Mean Value Function Research Articles

Assessing Software Reliability Based on NHPP Using SPC

Software reliability in the software development process is an important issue. Software process improvement helps in finishing with reliable software product. In this field, SPC (Statistical process control) is a method of process management through application of statistical analysis, which involves and includes the defining, measuring, controlling, and improving of the processes. In measuring software reliability control charts can be used as efficient and appropriate SPC Tools. The proposed process involves evaluation of the parameter of the mean value function and hence the values of the mean value function at various inter failure times to develop relevant time control chart. In this paper, was proposed a control mechanism, based on time between failures observations using Burr distribution property, which is based on Non Homogenous Poisson Process (NHPP).

A fully stochastic approach bridging the microscopic behavior of individual microorganisms with macroscopic ensemble dynamics in surface flow networks

Prediction of microbial surface water contamination is a formidable task because of the inherent randomness of environmental processes driving microbial fate and transport. In this article, we develop a theoretical framework of a fully stochastic model of microbial transport in watersheds, and apply the theory to a simple flow network to demonstrate its use. The framework bridges the gap between microscopic behavior of individual microorganisms and macroscopic ensemble dynamics. This scaling is accomplished within a single mathematical framework, where each microorganism behaves according to a continuous‐time discrete‐space Markov process, and the Markov behavior of individual microbes gives rise to a nonhomogeneous Poisson random field that describes microbial population dynamics. Mean value functions are derived, and the spatial and temporal distribution of water contamination risk is computed in a straightforward manner.

Statistical superposition of crosstalk effects in cable bundles

This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference. In this study, statistical characterization of crosstalk in cable bundles, which is available in literature for the case of one source of interference, is extended to the case of several sources operating simultaneously. The superposition of crosstalk effects is analysed in statistical terms, also taking into account the correlation between crosstalk contributions. A further random contribution, which is included in the proposed statistical model, is given by the phase relationship between the sources of interference. Analytical approximate expressions for the crosstalk mean value, variance, and probability density function are derived as functions of the cable bundle features and sources.

Monitoring Pareto Type IV SRGM using SPC

The Reliability of the Software Process can be monitored efficiently using Statistical Process Control (SPC). SPC is the application of statistical techniques to control a process. SPC is a study of the best ways of describing and analyzing the data and then drawing conclusion or inferences based on available data. With the help of SPC the software development team can identify software failure process and find out actions to be taken which assures better software reliability. This paper provides a control mechanism based on the cumulative observations of Interval domain data using mean value function of Pareto type IV distribution, which is based on Non-Homogenous Poisson Process (NHPP). The unknown parameters of the model are estimated using maximum likelihood estimation approach. Besides it also presents an analysis of failure data sets at a particular point and compares Pareto Type II and Pareto Type IV models.

A Bayesian Approach to Upscaling and Downscaling of Aircraft Measurements of Ice Particle Counts and Size Distributions

AbstractThis study addresses the issue of how to upscale cloud-sized in situ measurements of ice to yield realistic simulations of ice clouds for a variety of modeling studies. Aircraft measurements of ice particle counts along a 79-km zigzag path were collected in a Costa Rican cloud formed in the upper-level outflow from convection. These are then used to explore the applicability of Bayesian statistics to the problems of upscaling and downscaling. Using the 10-m particle counts, the analyses using Bayesian statistics provide estimates of the probability distribution function of all possiblemeanvalues corresponding to these counts. The statistical method of copulas is used to produce an extensive ensemble of estimates of these mean values, which are then combined to derive the probability density function (pdf) of mean values at 1-km resolution. These are found to compare very well to the observed 1-km particle counts when spatial correlation is included. The profiles of the observed and simulated mean counts along the flight path show similar features and have very similar statistical characteristics. However, because the observed and the simulated counts are both the results of stochastic processes, there is no way to upscale exactly to the observed profile. Each simulation is a unique realization of the stochastic processes, as are the observations themselves. These different realizations over all the different sizes can then be used to upscale particle size distributions over large areas.

Inverse Rayleigh Software Reliability Growth Model

A Non Homogenous Poisson Process (NHPP) with its mean value function generated by the cumulative distribution function of inverse Rayleigh distribution is considered. It is modeled to assess the failure phenomenon of a developed software. When the failure data is in the form of number of failures in a given interval of time the model parameters are estimated by the maximum likelihood method. The performance of the model using four data sets is discussed in comparison with existing models.

