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Total Time on Test Transforms of Order n and Their Implications in Reliability Analysis

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

N. Unnikrishnan Nair ,
P. G. Sankaran  and
B. Vinesh Kumar
N. Unnikrishnan Nair*
Affiliation:
Cochin University of Science and Technology
P. G. Sankaran*
Affiliation:
Cochin University of Science and Technology
B. Vinesh Kumar*
Affiliation:
Cochin University of Science and Technology
*
∗Postal address: Department of Statistics, Cochin University of Science and Technology, Cochin, 682 022, India.
∗∗Email address: pgsankaran@cusat.ac.in
∗Postal address: Department of Statistics, Cochin University of Science and Technology, Cochin, 682 022, India.
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Abstract

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In this paper we study the properties of total time on test transforms of order n and examine their applications in reliability analysis. It is shown that the successive transforms produce either distributions with increasing or bathtub-shaped failure rates or distributions with decreasing or upside bathtub-shaped failure rates. The ageing properties of the baseline distribution is compared with those of transformed distributions, and a partial order based on nth-order transforms and their implications are discussed.

Keywords

Total time on test transformpartial orderageing conceptcharacterization

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 62N05: Reliability and life testing
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1126 - 1139
Copyright
Copyright © Applied Probability Trust 2008 

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