Estudio De Distribuciones De Confiabilidad

Probability Distributions
Used in
Reliability Engineering

Probability Distributions
Used in
Reliability Engineering

Andrew N. O’Connor

Center for Risk and Reliability
0151 Glenn L Martin Hall
University of Maryland
College Park, Maryland

Published by the Reliability Information Analysis Center (RIAC)
ISBN-10:
ISBN-13:

1-933904-06-2
978-1-933904-06-1

(Hardcopy)(Hardcopy)

ISBN-10:
ISBN-13:

1-933904-07-0
978-1-933904-07-8

(Electronic)
(Electronic)

Copyright © 2011 by the Center for Reliability Engineering
University of Maryland, College Park, Maryland, USA
All rights reserved. No part of this book may be reproduced or transmitted in any form or
by any means, electronic or mechanical, including photocopying, recording, or by any
informationstorage and retrieval system, without permission in writing from The Center
for Reliability Engineering, Reliability Engineering Program.

The Center for Risk and Reliability
University of Maryland
College Park, Maryland 20742-7531

In memory of Willie Mae Webb

This book is dedicated to the memory of Miss Willie Webb who
passed away on April 10 2007 while working at the Center for
Riskand Reliability at the University of Maryland (UMD). She
initiated the concept of this book, as an aid for students
conducting studies in Reliability Engineering at the University of
Maryland. Upon passing, Willie bequeathed her belongings to
fund a scholarship providing financial support to Reliability
Engineering students at UMD. The proceeds from this book will go
directly towards theMiss Willie M. Webb Scholarship.

Preface
Reliability Engineers are required to combine a practical understanding of material
science and engineering with statistics. The reliability engineer’s understanding of
statistics is focused on the practical application of a wide variety of accepted statistical
methods. Most reliability texts provide only a basic introduction to probabilitydistributions or only provide a detailed reference to few distributions. Detailed statistician
texts provide theoretical detail which is outside the scope of likely reliability engineering
tasks. As such the objective of this book is to provide a single reference text of closed
form probability formulas and approximations used in reliability engineering.
This book provides details on 22 probabilitydistributions. Each distribution section
provides a graphical visualization and formulas for distribution parameters, along with
distribution formulas. Common statistics such as moments and percentile formulas are
followed by likelihood functions and in many cases the derivation of maximum likelihood
estimates. Bayesian non-informative and conjugate priors are provided followed by a
discussionon the distribution characteristics and applications in reliability engineering.
Each section is concluded with online and hardcopy references which can provide
further information followed by the relationship to other distributions.
The book is divided into six parts. Part 1 provides a brief coverage of the fundamentals
of probability distributions within a reliability engineering context.Part 1 is limited to
concise explanations aimed to familiarize readers. For further understanding the reader
is referred to the references. Part 2 to Part 6 cover Common Life Distributions, Bathtub
Distributions, Univariate Continuous Distributions, Univariate Discrete Distributions and
Multivariate Distributions respectively.
This book refers to software available at www.enre.umd.edu/tools.htmaimed at
students and academic staff which allow users to:
•
Plot distributions and interactively vary distribution parameters to provide
understanding on the effect each parameter has on the probability distribution
function, cumulative distribution function and hazard rate.
•
Export probability distribution plots directly to the printer, picture or to a chart
object in Microsoft...