International Science Index
Performance of the Strong Stability Method in the Univariate Classical Risk Model
In this paper, we study the performance of the strong
stability method of the univariate classical risk model. We interest to
the stability bounds established using two approaches. The first based
on the strong stability method developed for a general Markov chains.
The second approach based on the regenerative processes theory . By
adopting an algorithmic procedure, we study the performance of the
stability method in the case of exponential distribution claim amounts.
After presenting numerically and graphically the stability bounds, an
interpretation and comparison of the results have been done.
Optimal Mitigation of Slopes by Probabilistic Methods
A probabilistic formulation to assess the slopes safety under the hazard of strong storms is presented and illustrated through a slope in Mexico. The formulation is based on the classical safety factor (SF) used in practice to appraise the slope stability, but it is introduced the treatment of uncertainties, and the slope failure probability is calculated as the probability that SF<1. As the main hazard is the rainfall on the area, statistics of rainfall intensity and duration are considered and modeled with an exponential distribution. The expected life-cycle cost is assessed by considering a monetary value on the slope failure consequences. Alternative mitigation measures are simulated, and the formulation is used to get the measures driving to the optimal one (minimum life-cycle costs). For the example, the optimal mitigation measure is the reduction on the slope inclination angle.
Stochastic Repair and Replacement with a Single Repair Channel
This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.
Availability Analysis of Milling System in a Rice Milling Plant
The paper describes the availability analysis of milling system of a rice milling plant using probabilistic approach. The subsystems under study are special purpose machines. The availability analysis of the system is carried out to determine the effect of failure and repair rates of each subsystem on overall performance (i.e. steady state availability) of system concerned. Further, on the basis of effect of repair rates on the system availability, maintenance repair priorities have been suggested. The problem is formulated using Markov Birth-Death process taking exponential distribution for probable failures and repair rates. The first order differential equations associated with transition diagram are developed by using mnemonic rule. These equations are solved using normalizing conditions and recursive method to drive out the steady state availability expression of the system. The findings of the paper are presented and discussed with the plant personnel to adopt a suitable maintenance policy to increase the productivity of the rice milling plant.
Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution
This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.
Software Reliability Prediction Model Analysis
Software reliability prediction gives a great opportunity to measure the software failure rate at any point throughout system test. A software reliability prediction model provides with the technique for improving reliability. Software reliability is very important factor for estimating overall system reliability, which depends on the individual component reliabilities. It differs from hardware reliability in that it reflects the design perfection. Main reason of software reliability problems is high complexity of software. Various approaches can be used to improve the reliability of software. We focus on software reliability model in this article, assuming that there is a time redundancy, the value of which (the number of repeated transmission of basic blocks) can be an optimization parameter. We consider given mathematical model in the assumption that in the system may occur not only irreversible failures, but also a failure that can be taken as self-repairing failures that significantly affect the reliability and accuracy of information transfer. Main task of the given paper is to find a time distribution function (DF) of instructions sequence transmission, which consists of random number of basic blocks. We consider the system software unreliable; the time between adjacent failures has exponential distribution.
Statistical Description of Wave Interactions in 1D Defect Turbulence
We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.
An Evaluation of Average Run Length of MaxEWMA and MaxGWMA Control Charts
Exponentially weighted moving average control chart (EWMA) is a popular chart used for detecting shift in the mean of parameter of distributions in quality control. The objective of this paper is to compare the efficiency of control chart to detect an increases in the mean of a process. In particular, we compared the Maximum Exponentially Weighted Moving Average (MaxEWMA) and Maximum Generally Weighted Moving Average (MaxGWMA) control charts when the observations are Exponential distribution. The criteria for evaluate the performance of control chart is called, the Average Run Length (ARL). The result of comparison show that in the case of process is small sample size, the MaxEWMA control chart is more efficiency to detect shift in the process mean than MaxGWMA control chart. For the case of large sample size, the MaxEWMA control chart is more sensitive to detect small shift in the process mean than MaxGWMA control chart, and when the process is a large shift in mean, the MaxGWMA control chart is more sensitive to detect mean shift than MaxEWMA control chart.
Reliability Approximation through the Discretization of Random Variables using Reversed Hazard Rate Function
Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.
Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples
In the present communication, stochastic comparison
of a series (parallel) system having heterogeneous components with
random lifetimes and series (parallel) system having homogeneous
exponential components with random lifetimes has been studied.
