scholarly journals The hazard rate function of the logistic Birnbaum-Saunders distribution: Behavior, associated inference, and application

2021 ◽  
Vol 33 (7) ◽  
pp. 101580
Author(s):  
Farouq Mohammad A. Alam ◽  
Abeer Mansour Almalki
Keyword(s):  
Hazard Rate ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Distribution Behavior

Reliability Concepts

2018 ◽  
pp. 1-22
Keyword(s):  
Hazard Rate ◽  
Failure Process ◽  
Reliability Function ◽  
Rate Function ◽  
Cumulative Distribution ◽  
Hazard Rate Function ◽  
Reliability Engineering ◽  
Probability Models ◽  
Engineering Design Process ◽  
Basic Concepts

The first chapter introduces basic concepts of Reliability and their relationships. Four probability functions—reliability function, cumulative distribution function, probability density function, and hazard rate function—that completely characterize the failure process are defined. Three failure rates—MTBF, MTTF, MTTR—that play important role in reliability engineering design process are explained here. The three patterns of failures, DFR, CFR, and IFR, are discussed with reference to the bathtub curve. Two probability models, Exponential and Weibull, are presented. Series and parallel systems and application areas of reliability are also presented.

Bounds for the hazard rate and the reversed hazard rate of the convolution of dependent random lifetimes

2019 ◽  
Vol 56 (4) ◽  
pp. 1033-1043 ◽  
Author(s):  
Félix Belzunce ◽  
Carolina Martínez-Riquelme
Keyword(s):  
Recent Result ◽  
Upper Bound ◽  
Hazard Rate ◽  
Rate Function ◽  
Semiparametric Models ◽  
Hazard Rate Function ◽  
Reversed Hazard Rate ◽  
Parametric And Semiparametric Models ◽  
Reversed Hazard Rate Function

AbstractAn upper bound for the hazard rate function of a convolution of not necessarily independent random lifetimes is provided, which generalizes a recent result established for independent random lifetimes. Similar results are considered for the reversed hazard rate function. Applications to parametric and semiparametric models are also given.

A stochastic process for modeling failures of a system having a non-monotonic hazard rate function

2019 ◽  
Vol 233 (5) ◽  
pp. 731-746
Author(s):  
Lucianne Varn ◽  
Stefanka Chukova ◽  
Richard Arnold
Keyword(s):  
Stochastic Process ◽  
Hazard Rate ◽  
Repair Process ◽  
Rate Function ◽  
Hazard Rates ◽  
Failure Rates ◽  
Hazard Rate Function ◽  
Repairable Systems ◽  
System Failures ◽  
Quantities Of Interest

Reliability literature on modeling failures of repairable systems mostly deals with systems having monotonically increasing hazard/failure rates. When the hazard rate of a system is non-monotonic, models developed for monotonically increasing failure rates cannot be effectively applied without making assumptions on the types of repair performed following system failures. For instance, for systems having bathtub-shaped hazard rates, it is assumed that during the initial, decreasing hazard rate phase, all repairs are minimal. These assumptions on the type of general repair can be restrictive. In order to relax these assumptions, it has been suggested that general repairs in the initially decreasing phase can be modeled as “aging” the system. This approach however does not preserve the order of effectiveness of the types of general repair as defined in the literature. In this article, we develop a set of models to address these shortcomings. We propose a new stochastic process to model consecutive failures of repairable systems having non-monotonic, specifically bathtub-shaped, hazard rates, where the types of general repair are not restricted and the order of the effectiveness of the types of repair is preserved. The proposed models guarantee that a repaired system is at least as reliable as one that has not failed (or equivalently one that has been minimally repaired). To illustrate the models, we present multiple examples and simulate the failure-repair process and estimate the quantities of interest.

scholarly journals Slashed Lomax Distribution and Regression Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1877
Author(s):  
Huihui Li ◽  
Weizhong Tian
Keyword(s):  
Regression Model ◽  
Hazard Rate ◽  
Rate Function ◽  
Model Parameters ◽  
Asymmetric Distribution ◽  
Hazard Rate Function ◽  
Simulation Studies ◽  
Ecm Algorithm ◽  
Lomax Distribution ◽  
Skewness And Kurtosis

In this article, the slashed Lomax distribution is introduced, which is an asymmetric distribution and can be used for fitting thick-tailed datasets. Various properties are explored, such as the density function, hazard rate function, Renyi entropy, r-th moments, and the coefficients of the skewness and kurtosis. Some useful characterizations of this distribution are obtained. Furthermore, we study a slashed Lomax regression model and the expectation conditional maximization (ECM) algorithm to estimate the model parameters. Simulation studies are conducted to evaluate the performances of the proposed method. Finally, two sets of data are applied to verify the importance of the slashed Lomax distribution.

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