Mathematics

Problem statement: The aim of this study is to generalize reliability equivalence technique to apply it to a system consists of m independent and non-identical lifetimes distributions, with mixed failure lifetimes f 1 (t),f 2 (t),…,f m (t). Approach: We shall improve the system by using some reliability techniques: (i) reducing the failure for some lifetimes; (ii) add hot duplication component; (iii) add cold duplication component; (iv) add cold duplication component with imperfect switch. We start by establishing two different types of reliability equivalence factors, the Survival Reliability Equivalence (SRE) and Mean Reliability Equivalence (MRE) factors. Also, we introduced a numerical illustrative example. Results: The system reliability function and mean time to failure will be used as reference of the system performances. For this reason, we obtain the reliability functions and mean time to failures of the original and improved systems using each improving methods. Conclusion: The results can be used to distinguish between the original and improved systems performances and calculate the equivalent between different cases of improving methods.

Abstract. This paper discusses the reliability equivalences of a parallel-series system. It is assumed that the system components are independent and identical. Each has a constant failure rate. We assumed three different method to improve the system. Both the reliability function ...

This paper introduces three different types of the reliability equivalence factors of a parallel-series system consists of four independent and identical components. The lifetime of the system component is assumed to follow exponential distribution. The reliability function and mean time to ...

Problem statement: In reliability theory and operations research, there are many methods and techniques to improve the performance of a system. The aim of this study is to generalize reliability equivalence technique to apply it to a mixed failure lifetimes system f 1 (t), f 2 (t) with delayed time. Approach: We shall improve the system by using some reliability techniques: (i) reducing the failure for some lifetimes; (ii) add hot duplication components; (iii) add cold duplication components; (iv) add cold duplication components with imperfect switches. We start by establishing two different types of reliability equivalence factors, the Survival Reliability Equivalence (SRE) and Mean Reliability Equivalence (MRE) factors. Also, we introduced some numerical results. Results: The system reliability function and mean time to failure will be used as reference of the system performances. For this reason, we obtain the reliability functions and mean time to failures of the original and improved systems using each improving methods. Conclusion: The results can be used to distinguish between the original and improved systems performances and calculate the equivalent between different cases of improving methods.

The availability equivalence factors of a general repairable parallel-series system are discussed in this paper considering the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent factors of the system are derived. The results derived in this paper generalize those given in the literature. A numerical example is introduced to illustrate how the idea of this work can be applied.

In this article, the failure rates of the system's components are functions of time t. We study two cases (i) the life time distribution of a components has two stages with increasing failure rates, (ii) the failure rates of the components have the two stages. The reliability equivalence factors of some systems with identical components are obtained. Two different methods are used to improve the given systems. Numerical examples are presented to interpret how one can utilize the obtained results. Some special cases are obtained from our results.

In this paper, we derive new matrix representation for Daehee numbers and polynomials, the λ-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on Daehee numbers and polynomials. Moreover, we obtained some new results for Daehee and Bernoulli numbers and polynomials.

This paper introduces studies on exponentaited generalized Weibull - Gompertz distribution EGWGD which generalizes a lot of distributions. Several properties of the EGWGD such as reversed (hazard) function, moments, maximum likelihood estimation, mean residual (past) lifetime, MTTF, MTTR, MTBF, maintainability, availability and order statistics are studied in this paper. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well-known distributions

In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood method is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order λ-Daehee numbers and polynomials and the twisted λ-Daehee numbers and polynomials of order k. This helps us to obtain simple and short proofs of many previous results on higher order Daehee numbers and polynomials. Moreover, we obtained recurrence relation, explicit formulas and some new results for these numbers and polynomials. Furthermore, we investigated the relation between these numbers and polynomials and Stirling numbers, Nörlund and Bernoulli numbers of higher order. The results of this article gives a generalization of the results derived very recently by El-Desouky and Mustafa .

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode are investigated. The method of maximum likelihood is used for estimating the model parameters. An applications to real data is carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.

In this paper, a system of five components is studied; one of these components is a bridge network component. Each of these components has a non-constant failure rate. The system components have linear failure rate lifetime distribution. The given system is improved by using three methods: reduction, warm standby with perfect switch and warm standby with imperfect switch. The reliability equivalence factors of the bridge structure system are obtained. The γ-fractiles are obtained to compare the original system with these improved systems. Finally, we present numerical results to show the difference between these methods.

Recently, Sarhan (2009) introduced a new distribution named generalized quadratic hazard rate distribution. In this study, we define a bivariate Generalized Quadratic Hazard Rate Distribution (BGQHRD). The joint cumulative distribution function and joint survival function are derived in compact forms. Several properties of BGQFRD have been discussed. The conditional probability density function, rth moments and joint and marginal moment generating functions are obtained. Parameters estimators using the maximum likelihood method are obtained. A numerical illustration is used to obtain maximum likelihood estimators (MLEs). Moreover, we study the behavior of the estimators numerically.

This paper gives a new generalization of higher order Daehee and Bernoulli numbers and polynomials. We define the multiparameter higher order Daehee numbers and polynomials of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. The relations between these numbers and Stirling and Bernoulli numbers are obtained. Furthermore, some interesting special cases of the generalized higher order Daehee and Bernoulli numbers and polynomials are deduced.

The performance of a repairable bridge network system is improved by using the availability equivalence factors. All components for the bridge system have constant failure and repair rates. The system is improved through the use of five methods: reduction, increase, hot duplication, warm duplication, and cold duplication methods. The availability of the original and improved systems is derived. Two types of availability equivalence factors of the system are obtained to compare different system designs. Numerical example to interpret how to utilize the obtained results is provided.

This article focuses on using E-Bayesian estimation for the Weibull distribution based on adaptive type-I progressive hybrid censored competing risks (AT-I PHCS). The case of Weibull distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E-Bayesian estimation is discussed by considering three different prior distributions for the hyper-parameters. The E-Bayesian estimators as well as the corresponding E-mean square errors are obtained by using squared and LINEX loss functions. Some properties of the E-Bayesian estimators are also derived. A simulation study to compare the various estimators and real data application is applied to show the applicability of the different estimators are proposed.

In this article we introduce a new four-parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it's statistical properties are obtained including ordinary and incomplete moments, quantile and mode, the moment generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is given. Moreover, we give the advantage of the OGE-FWE distribution by an application using real data.

This paper introduces a new four parameters model called the Weibull Generalized Flexible Weibull extension (WGFWE) distribution which exhibits bathtub-shaped hazard rate. Some of it's statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

We derive new matrix representation for higher-order changhee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on higher-order changhee numbers and polynomials. Moreover, we obtain recurrence relations, explicit formulas and some new results for these numbers and polynomials. Furthermore, we investigate the relations between these numbers and polynomials and Stirling numbers, Norlund and Bernoulli numbers of higher-order. Some numerical results using Mathcad program are introduced.