch, Cyntha A. Struthers, Duncan C. Thomas (auth.), Jane F. Gentleman, G. A. Whitmore (eds.)

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Lecture Notes in Statistics 94
Edited by S. Fienberg, J. Gani, K. Krickeberg,
1. Oikin, and N. Wermuth
Jane F. Gentleman and G. A. Whitmore
(Editors)
Case Studies in
Data Analysis
Springer-Verlag
New York Berlin Heidelberg London Paris
Tokyo Hong Kong Barcelona Budapest
Jane F. Gentleman G.A. Whitmore
Health Statistics Division Faculty of Management
Statistics Canada McGill University
Ottawa Montreal
Ontario KIA OT6 Quebec H3A 105
Canada Canada
library of Congress Cataloging-in-Publication Data Available
Printed on acid-free paper.
© 1994 Springer-Verlag New York, Inc.
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Camera ready copy provided by the editor.
9 8 7 6 5 432 1
ISBN-13:978-0-387-94410-4 e-ISBN-13:978-1-4612-2688-8
DOl: 10.1007/978-1-4612-2688-8
Preface
This volume is a collection of eight Case Studies in Data Analysis that
appeared in various issues of the Canadian Journal of Statistics (OS) over a twelve
year period from 1982 to 1993. One follow-up article to Case Study No.4 is also
included in the volume.
The OS's Section on Case Studies in Data Analysis was initiated by a
former editor who wanted to increase the analytical content of the journal. We were
asked to become Section Co-Editors and to develop a format for the case studies.
Each case study presents analyses of a real data set by two or more analysts
or teams of analysts working independently in a simulated consulting context. The
section aimed at demonstrating the process of statistical analysis and the possible
diversity of approaches and conclusions. For each case study, the Co-Editors found
a set of real Canadian data, posed what they thought was an interesting statistical
problem, and recruited analysts working in Canada who were willing to tackle it.
The published case studies describe the data and the problem, and present and
discuss the analysts' solutions. For some case studies, the providers of the data were
invited to contribute their own analysis.
Although the section attempted to mirror the data-analytic process of real
life problem solving, the reports are necessarily somewhat artificial because the Co
Editors and the analysts had to work under abnormal constraints. The Co-Editors
had to limit the scope and complexity of the data and the problem so that the case
study remained manageable. On their part, the analysts had to accept the data as
provided without having been able to participate in defining the problem, designing
the experiment, or supervising the collection of the data. Finally, limited tim:e and
journal space necessarily restricted the analysts' freedom of investigation and
reporting. The Co-Editors offered editorial advice to the analysts and sometimes
obtained outside technical reviews. But, given the desire to reflect a real-life
consulting situation in which refereeing and error correction are not generally
performed, the Co-Editors attempted to limit to some extent their criticisms and
requests for revision.
The Co-Editors strove to obtain data of varying types and from assorted
subject matter areas. The data sets analyzed include data from a large household
survey (Case Study No.7 on child care needs), data gathered in an industrial setting
(Case Study No. 1 on equipment failure times), administrative data from the field
of criminal statistics (Case Study No.4 on homicide time trends), medical data (Case
Study No.2 on damage to firefighters'lungs), environmental data (Case Study No.
3 on iceberg paths and Case Study No.5 on extreme wind speeds), laboratory data
emanating from a designed experiment (Case Study No. 8 on mutagenicity of
environmental chemicals), and market research data (Case Study No.6 on beer
preferences).
The only trimming of the data sets involved sometimes reducing the number
of variables in order to confine the problem to a manageable size. To preserve the
realism of the analytical situation, no observations were ever removed. Each
published case study displays a representative fragment of the data, and in one case,
all of the data are presented. Copies of the case study data were made available to
readers, who were invited to submit their own follow-up analyses to the section.
Readers of this volume may obtain copies of the case study data at a
nominal cost. Data for all case studies except Case Study No.7 are available upon
request from the Statistical Society of Canada, Dunton Tower, 6th Floor, Carleton
University, Ottawa, Ontario, Canada KIS 5B6. For Case Study No.7, Statistics
Canada has kindly agreed to make the Family History Survey data tape and
documentation available; contact the Housing Family and Social Statistics Division,
Statistics Canada, Ottawa, Ontario, Canada KIA OT6.
Case Study No.8 marks the end of the series. We were honored and
pleased that the Statistical Society of Canada chose to recognize the Section in
general and Case Study No.8 in particular by presenting us with the 1993 Canadian
Journal of Statistics Award, which annually recognizes a CJS article for excellence,
innovation and presentation.
