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Selecting a system or a subset of systems that have the best performance among many alternative systems is an important area of research. All efforts are paid to do this selection with a high probability of correct selection P (C S). In this paper, we compare the performance of two popular procedures used to select the best systems, namely, the method of Kim and Nelson () which is considered as a ranking and selection procedure, and the Optimal Computing Budget Allocation ( ℬ) procedure. Both of these procedures determine the number of samples for each system that are needed to achieve the maximum P (C S). Recently, the ℬ has been developed in order to be able to approximate the value of P (C S) , so both procedures approximate the value of P (C S). To do the comparison, we implement the two methods on two examples; one is a generic example and the other one involves a management of inventory model. The two examples assure that the ℬ method always outperforms the method. [ABSTRACT FROM AUTHOR]

The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models. [ABSTRACT FROM AUTHOR]

Recently, intuitionistic fuzzy sets and numbers are widely interesting in the literature, and many types of Intuitionistic Fuzzy Numbers (IFN's) are studied and applied to different mathematical and real life problems. In this paper, an algorithm to approximate general IFN's by the n-Intuitionistic Polygonal Fuzzy Number (n-IPFN) is introduced. The approximation facilitates the calculations due to its linearity, not to mention its realisticity and flexibility. After that, a new method to rank IFN's is introduced and applied to the n-IPFN. Based on that, convenient arithmetic operations for n-IPFN's that preserve the ranking values are proposed and shown to satisfy the most important properties. As a result, defining a ranking equivalence relation gave a strong algebraic structure that is isomorphic to the real numbers set. Finally, some definitions are proposed for dealing with matrices, functions, equalities and inequalities with n-IPFN's. [ABSTRACT FROM AUTHOR]