Statistics

Abstract A certain type of queueing system that is quite common in manufacturing systems occurs when the time between the arrivals of items approximately follows an exponential distribution with rate λ , the services are mechanized and their times may be considered approximately constant ( b ). In Kendall notation, such a queueing system is well known as an M ∕ D ∕ 1 queue; despite being one of the simplest queueing models, it has wide applicability to numerous practical situations as a first approximation by a steady-state model before a deeper analysis can be performed by means of more sophisticated transient-regime stochastic models that consider, for example, burst arrival, block arrivals, congestion, and so on. In queues, one very important parameter that must estimated is the traffic intensity, defined for an M ∕ D ∕ 1 queue as ρ = λ b . This article aims to investigate statistical methods to estimate ρ , namely, the maximum likelihood and Bayes estimators, by considering the number of customers present in the system at successive departure epochs, which is a very natural way to collect data. An extensive set of computational results from Monte Carlo simulations is shown to establish the efficiency and effectiveness of the proposed approaches, which will possibly enhance practical applications.

The paper is concerned with the problem of change point for the inter arrival time distribution for the M / M /1 queueing system by considering the number of customers present in the system. Bayesian estimators of traffic intensities, before the change $$(\rho _1)$$ ( ρ 1 ) and after the change $$(\rho _2)$$ ( ρ 2 ) , and the change point m are derived using the informative as well as non-informative priors under different loss functions. Finally a numerical example along with a practical example is given to illustrate the results.

Abstract Although queueing models in the mathematical field of queueing theory are mainly studied in the steady-state regime and practical applications are interested mostly in queues in transient situations subject to burst arrivals and congestion, their use is still justified as a first step towards a more complex and thorough analysis. In these practical applications, parameters such as the traffic intensity, which is the ratio between the arrival rate and service rate, are unknown and need to be estimated statistically. In this study, a Markovian arrival and deterministic single-server queueing system, known in Kendall notation as an M ∕ D ∕ 1 queueing model, is considered. This is one of the simplest queueing models with deterministic service time and may be seen as an approximation of a variety of applications in the performance evaluation of production management, telecommunications networks, and other areas. The main goal of this manuscript is to propose a methodology to determine the sample size for an M ∕ D ∕ 1 queueing system under the Bayesian setup by observing the number of customer arrivals during the service time of a customer. To verify the efficiency and efficacy of the proposed approach, an extensive set of numerical results is presented and discussed.

In this paper we discuss the problem of change point for the interarrival time distribution in the context of exponential families for the queueing system. We consider the problem of detecting an influential point concerning change-point using Bayes factors. Numerical examples are simulated using Monte Carlo methods for various sample sizes of the arriving customers at different positions of change based on the Erlang distribution

The aims of the study were to describe the noise levels at an open cast chromite mine in Odisha, India, and the hearing threshold of its workers and to associate their hearing loss with their age, work station and length of employment at the mine. We performed a cross-sectional study of the hearing threshold of chromite mine workers. Audiometric data from 500 subjects was collected at the mines' hospital in the Sukinda Valley of Jajpur, Odisha, India. The latest audiometry data available for the period 2002 to 2008 was used in the analysis. Audiometric screening was performed using an audiometer (TRIVENI TAM-25 6025A) in a quiet environment by qualified technicians, audiologists or physicians. Tests were conducted on the subjects after they had completely rested for 16 hours or more after their day shift. A maximum of 262 subjects (52.4%) were employed in the work zone area and a minimum of 2 subjects (0.4%) had less than 5 years working experience. The age of the subjects range...

In this paper an attempt has been made to evaluate the hearing loss of workmen (subjects) in an open cast Chromite mines with respect to age, working experience and work stations. The age group 50–60 years is found to be the biggest age group suffering significant hearing loss on both the ears. Also, the Work Zone area is found to be most significant area affecting hearing loss on both the ears. However, the subjects having experience of 30–35 and 25–30 years have the most significant hearing loss on the left and right ears, respectively. Also, there is no significant difference of hearing loss exhibited by the subjects on both ears at the age group of 50–60 years and to the subjects working in the work zone area.