The production of this series has been challenging, educational, and
enjoyable to us. We thank the case study analysts and data providers for their
participation in this enterprise. We also thank the editors, managing editors and
others who have assisted us in publishing these case studies. We especially want to
thank Karen Robertson of McGill University who has so competently handled case
study manuscripts and extensive correspondence during the term of the series and
who has painstakingly assembled the manuscript of this book in camera-ready form.
We hope that readers of this collection will find the case studies interesting
and instructive and that the analyses and data will prove to be useful for teaching
purposes.
Jane F. Gentleman, Statistics Canada
G. A Whitmore, McGill University
CONTENTS
Preface v
Reference Information for Case Studies viii
Measuring the Impact of an
Intervention on Equipment Lives 1
Measurements of Possible Lung Damage
to Firefighters at the Mississauga Train
Derailment 25
Iceberg Paths and Collision Risks for Fixed
Marine Structures 45
Temporal Patterns in Twenty Years of
Canadian Homicides 71
Extreme-value Analysis of Canadian
Wind Speeds 119
Beer Chemistry and Canadians' Beer
Preferences 145
Estimation of the Need for Child
Care in Canada 177
Estimation of the Mutagen Potency
of Environmental Chemicals Using
Short-term Bioassay 219
Reference Information for Case Studies
The following list presents the original journal reference information for the case
studies in this collection.
Case Study No.1. G. A Whitmore and J. F. Gentleman: "Measuring the
impact of an inteJVention on equipment lives", in Case Studies in Data
Analysis (with contributed analyses by J.D. Kalbfleisch and C.A Struthers
and by D.C. Thomas), CabadianJournal of Statistics, 10, 1982, pp. 237-259.
Case Study No.2. J. F. Gentleman and G. A Whitmore: "Measurement
of possible lung damage to firefighters at the Mississauga train derailment",
in Case Studies in Data Analysis (with contributed analyses by R. Kusiak
and J. Roos and by K. J. Worsley), Canadian Journal of Statistics, 12, 1984,
pp.7-25.
Case Study No.3. G. A Whitmore and J. F. Gentleman: "Iceberg paths
and collision risks for fixed marine structures", in Case Studies in Data
Analysis (with contributed analyses by M. Moore and F. Zwiers), Canadian
Journal of Statistics, 13, 1985, pp. 83-108.
Case Study No.4. J. F. Gentleman and G. A Whitmore: "Temporal
patterns in twenty years of Canadian homicides", in Case Studies in Data
Analysis (with contributed analyses by C. McKie, by A I. McLeod, I. B.
MacNeill and J. D. Bhattacharyya, and by A Nakamura and M. Nakamura),
Canadian Journal of Statistics, 13, 1985, pp. 261-291.
Follow-up article to Case Study No.4. E. B. Dagum, G. Huot and M. Morry:
"A new look at an old problem: Finding temporal patterns in homicide
series. A Canadian problem ", in Case Studies in Data Analysis (with
contributed discussion by A I. McLeod and I. B. MacNeill and by A
Nakamura and M. Nakamura), Canadian Journal of Statistics, 16,1988, pp.
117-134.
Case Study No.5. G. A Whitmore and J. F. Gentleman: "Extreme-value
analysis of Canadian wind speeds," in Case Studies in Data Analysis (with
contributed analyses by F. W. Zwiers and W. H. Ross), Canadian Journal
of Statistics, 15, 1987, pp. 311-337.
Case Study No.6. G. A. Whitmore and J. F. Gentleman: "Beer chemistry
and Canadians' beer preferences," in Case Studies in Data Analysis (with
contributed analyses by J.-P. Carmichael,G. Daigle and L.-P. Rivest and by
B. Li and A J. Petkau), Canadian Journal of Statistics, 18,1990, pp. 93-125.
Case Study No.7. J. F. Gentleman and G. A Whitmore: "Estimation of the
need for child care in Canada," in Case Studies in Data Analysis (with
contributed analyses by E. M. Gee and J. B. McDaniel and by C. A
Struthers), Canadian Journal of Statistics, 19, 1991, pp. 241-282.
Case Study No.8. J. F. Gentleman and G. A Whitmore: "Mutagenic
potency of environmental chemicals," in Case Studies in Data Analysis (with
contributed analyses by G. A Darlington, by B. J. Eastwood and by B. G.
Leroux and D. Krewski), Canadian Journal of Statistics, 21, 1993, pp. 421-
465.
