Joby K Jose

Kannur University · Department of Statistical Sciences

Time-dependent stress-strength reliability engages with the chance of survival for systems with dynamic strength and/or dynamic stress. When a system is allowed to run continuously, each run will cause a change in the strength of the system. The repeated occurrence of stress on the system over each run will affect the survival capacity of the syste...

This paper deals with study and estimation of stress-strength reliability for a system where strength and stress components are connected in series with cold standby redundancy at system level. It is supposed that the random stress and strength both follow Kumaraswamy half-logistic distribution. In this redundant system, we consider that there N su...

Stress-strength modeling has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, psychology, biology, genetics, medicine etc. Phase-type distribution is a generalized class of distributions that is closed under several mathematical operations like maxima, minima, convolution,...

An additive power-transformed half-logistic distribution is proposed to model lifetime data having bathtub-shaped hazard rate function. The model is derived as the sum of hazard rates of two independently distributed power transformed half-logistic distributions. Some properties of the model like shapes of hazard function, quantile function, mean t...

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, t...

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 time points. Then we can assume a decrease in the strength of the system during the completion of each run. Let the strength of the system decreases by a c...

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...

In this paper, we analyze an M/PH/1 queuing system with optional re-service. In this queueing system the interarrival time distribution is exponential with mean 1=k, service time and re-service time distribution follows continuous time phase-type distribution and each customer will be re-serviced with probability 'p'. We have obtained the expressio...

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 queue parameters λ, µ and various queue characteristics using Mckay’s bivariate gamma prior distribution for (λ, µ) for a stationary M/M/1 queue as it s...

This book entitled Advances in Statistical Methods is an interesting collection of invited talks and papers presented in the NATIONAL CONFERENCE ON ADVANCES IN STATISTICAL METHODS (NCASM)-2018 organized by the Department of Statistical Sciences, Kannur University, Kerala, India during 08 - 10 November 2018. The proccedings of the conference is shap...

The estimation of stress-strength reliability in a time-dependent context deals with either the stress or strength or both dynamic. The repeated occurrence of stress in random intervals of time induces a change in the distribution of strength over time. In this paper, we study the stress-strength reliability of a system whose strength reduces by a...

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...

This article describes Bayes estimation of various queue characteristics such as queue parameters k and l, and queue performance measures like traffic intensity, expected waiting time in the queue, and expected queue size of M=E k =1 model using Mckay's bivariate gamma distribution as prior under squared error loss function as well as entropy loss...

In this paper, we consider the Bayesian inference of M/M/R queue with R heterogeneous servers with service rates μ 1 , μ 2 ,. .. , μ R , where μ 1 > μ 2 > ⋅ ⋅ ⋅ > μ 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 a...

In many of the real-life situations, the strength of a system and stress applied to it changes as time changes. In this paper, we consider time-dependent stress–strength reliability models subjected to random stresses at random cycles of time. Each run of the system causes a change in the strength of the system over time. We obtain the stress–stren...

The following article deals with studying the reliability of multicomponent stress-strength model assuming that the strength components are independently and identically distributed as power transformed half-logisitc distribution. The strength components which are subject to a common stress is assumed to be independent with either Weibull distribut...

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 strength following mixture of discrete phase type distributions is also considered. Matrix based expressions are obtained for stress-strength reliability an...

In this paper we consider the Bayesian inference of Markovian queueing model with two heterogeneous servers with service rate µ 1 and µ 2 where µ 1 > µ 2. Assuming Mckays bivariate gamma prior distribution for service rates (µ 1 , µ 2) and gamma prior distribution for arrival rate λ, closed form expressions for the Bayes estimates of the queue para...

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 distribution are studied and observed that the distribution can be used for modeling heavy tailed data. Further the expression for stress strength reliability of a...

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 investigati...

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...

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 q n if he finds n (n > 0) customers in the system on his arrival, we consider two models based on the balking n...

In this paper we obtain the Bayes estimate of the arrival rate  , service rate  and traffic intensity  of an M/M/1 queueing model using bivariate prior distribution of ( , ). The posterior distribution and credible sets for traffic intensity and predictive distribution of number in the system are also derived .

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...

In this paper we investigate the infinite divisibility property of the steady state distribution of certain queue characteristics like queue length, waiting time, number of customers served during the busy period etc. of certain Markovian single/bulk arrival queueing models with general service time distribution. Our investigation is further extend...