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This paper deals with the estimation of the stress-strength reliability of time-dependent models. Suppose that a system is allowed to run continuously and is subjected to random stress at random ti...

A stationary M/M/1 queueing model satisfies the equilibrium condition that the arrival rate, λ is less than or equal to the service rate, µ. In this paper, we have discussed the Bayes estimation of...

This paper deals with the problem of maximum likelihood and Bayesian estimation of stress-strength reliability involving paired observation with ties using bivariate exponentiated half-logistic distribution. This problem is of importance because in some real applications the strength of the component is highly dependent on the stress experienced by it. A bivariate extension of exponentiated half-logistic is discussed and an expression for the stress-strength reliability is obtained. This model is also useful to analyse data having the unusual feature of having a number of pairs with tied scores, even when the scores are continuous. The maximum likelihood estimate and interval estimate of the stress-strength reliability has been developed. The Bayes estimates of the stress-strength reliability under squared error loss function are obtained using importance sampling technique. Simulation studies are conducted to evaluate the performance of maximum likelihood and Bayes estimates. Two real-life data sets are analysed to numerically illustrate the usefulness of the developed method.

This article describes Bayes estimation of various queue characteristics such as queue parameters λ and μ, and queue performance measures like traffic intensity, expected waiting time in the queue,...

In this paper, the stress-strength reliability of single and multi-component systems are estimated assuming discrete phase type distribution for stress and strength components. The systems with str...

The present study was designed to investigate the potential of the biopolymeric nanoparticle, formulated solely from natural resources using zein from maize as the core, pectin from ivy gourd as shell and ethyl acetate fraction of the plant Mimosa pudica as the drug. The plant-mediated biosynthesis of the biopolymeric nanoparticle was done by sonication method. The morphology and size of nanoparticles were characterized by Scanning Electron Microscopy and the thermal stability was studied with the aid of Thermogravimetric Analysis and Differential Scanning Calorimetric studies. An in vitro drug release study was conducted to study the release of the plant extract from the nanoparticle and the mechanism of release was deduced by substituting the values to various mathematical models. The SEM investigation of developed nanoparticles revealed that the particles are amorphous, spherical in shape with a size ranging from 150 to 200 nm diameters. The FT-IR characterization study confirmed the incorporation of all the components in Nanoparticle. The investigation on thermal stability was achieved by thermogravimetric and differential scanning calorimetric studies and the results revealed that the particles are stable upto120 °C. Sustained drug release was observed in in vitro drug release studies at intestinal pH. To establish the mechanism of release the data were substituted to various mathematical models and was found to follow zero order and Higuchi mechanisms. Keywords: Anti-diabetic, Nanoparticle, Mimosa pudica, Zein, Pectin

This article deals with inferences on stress strength reliability in a multicomponent system for Type I generalized half-logistic distribution. It is assumed that the strength and stress components are independently distributed. In this work, we develop some statistical properties of the type I generalized half-logistic distribution. Furthermore, the expression for stress strength reliability for a multicomponent setup was obtained and studied. Two methods to estimate the multicomponent stress-strength reliability maximum likelihood and Bayesian estimation were employed. The Bayes estimates of the multicomponent stress strength reliability are obtained under squared error loss function and using gamma priors for the parameters. Simulation studies were conducted to assess the efficiency of the methods. The importance of this model was studied by applying it to a real life data set.

A new probability model obtained by generalizing the power transformed half logistic distribution is introduced by transforming the type II beta distribution. The basic properties of the distributi...

The time-dependent stress-strength reliability models deal with systems whose strength or the stress imposed on it or both are time-dependent. In this paper, we consider time-dependent stress-strength reliability model which is subjected to constant stress and it causes a change in the strength of the system over each run of the system. Assuming a continuous phase-type distribution for the initial strength and exponential distribution for the duration of each run of the system called cycle time we derived the expression for the stress-strength reliability of the system at time t. The model is further extended to the cases where cycle time distribution is Gamma and Weibull. Simulation studies are conducted to assess the variations in stress-strength reliability, R(t) at different time points, corresponding to the changes in the initial strength distribution and cycle time distribution. Resumen Los modelos de confiabilidad tensión-resistencia dependientes del tiempo tratan con sistemas cuya fuerza o el estrés que se le impone o ambos dependen de tiempo. En este artículo, consideramos modelos de confiabilidad de resistencia-tensión dependientes del tiempo que está sometido a un estrés constante y provoca un cambio en la fuerza del sistema después de cada ejecución del sistema. Asumiendo una fase continua distribución de tipo para la fuerza inicial y distribución exponencial para la duración de cada ejecución del sistema llamado tiempo de ciclo que obtuvimos la expresión de la fiabilidad tensión-resistencia del sistema en el tiempo t. El modelo se amplía aún más a los casos en los que la distribución del tiempo de ciclo es Gamma y Weibull. Se realizan estudios de simulación para evaluar las variaciones en la confiabilidad tensión-resistencia, R(t) en diferentes puntos de tiempo, correspondiente a los cambios en la distribución y el ciclo de la fuerza inicial distribución del tiempo.

