M. J. S. Khan

Bio: M. J. S. Khan is an academic researcher from Aligarh Muslim University. The author has contributed to research in topics: Order statistic & Burr distribution. The author has an hindex of 5, co-authored 12 publications receiving 50 citations. Previous affiliations of M. J. S. Khan include Banasthali Vidyapith & Ambedkar University Delhi.

UMVU Estimation of Reliability Function and Stress–Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records

Abstract: SYNOPTIC ABSTRACTIn this study, we have obtained the uniformly minimum variance unbiased estimator (UMVUE) of reliability function and stress–strength reliability for one parameter proportional reversed hazard rate family of distribution based on lower record values. Further, the results are reduced for power function distribution, exponentiated Weibull distribution, generalized exponential distribution, generalized Rayleigh (also known as Burr type X) distribution and Topp–Leone distribution. Also, the UMVU estimator and maximum likelihood estimator are compared through simulation.

Generalized Order Statistics from Chen Distribution and its Characterization

Abstract: In this paper, we have established the recurrence relations for single and product moments of generalized order statist ics from Chen distribution. The result includes as particular c ases of recurrence relations for moments of order statistic s, sequential order statistics, progressive type II censored order statistics andkth records. Further, using the recurrence relation for single moments, we have obtained the characterization result for Chen distrib ution.

On moments of dual generalized order statistics from Topp-Leone distribution

Abstract: In this paper, we have derived exact and explicit expressions for the ratio and inverse moments of dual generalized order statistics from Topp-Leone distribution. This result includes the single an...

Characterization of continuous distributions through conditional expectation of function of generalized order statistics-an alternative approach

Abstract: A general form of continuous distribution has been characterized through the conditional expectation of function of generalized order statistics and record values using Meijer’s G-function. Further, various deductions for order statistics, records, sequential order statistics and progressively censored samples are discussed.

On ratio and inverse moment of generalized order statistics from burr distribution

Abstract: In this paper, the ratio and inverse moments of generalized order statistics (gos) when 1 1 n m m m      and i j    are obtained for Burr distribution using hypergeometric function and some of its deductions are also discussed.

Table Of Integrals Series And Products

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Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications

Abstract: In this paper, a new flexible generator of distributions is proposed. Some of its fundamental properties including quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, mean...

Optimization and estimation in system reliability allocation problem

Abstract: Designing an optimal reliability system with a minimum cost is one of the challenging problems in engineering field over the years. Estimating the subsystem reliability and determining the optimal number of component allocation will give an insight into the adequate performance of the entire system under study. In some scenarios, if a subsystem fails, then the whole system will fail, thus posing a severe threat to the safety of engineers and personnel involved. Hence, the need to optimally determine and allocate the required number of components as well as estimating their reliability so that the system’s safety would be guaranteed. In this paper, two procedures for estimating system reliability function are proposed using the maximum likelihood estimators and uniformly minimum variance unbiased estimators. The reliability functions of some selected lifetime distributions are estimated using the proposed procedures via a simulation study. The study presents a hybrid concept of estimation and optimization theory in reliability allocation problem. The work illustrated through a case study, and an optimization technique used to determine the optimal number of components at a minimum cost. The study would be useful for decision-makers in heavy industries/complex systems to help estimate the reliability of system components, optimize the allocation and manufacturer selection problems.

Stress–strength reliability of a non-identical-component-strengths system based on upper record values from the family of Kumaraswamy generalized distributions

Abstract: In an attempt to produce more realistic stress–strength models, this article considers the estimation of stress–strength reliability in a multi-component system with non-identical component strengt...

On some nonstandard software reliability models

Abstract: The Hausdorff approximation of the shifted Heaviside function ht0(t) by sigmoidal functions based on the Song–Chang–Pham [2] cumulative functions is investigated and an expression for the error of the best approximation is obtained in this paper. The results of numerical examples confirm theoretical conclusions and they are obtained using programming environment Mathematica. We give also real-world examples with data provided in [4] using Song–Chang– Pham [2] software reliability model. Dataset included [5] Year 2000 compatibility modifications, operating system upgrade, and signaling message processing. AMS Subject Classification: 41A46, 68N30