Functional inequalities for discrete gradients and application to the geometric distribution

Background and Aim: With an increase in demands about reliability of industrial machines following continuous or discrete distribution, the important thing to be noticed is that in all previous researches where systems are having more than one failure no iteration technique has been studied to separate the failed unit on basis of its failure. Therefore, aim of our paper is to analyze the real industrial discrete problem following cold standby units arranged in parallel manner with newly concept of inspection procedure for failed units to inspect the exact failure and being communicator to the repairman for repairing exact failed part of unit for saving time and maintenance cost. Methods: The geometric distribution and regenerative techniques had been applied for calculating different reliability measures like mean time to system failure, availability of a system, inspection, repair and failed time of unit. Results: Graphical and analytical study had also been done to analyze the increasing/decreasing behavior of profit function w.r.t repair and failure rate. The system responded properly in fulﬁlling his basic needs. Conclusion: The calculated value of all reliability parameter is helpful for studying any other models following same concept under different environmental conditions. Thus, it concluded that, reliability increases/decreases with increase in repair/failure rate. Also, the evaluated results by this paper provides the better reliability testing strategies that helps to develop new techniques which leads to increase the effectiveness of system.

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Choosing the best eestimated regression equation for data subject to geometric distribution (Student data as a case study)

Journal of Physics Conference Series ◽

10.1088/1742-6596/1879/3/032045 ◽

2021 ◽

Vol 1879 (3) ◽

pp. 032045

Author(s):

Osanma Abdulazeez kadhim Al-Quraishi

Keyword(s):

Geometric Distribution ◽

Regression Equation ◽

Student Data ◽

Data Subject

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Bi-additive s-functional inequalities and biderivation in modular spaces

The Journal of Analysis ◽

10.1007/s41478-021-00311-y ◽

2021 ◽

Author(s):

T. L. Shateri

Keyword(s):

Functional Inequalities ◽

Modular Spaces

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Functional Inequalities for Two-Level Concentration

Potential Analysis ◽

10.1007/s11118-021-09900-9 ◽

2021 ◽

Author(s):

Franck Barthe ◽

Michał Strzelecki

Keyword(s):

Sobolev Inequality ◽

Poincaré Inequality ◽

Logarithmic Sobolev Inequality ◽

Probability Measures ◽

Exponential Rate ◽

Functional Inequalities ◽

Concentration Inequality ◽

Poincare Inequality ◽

Free Concentration ◽

Concentration Property

AbstractProbability measures satisfying a Poincaré inequality are known to enjoy a dimension-free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension-free concentration property, known as two-level concentration. We show that a similar phenomenon occurs for the Latała–Oleszkiewicz inequalities, which were devised to uncover dimension-free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.

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Use of Basu-Dhar bivariate geometric distribution in the analysis of the reliability of component series systems

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-05-2018-0115 ◽

2019 ◽

Vol 36 (4) ◽

pp. 569-586

Author(s):

Ricardo Puziol Oliveira ◽

Jorge Alberto Achcar

Keyword(s):

Bayesian Approach ◽

Geometric Distribution ◽

Bivariate Distribution ◽

Dependence Structure ◽

Series System ◽

Engineering Applications ◽

Data Set ◽

Content Type ◽

Bivariate Geometric Distribution ◽

Series Systems

Purpose The purpose of this paper is to provide a new method to estimate the reliability of series system by using a discrete bivariate distribution. This problem is of great interest in industrial and engineering applications. Design/methodology/approach The authors considered the Basu–Dhar bivariate geometric distribution and a Bayesian approach with application to a simulated data set and an engineering data set. Findings From the obtained results of this study, the authors observe that the discrete Basu–Dhar bivariate probability distribution could be a good alternative in the analysis of series system structures with accurate inference results for the reliability of the system under a Bayesian approach. Originality/value System reliability studies usually assume independent lifetimes for the components (series, parallel or complex system structures) in the estimation of the reliability of the system. This assumption in general is not reasonable in many engineering applications, since it is possible that the presence of some dependence structure between the lifetimes of the components could affect the evaluation of the reliability of the system.

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On a certain stability of the Hermite–Hadamard inequality

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0291 ◽

2008 ◽

Vol 465 (2102) ◽

pp. 571-583 ◽

Cited By ~ 5

Author(s):

Attila Házy ◽

Zsolt Páles

Keyword(s):

Functional Inequalities ◽

Hadamard Inequality ◽

Real Functions ◽

The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

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