On the exact distribution and mean value function of a geometric process with exponential interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power series expansion is derived for the geometric renewal function by using an integral equation and evaluated in a computational perspective. Further, an extension is provided for the power series expansion of the geometric renewal function in the case of the Weibull distribution.

NHPP소프트웨어 신뢰도 성장모형에서 베이지안 모수추정과 예측

본 논문은 NHPP 소프트웨어 신뢰성모형에서 모수추정과 고장시간에 대한 예측을 다루고자 한다. 소프트웨어 신뢰성모형 Goel-Okumoto모형에서 평균값 함수에 대한 최우추정과 경험적 사전분포를 가정한 공액사전분포에서 베이지안 추정을 다루었다. 실제 자료에서 두 가지 추정법에 의한 모수 추정값을 제공하였으며, 모형의 적합성을 판정하고, 고장수에 대한 예측값을 비교하였다. In this paper we consider the NHPP software reliability model. And we deal with the maximum likelihood estimation and the Bayesian estimation with conjugate prior for parameter inference in the mean value function of Goel-Okumoto model (1979). The parameter estimates for the proposed model is presented by MLE and Bayes estimator in data set. We compare the predicted number of faults with the actual data set using the proposed mean value function.

Predictions of MLE and LSE in NHPP Software Reliability Model

We propose a mean value function for software failures in NHPP software reliability model. And we deal with the maximum likelihood estimation and the least squares estimation in the proposed mean value function. The explicit mean value function solution for the proposed model is presented by MLE and LSE in two data sets. The values of SSE and MSE is presented in two data sets by MLE and LSE. We compare the predicted number of faults with the actual two data sets using the proposed mean value function.

Exponential two step approach for Time Domain based Software Process Control

Software Reliability Growth Model is a mathematical model of how the software reliability improves as faults are detected and repaired. In this paper we propose a control mechanism based on the cumulative quantity between observations of time domain failure data using mean value function of Goel-Okumoto model, which is based on Non Homogenous Poisson Process. The model parameters are estimated by a two step approach. Software reliability process can be monitored efficiently by using Statistical Process Control. Control charts are widely used for process monitoring. It assists the software development team to identify failures and actions to be taken during software failure process and hence, assures better software reliability.Â

Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations

A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green’s function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α, the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.

Three new stochastic local search algorithms for continuous optimization problems

This paper introduces three new stochastic local search metaheuristics algorithms namely, the Best Performance Algorithm (BPA), the Iterative Best Performance Algorithm (IBPA) and the Largest Absolute Difference Algorithm (LADA). BPA and IBPA are based on the competitive nature of professional athletes, in them desiring to improve on their best recorded performances. LADA is modeled on calculating the absolute difference between two numbers. The performances of the algorithms have been tested on a large collection of benchmark unconstrained continuous optimization functions. They were benchmarked against two well-known local-search metaheuristics namely, Tabu Search (TS) and Simulated Annealing (SA). Results obtained show that each of the new algorithms delivers higher percentages of the best and mean function values found, compared to both TS and SA. The execution times of these new algorithms are also comparable. LADA gives the best performance in terms of execution time.

Assessing Pareto Type II Software Reliability using SPC

Software reliability is one of the most important characteristics of software quality. Its measurement and management technologies employed during software life cycle are essential for producing and maintaining quality/reliable software systems. It can also be monitored efficiently using Statistical Process Control (SPC). It assists the software development team to identify and actions to be taken during software failure process and hence, assures better software reliability. In this paper we propose a control mechanism based on the cumulative observations of Interval domain data using mean value function of Pareto type II distribution, which is based on Non-Homogenous Poisson Process (NHPP). The maximum likelihood estimation approach is used to estimate the unknown parameters of the model. We also present an analysis of failure data sets at a particular point.