Further, conditions under which such a comparison is possible has
A Hidden Markov Model for Modeling Pavement Deterioration under Incomplete Monitoring Data
In this paper, the potential use of an exponential
hidden Markov model to model a hidden pavement deterioration
process, i.e. one that is not directly measurable, is investigated. It is
assumed that the evolution of the physical condition, which is the
hidden process, and the evolution of the values of pavement distress
indicators, can be adequately described using discrete condition states
and modeled as a Markov processes. It is also assumed that condition
data can be collected by visual inspections over time and represented
continuously using an exponential distribution. The advantage of
using such a model in decision making process is illustrated through
an empirical study using real world data.
Confidence Intervals for Double Exponential Distribution: A Simulation Approach
The double exponential model (DEM), or Laplace
distribution, is used in various disciplines. However, there are issues
related to the construction of confidence intervals (CI), when using
the distribution.In this paper, the properties of DEM are considered
with intention of constructing CI based on simulated data. The
analysis of pivotal equations for the models here in comparisons with
pivotal equations for normal distribution are performed, and the
results obtained from simulation data are presented.
Systems with Queueing and their Simulation
In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied
Analysis of Linked in Series Servers with Blocking, Priority Feedback Service and Threshold Policy
The use of buffer thresholds, blocking and adequate
service strategies are well-known techniques for computer networks
traffic congestion control. This motivates the study of series queues
with blocking, feedback (service under Head of Line (HoL) priority
discipline) and finite capacity buffers with thresholds. In this paper,
the external traffic is modelled using the Poisson process and the
service times have been modelled using the exponential distribution.
We consider a three-station network with two finite buffers, for
which a set of thresholds (tm1 and tm2) is defined. This computer
network behaves as follows. A task, which finishes its service at
station B, gets sent back to station A for re-processing with
probability o. When the number of tasks in the second buffer exceeds
a threshold tm2 and the number of task in the first buffer is less than
tm1, the fed back task is served under HoL priority discipline. In
opposite case, for fed backed tasks, “no two priority services in
succession" procedure (preventing a possible overflow in the first
buffer) is applied. Using an open Markovian queuing schema with
blocking, priority feedback service and thresholds, a closed form
cost-effective analytical solution is obtained. The model of servers
linked in series is very accurate. It is derived directly from a twodimensional
state graph and a set of steady-state equations, followed
by calculations of main measures of effectiveness. Consequently,
efficient expressions of the low computational cost are determined.
Based on numerical experiments and collected results we conclude
that the proposed model with blocking, feedback and thresholds can
provide accurate performance estimates of linked in series networks.
Advanced Stochastic Models for Partially Developed Speckle
Speckled images arise when coherent microwave,
optical, and acoustic imaging techniques are used to image an object, surface or scene. Examples of coherent imaging systems include synthetic aperture radar, laser imaging systems, imaging sonar
systems, and medical ultrasound systems. Speckle noise is a form of object or target induced noise that results when the surface of the object is Rayleigh rough compared to the wavelength of the illuminating radiation. Detection and estimation in images corrupted
by speckle noise is complicated by the nature of the noise and is not
as straightforward as detection and estimation in additive noise. In
this work, we derive stochastic models for speckle noise, with an emphasis on speckle as it arises in medical ultrasound images. The
motivation for this work is the problem of segmentation and tissue classification using ultrasound imaging. Modeling of speckle in this
context involves partially developed speckle model where an underlying Poisson point process modulates a Gram-Charlier series
of Laguerre weighted exponential functions, resulting in a doubly
stochastic filtered Poisson point process. The statistical distribution of partially developed speckle is derived in a closed canonical form.
It is observed that as the mean number of scatterers in a resolution cell is increased, the probability density function approaches an
exponential distribution. This is consistent with fully developed speckle noise as demonstrated by the Central Limit theorem.
VoIP Source Model based on the Hyperexponential Distribution
In this paper we present a statistical analysis of Voice
over IP (VoIP) packet streams produced by the G.711 voice coder
with voice activity detection (VAD). During telephone conversation,
depending whether the interlocutor speaks (ON) or remains silent
(OFF), packets are produced or not by a voice coder. As index of
dispersion for both ON and OFF times distribution was greater than
one, we used hyperexponential distribution for approximation of
streams duration. For each stage of the hyperexponential distribution,
we tested goodness of our fits using graphical methods, we calculated
estimation errors, and performed Kolmogorov-Smirnov test.
Obtained results showed that the precise VoIP source model can be
based on the five-state Markov process.