Analysis of Failure and Survival Data

Peter J. Smith

• Publisher: Chapman and Hall/CRC
• Year: 2017
• Print ISBN:
  9781584880752
• eBook ISBN:
  9781351989671
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Analysis of Failure and Survival Data is an essential textbook for graduate-level students of survival analysis and reliability and a valuable reference for practitioners. It focuses on the many techniques that appear in popular software packages, including plotting product-limit survival curves, hazard plots, and probability plots in the context of censored data. The author integrates S-Plus and Minitab output throughout the text, along with a variety of real data sets so readers can see how the theory and methods are applied. He also incorporates exercises in each chapter that provide valuable problem-solving experience.

In addition to all of this, the book also brings to light the most recent linear regression techniques. Most importantly, it includes a definitive account of the Buckley-James method for censored linear regression, found to be the best performing method when a Cox proportional hazards method is not appropriate.

Applying the theories of survival analysis and reliability requires more background and experience than students typically receive at the undergraduate level. Mastering the contents of this book will help prepare students to begin performing research in survival analysis and reliability and provide seasoned practitioners with a deeper understanding of the field.

CHAPTER 1

Survival Distributions

1.1 Basic concepts

Survival analysis involves the study of lifetime distributions. By this we mean lifetimes of people, of cancer patients, of industrial robots, of components, of cogs, of software. We consider a broad range of applications both industrial and biological.

Example 1.1

Failure data for reduction cells in aluminium smelting

Lifetime data commonly occur in the engineering environment. In this example from a Canadian aluminium smelter, alumina is liquefied in a steel-lined box (or cell) which is built to withstand extremely high temperatures. In the smelting process, aluminium is produced as a byproduct when the cell functions like a battery with molten alumina as the electrolyte. The cell needs to be replaced when the carbon lining cracks, allowing impurities into the process. The failure time data listed were part of a larger data set and represent days of service until cell replacement.

We will be concerned with not only observing lifetime data, recording it, displaying it, but also consideration of factors affecting lifetimes, explanatory variables that help explain observed lifetimes. A typical example of survival data is given in Example 1.2, where lifetime refers to time from carcinogen injection to time of death in experimental laboratory mice. The data therefore represent death times as well as lifetimes. For this particular data there are observations on both mice kept under standard laboratory conditions and mice kept in a germ-free environment during the course of the trial — these experimental...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication Page
• Table of Contents
• Preface
• 1 Survival Distributions
• 2 Hazard Models
• 3 Reliability of Systems
• 4 Data Plots
• 5 Censoring and Lifetables
• 6 The Product-Limit Estimator
• 7 Parametric Survival Models under Censoring
• 8 Fitting Parametric Regression Models
• 9 Cox Proportional Hazards
• 10 Linear Regression with Censored Data
• 11 Buckley-James Diagnostics and Applications
• References
• Index