Measuring the Impact of an IntelVention
on Equipment Lives
Measuring the impact of an intervention on
equipment lives
Key words and phrases: Equipment-failure data, survival analysis, intervention anal
ysis, Cox regression, Poisson process, legal proceeding.
AMS 1980 subject classifications: Primary 62N05; secondary 62J99, 62M99.
ABSTRACT
A 1967 strike at a Quebec aluminum smelter resulted in the uncontrolled shutdown of
aluminum-reduction cells in the smelter's potrooms. In a subsequent legal action against the
union which was before the courts for more than a decade. the company claimed that the
shutdown had reduced the operating lives of the hundreds of cells in service at the time. This
study describes the background and outcome of the court case and presents the data used by
expert witnesses to argue for and against the company's claim. Our analysts independently
examine the data and arrive at their own conclusions.
1. STUDY DESCRIPTION
1. 1. The Setting.
Aluminum is produced in an electrolytic cell operating at a very high temperature.
The anode is a carbon electrode. The cathode is a carbon-lined crucible which
contains the molten aluminum and electrolyte. Steel stubs and bars embedded in the
anode and in the cathode lining act as conductors for the cell. These aluminum
reduction cells-or pots, as they are sometimes called-are arranged in series in
smelter potrooms. A moderate-size smelter may have several hundred cells in
operation at one time. These cells generally have operating lives measured in years,
but eventually fail because of distortion of the crucible or because of cracking of the
pot lining, which leads to loss of contents or iron contamination of the molten
aluminum.
2 Case Studies in Data Analysis
Case Study No.1, Pages 1-23
In 1967, at the present Canadian Reynolds Metals Company smelter in Baie
Comeau, Quebec, electric power to the potrooms was cut during a labour dispute,
resulting in an uncontrolled shutdown of the cells. The consequent cooling of cell
contents and the subsequent difficulties of restarting the cells after the disruption
ended were believed by the company to have damaged all or some of the cells in
service at the time of the shutdown. The shutdown eventually led to a legal action by
the Company against the smelter workers' union (Confederation des Syndicats
Nationaux) and others to recover costs associated with lost production and damage
to equipment. The case of Societe Canadienne de Metaux Reynolds Limitee v.
Confederation des Syndicats Nationaux et Autres was heard in Quebec Superior
Court before Judge Vincent Masson. The legal proceedings were complex and
lengthy-a decision was finally rendered on 6 February 1979, after being before the
court for more than a decade. This statistical study is concerned with one issue which
arose in the proceedings in 1977, namely, the statistical estimation of the total loss of
operating life, if any, for the several hundred cells in service at the time of the
uncontrolled shutdown.
1.2. The Data.
The data for this study were extracted from Court Exhibit D-9 and are found in
Tables A-I and A-2 of the Appendix.
Table A-I contains failure data for 499 cells, of which 349 were in circuit at the
time of the shutdown (subsequently referred to as the intervention). The cells vary in
both design and time in circuit. Consider first the matter of design. Because of the
economic importance of extending the operating life of an aluminum-reduction cell,
there is continual experimentation with new designs and with variations of established
designs. New designs or design variations are tested in groups of cells which are
installed in the normal course of replacing failed cells. Design groups in this case
vary in size from a handful to a few dozen cells. The standard cell design in use at
the time of the intervention is denoted in Table A-l(a) by the generic label A. Within
type-A cells, however, there are twenty minor design variants which are labelled AI,
A2, ... , A20. Table A-l(a) contains data for 395 cells of the standard design, of
which 297 were in service at the time of the intervention. The data in Table A-l(b)
refer to experimental cells. Labels B, C, ... , K identify experimental groups of cells
having distinct and largely untried design features.
Operating experience with all ofthe cells in a design group is relevant for estimating
the remaining life of cells in the group which were still in service at the intervention.
Thus, Table A-I contains data for all of the cells of each design group represented
by one or more cells in service at the time of the intervention. Specifically, for each
cell, the table shows its failure age (in days) and its age at intervention (in days).
Note, therefore, that any cell for which the age at intervention exceeds the failure age
did not experience the intervention. For example, refer to design group Al in Table
A-l(a). This first variant of the standard design consists of20 cells, of which the first
17 failed before the intervention and the last 3 were still in service at the time of the
intervention. The first cell, for instance, failed at age 468 days and would have been
2236 days old if it had survived until the day of the intervention. In contrast, the last
cell failed at age 2541 days, 254 days after the intervention. On the day of the
intervention, its age was 2287 days.
The cells in each group are ordered by failure age. The failure ages given in the
tables exclude the days during which cells were out of service during the shutdown.