the parallel systems are special important types of coherent structures and have many applications in various areas.in this paper we consider a two-exchangeable-component parallel system for the generalized farlie-gumbel-morgenstern (generalized fgm) distribution. we study the reliability properties of the residual lifetime of the system under the condition that both components of the system ar...

We present an analytic model for the performance evaluation of hierarchical cellular systems, which can provide multiple routes for calls through overflow from one cell layer to another. Our model allows the case where both the call time and the cell residence time are generally distributed. Based on the characterization of the call time by a hyper-Erlang distribution, the Laplace transform of ...

The Equivalent Random Method (ERM) has been widely used to predict blocking probabilities at overflow service stations. The method assumes that service times follow an exponential distribution. While this may be a reasonable assumption for voice traffic, it is not a good assumption for dial-up Internet traffic, where service times typically have a coefficient of variation (standard deviation/me...

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

In Statistical Process Control (SPC) there exists a need to model the run-length distribution of a Q-chart that monitors the process mean when measurements are from an exponential distribution with an unknown parameter. To develop exact expressions for the probabilities of run-lengths the joint distribution of the charting statistics is needed. This gives rise to a new distribution that can be ...

In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta, Gupta, and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, th...

Two SEIR models with quarantine and isolation are considered, in which the latent and infectious periods are assumed to have an exponential and gamma distribution, respectively. Previous studies have suggested (based on numerical observations) that a gamma distribution model (GDM) tends to predict a larger epidemic peak value and shorter duration than an exponential distribution model (EDM). By...

Definition 1.1 Let N(0, 1) denote the one dimensional normal distribution. This distribution has density n(x) = e−x 2/2/ √ 2π. LetNd(0, 1) denote the d-dimensional Gaussian distribution, induced by picking each coordinate independently from the standard normal distribution N(0, 1). Let Exp(λ) denote the exponential distribution, with parameter λ. The density function of the exponential distribu...

We demonstrate a new type of weak measurement based on the dynamics of spontaneous emission. The pointer in our scheme is given by the Lorentzian distribution characterizing atomic exponential decay via emission of a single photon. We thus introduce weak measurement, so far demonstrated nearly exclusively with laser beams and Gaussian statistics, into the quantum regime of single emitters and s...