ON CLASSES OF LIFETIME DISTRIBUTIONS WITH UNKNOWN AGE

Some class properties of the used better (worse) than aged [UBA (UWA)] and the used better (worse) than aged in expectation [UBAE (UWAE)] classes of lifetime distributions are considered. Relationships with the decreasing (increasing) mean residual lifetime [DMRL (IMRL)] class and the decreasing (increasing) variance residual lifetime [DVRL (IVRL)] class are established. Discrete UBA and UWA distributions are introduced and studied. Characterizations of UBA and UWA distributions are derived by using discrete aging properties of mixed Poisson distributions. Applications of these results to queueing theory and ruin are then considered. In particular, preservation of UBA (UWA) and UBAE (UWAE) under a transform of life distributions is given.

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A Dynamic Failure Time Degradation-Based Model

Symmetry ◽

10.3390/sym12091532 ◽

2020 ◽

Vol 12 (9) ◽

pp. 1532

Author(s):

Abdulhakim A. Albabtain ◽

Mansour Shrahili ◽

Lolwa Alshagrawi ◽

Mohamed Kayid

Keyword(s):

Hazard Rate ◽

Failure Time ◽

Degradation Process ◽

Residual Lifetime ◽

Time To Failure ◽

Lifetime Distributions ◽

Mean Residual Lifetime ◽

Aging Properties ◽

Degradation Models ◽

Characterization Property

A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established.

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Entropy-based measure of uncertainty in past lifetime distributions

Journal of Applied Probability ◽

10.1017/s002190020002266x ◽

2002 ◽

Vol 39 (02) ◽

pp. 434-440 ◽

Cited By ~ 34

Author(s):

Antonio Di Crescenzo ◽

Maria Longobardi

Keyword(s):

Shannon Entropy ◽

Lifetime Distribution ◽

Residual Entropy ◽

Residual Lifetime ◽

Lifetime Distributions ◽

The Past ◽

Life Distributions ◽

Measure Of Uncertainty

As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

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The Complementary Exponentiated Exponential Geometric Lifetime Distribution

Journal of Probability and Statistics ◽

10.1155/2013/502159 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Francisco Louzada ◽

Vitor Marchi ◽

James Carpenter

Keyword(s):

Practical Importance ◽

Formal Proof ◽

Residual Lifetime ◽

Lifetime Distributions ◽

Hazard Functions ◽

New Family ◽

Maximum Likelihood Procedure ◽

Mean Residual Lifetime ◽

Risk Scenario ◽

Modified Weibull

We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments,rth moment of theith order statistic, mean residual lifetime, and modal value. Inference is implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the modified Weibull, and the generalized exponential-Poisson distribution.

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Entropy-based measure of uncertainty in past lifetime distributions

Journal of Applied Probability ◽

10.1239/jap/1025131441 ◽

2002 ◽

Vol 39 (2) ◽

pp. 434-440 ◽

Cited By ~ 72

Author(s):

Antonio Di Crescenzo ◽

Maria Longobardi

Keyword(s):

Shannon Entropy ◽

Lifetime Distribution ◽

Residual Entropy ◽

Residual Lifetime ◽

Lifetime Distributions ◽

The Past ◽

Life Distributions ◽

Measure Of Uncertainty

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The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-1132 ◽

2021 ◽

Vol 9 (4) ◽

pp. 974-983

Author(s):

M. S Eliwa ◽

Medhat EL-Damcese ◽

A. H. El-Bassiouny ◽

Abhishek Tyag ◽

M. El-Morshedy

Keyword(s):

Weibull Distribution ◽

Rate Function ◽

Vital Role ◽

Point Of View ◽

Residual Lifetime ◽

Mathematical Properties ◽

Mean Residual Lifetime ◽

Aging Properties ◽

Two Parameters ◽

Result Analysis

Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k − out − of − n : F systems has gained a lot of attention in recent years from a theoretical and practical point of view. In the present article, we have studied some important stochastic and aging properties of residual lifetime of consecutive k − out − of − n : F systems under the condition n − k + 1, k ≤ n and all components of the system are working at time t. The mean residual lifetime (MRL) and its hazard rate function are proposed for the linear consecutive k − out − of − n : F (lin/con/k/n:F) and circular consecutive k − out − of − n : F (cir/con/k/n:F) systems. Furthermore, several mathematical properties of the proposed MRL are examined. Finally, the Weibull distribution with two parameters is used as an example to explain the theoretical results.

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