In this paper, we consider the Bayesian inference of M/M/𝑅 queue with 𝑅 heterogeneous servers with service rates \mu_{1},\mu_{2},\ldots,\mu_{R}, where \mu_{1}>\mu_{2}>\cdots>\mu_{R}. Assuming multivariate gamma prior distribution for service rates and gamma prior distribution for arrival rate 𝜆, we derive the conditional posterior densities of mean arrival rate and mean service rates. We apply the Markov chain Monte Carlo method and compute the Bayes estimates and credible interval for the M/M/3 queue, as a particular case of the M/M/𝑅 queue under squared error loss function, entropy loss function and linex loss function corresponding to a different set of hyperparameters.

In this paper we consider various continuous/discrete time queueing models with general service time distribution. With an aim to identify queueing models we examine the structural properties like infinite divisibility of the stationary distribution of various characteristics of different queueing models and report some new results. Our investigation is further extended to bulk arrival models and multiple vacation queueing models, revealing the structural aspects of their steady state distributions.

The study was initiated to determine the anticancer activity of a novel compound isolated from the plant Mimosa pudica. The structure of the compound was identified as a derivative of myricetin having alkyl, hydroxy alkyl and methyl substitutions on the basis of spectral evidences (UV-vis, FT-IR, 1H NMR and Mass spectra). The isolated compound was interpreted as 2-(2',6'-dimethyl-3',4',5'-alkyl or hydroxy alkyl substituted phenyl)-3-oxy-(alkyl or hydoxy alkyl)- 5,7-dihydroxy-chromen-4-one. In vitro evaluation of anticancer activity against human lung adenocarcinoma cell line (A549) and human erythroleukemic cell line (K562) were conducted using 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) assay. In vivo anticancer activity was determined against Dalton's Ascites Lymphoma (DAL) in Swiss albino mice. The mice were treated with intraperitoneal administration of the compound at 25mg/kg and 100mg/kg body weight and were compared with the normal, DAL control and standard drug cyclophosphamide treated groups. The histology revealed that the compound could protect the cellular architecture of liver and kidney. The results from the in vitro, in vivo and histological examinations confirmed the ethnopharmacological significance of the isolated compound and could be considered further for the development of an effective drug against cancer.

Introducing a new flexible model for lifetimes called Beta half Logistic distribution by compounding the Beta distribution and half logistic distributions, we explore its analytical characteristics and statistical properties. The maximum likelihood estimates of the model parameters are discussed and the usefulness of the new model is illustrated by means of data on remission times of bladder cancer patients.

This paper deals with the study of the reliability of multicomponent stress–strength model assuming that the strength components are independently and identically distributed as power transformed half-logistic (PHL) distribution. The strength components which are subject to a common stress are assumed to be independent with either Weibull distribution or PHL distribution. The maximum likelihood estimates of the multicomponent stress–strength reliability and its asymptotic confidence interval under the above said conditions are obtained. The Bayes estimates of the multicomponent stress–strength reliability are also obtained under squared error loss function and using gamma priors for the parameters. To evaluate the performance of the procedure, a simulation study is considered. For illustration purpose of the proposed model, two real life examples are given.

An M/M/1queueing system with finite system capacity and the customer impatience in the form of random balking is considered in this paper. Assuming an adaptive balking according to which a new customer will join the queue with probability qn if he finds n (n > 0) customers in the system on his arrival, we consider two models based on the balking nature. First we consider a model with all the arriving customers balk with constant probability. In the second model, balking probabilities of the arriving customer increases as the number of customers in the system increases. We obtain closed form expression for the stationary distribution of the system size and proposed a cost model to determine the system capacity that minimizes the cost function and give some numerical illustrations.

An M/M/1queueing system with the customer impatience in the form of random balking is considered in this paper. Effecting in the model a system size-based balking according to which a new customer will join the queue with probability q k if he finds k(≥0) customers in the system on his arrival, we obtained the stationary distribution of the system size, its mean and variance. Further the stationary characteristics of the system for various balking probability functions are investigated. The maximum likelihood estimate of the balking parameter is also discussed. The models we treated here find practical application in helping the management of any enterprises to provide adequate service for its customers with tolerable waiting, whenever, customer impatience becomes sufficiently strong and customers leave before being served.