Skip to content
Register Sign in Wishlist
Mathematical Theory of Reliability

Mathematical Theory of Reliability


Part of Classics in Applied Mathematics

  • Date Published: January 1996
  • availability: Available in limited markets only
  • format: Paperback
  • isbn: 9780898713695

£ 51.99

Available in limited markets only
Unavailable Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions - and only those based on plausible physical considerations - so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its re-publication.

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: January 1996
    • format: Paperback
    • isbn: 9780898713695
    • length: 274 pages
    • dimensions: 228 x 152 x 14 mm
    • weight: 0.368kg
    • availability: Available in limited markets only
  • Table of Contents

    Preface to the Classics Edition
    1. Introduction. Historical Background of the Mathematical Theory of Reliability
    Definitions of Reliability
    2. Failure Distributions. Introduction
    Typical Failure Laws
    The Exponential as the Failure Law of Complex Equipment
    Monotone Failure Rates
    Preservation of Monotone Failure Rate
    Additional Inequalities
    General Failure Rates
    3. Operating Characteristics of Maintenance Policies. Introduction
    Renewal Theory
    Replacement Based on Age
    Comparison of Age and Block Replacement Policies
    Random Replacement
    Repair of a Single Unit
    4. Optimum Maintenance Policies. Introduction
    Replacement Policies
    Inspection Policies
    5. Stochastic Models for Complex Systems. Introduction
    Markov Chains and Semi-Markov Processes
    Repairman Problems
    Marginal Checking
    Optimal Maintenance Policies under Markovian Deterioration
    6. Redundancy Optimization. Introduction
    Optimal Allocation of Redundancy Subject to Constraints
    Application to Parallel Redundancy Model
    Application to Standby Redundancy Model
    Complete Families of Undominated Allocations
    Optimal Redundancy Assuming Two Types of Failure
    7. Qualitative Relationships for Multicomponent Structures. Introduction
    Achieving Reliable Relay Circuits
    Monotonic Structures
    S-shaped Reliability Functions for Monotonic Structures
    k-out-of-n Structures
    Relationship between Structures Failure Rate and Component Failure Rates
    Appendix 1. Total Positivity
    Appendix 2. Test for Increasing Failure Rate
    Appendix 3. Tables Giving Bounds on Distributions with Monotone Failure Rate

  • Authors

    Richard E. Barlow, University of California, Berkeley

    Frank Proschan, Florida State University

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.