Analysis of Step-Stress Models

Existing Results and Some Recent Developments

Debasis Kundu, Ayon Ganguly

• Publisher: Academic Press
• Year: 2017
• Print ISBN:
  9780128097137
• eBook ISBN:
  9780081012406
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Analysis of Step-Stress Models: Existing Results and Some Recent Developments describes, in detail, the step-stress models and related topics that have received significant attention in the last few years. Although two books, Bagdonavicius and Nikulin (2001) and Nelson (1990), on general accelerated life testing models are available, no specific book is available on step-stress models. Due to the importance of this particular topic, Balakrishnan (2009) provided an excellent review for exponential step-stress models. The scope of this book is much more, providing the inferential issues for different probability models, both from the frequentist and Bayesian points-of-view. - Explains the different distributions of the Cumulative Exposure Mode - Covers many different models used for step-stress analysis - Discusses Step-stress life testing under the competing or complementary risk model

1

Introduction

Abstract

The life testing experiments are essential in different aspects in modern age. The most of the products are highly durable due to the advancement of science and technology. One of the problems that the experimenter faces during life testing experiment is to obtain adequate number of failures within an affordable time. Different techniques have been devised to overcome it. Two techniques, viz., censoring schemes and accelerated life tests are gaining popularity in recent times. In this chapter, we introduce different censoring schemes and accelerated life tests. The step-stress life test is introduced as a special case of accelerated life test. Several models have been proposed in literature to describe the lifetime under a step-stress life test. In this chapter we discuss cumulative exposure model, tempered random variable model, tempered failure model and cumulative risk model. Finally we conclude this chapter providing the organization of this manuscript.

Keywords

Accelerated life testing; Step-stress life test; Censoring schemes; Cumulative exposure model; Tampered variable model; Tampered failure rate model; Cumulative risk model

1.1 Life testing experiments and their difficulties

Life testing experiments have gained a significant amount of popularity in recent times. The main aim of any life testing experiment is to measure one or more reliability characteristics of the experimental units under consideration. In a very classical form of a life testing experiment, a certain number of identical items are placed on the test under normal operating conditions and the “time to failure” of all the items is recorded. The definition of the “time to failure” depends on the items considered. For example, “time to failure” may be the time after which a minimum satisfactory performance is not achieved for a piece of electronic equipment, or it may be the number of revolutions before a malfunctioning of a ball bearing. For testing the lifetime of an electric bulb, “time to failure” is the number of...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Abbreviations
• Symbols
• 1: Introduction
• 2: Cumulative exposure model
• 3: Other related models
• 4: Step-stress life tests with multiple failure modes
• 5: Miscellaneous topics
• Bibliography
• Author Index
• Subject Index