A Statistical Process Control to Monitor the Software Quality

is the only man made Omni Present system contributing immensely providing complex and critical services to mankind. It's increasing popularity and usefulness enforces us to measure the software quality. In this paper Time domain failure data is applied to Statistical Process Control(SPC) method to monitor the quality of a software system. We propose a Statistical Control Method over the cumulative quantity between observations of time domain failure data using mean value function of an Non Homogeneous Poisson Process(NHPP) based Logarithmic Poisson Execution Time Model(LPETM).Maximum Likelihood estimation(MLE) is used to estimate the unknown parameters of proposed model.The SPC method employs LPETM to construct the control limits. Two failure data sets are used.

Quasi renewal analysis of software reliability growth model incorporating testing efforts and time delay

The behaviour of the software failures with respect to time is to be assessed and can be examined by developing the software reliability growth models to achieve the desired level of the quality and reliability of the software system. The quasi-renewal process can be employed to integrate the information about the software testing and fault debugging activity in the software testing environment. This investigation is concerned with NHPP-based software reliability growth model with two types of faults distinguished by the amount of testing effort required to remove the faults. The quasi-renewal process is used to estimate the time delay period and to check the priority of the observed faults before the changing of code in the assessment of the software. The mean value function obtained is examined by taking a numerical illustration. The sensitivity analysis is also carried out to depict the effect of various parameters on the mean value function.

Confidence Interval Estimation of Software Reliability Growth Models based on Ohba’s Inflection S-shaped Model

Software reliability growth models with confidence intervals (SRGMs) are often utilized in software industry in that they provide useful information for software developers to decide the optimal software release time and to refine the quality of software testing tasks. Most SRGMs, nonetheless, do not have transparent explanations for the variance estimation of cumulative software errors. They might not be effective in deducing the confidence interval regarding the mean value function. In such cases, software developers cannot estimate the possible risk variation of software system by using the randomness of mean value function, and it might debase the practicability of applications. In this paper, we utilize Ohba’s Inflection Sshaped model to build the SRGM with confidence intervals that can assist the software developers in determining the optimal release time.

Impact of soil drainage to the radial stem growth of Norway spruce (Picea Abies L. Karst.) in peatland forests

Peatland Norway spruce (Picea abies L. Karst.) forests represent very valuable ecosystems with considerable importance for nature conservation. However, a lot of peatland forests have been drained or used for opencast mining of peat. Since dendrochronological and dendroecological studies on trees growing on peatlands in Europe are not many, this study aimed to reconstruct the impact of drainage to the growth of trees in forest stands older than 100 years in the moment of drainage. Dendrochronological analysis was performed on two 0.25-ha square sampling plots (50*50 m) in two pre-selected stands (control site vs. drained site) with similar natural conditions and age. The mean-value functions of the ring indices, comparing the drained site with the control site, in the period after 1940 revealed very similar radial-growth trends. After the year 1992, when one site was substantially drained, the radial-growth trends not showed any significant change. Likewise, the result of the independent two sample t-test for the period after 1992 has not revealed any substantial statistically important difference in the mean index between the control site and the drained site

Non-homogeneous Poisson Model for Mining Frequency of an Item from Data Stream

A data stream is essentially a virtually unbounded sequence of data items arriving at a rapid rate. Mining frequent patterns from the stream of data is a difficult task. This paper use non-homogeneous Poisson process to find the frequency of an item set from transactional data streams. We develop models by using mean value function from Goel–Okumoto model. The concept of split Poisson process and Bayesian model are used for developing a model for the prediction of number of arrivals of an item with in a particular time period.

Biodiversity and ecosystem multi-functionality: observed relationships in smallholder fallows in western Kenya.

Recent studies indicate that species richness can enhance the ability of plant assemblages to support multiple ecosystem functions. To understand how and when ecosystem services depend on biodiversity, it is valuable to expand beyond experimental grasslands. We examined whether plant diversity improves the capacity of agroecosystems to sustain multiple ecosystem services—production of wood and forage, and two elements of soil formation—in two types of smallholder fallows in western Kenya. In 18 grazed and 21 improved fallows, we estimated biomass and quantified soil organic carbon, soil base cations, sand content, and soil infiltration capacity. For four ecosystem functions (wood biomass, forage biomass, soil base cations, steady infiltration rates) linked to the focal ecosystem services, we quantified ecosystem service multi-functionality as (1) the proportion of functions above half-maximum, and (2) mean percentage excess above mean function values, and assessed whether plant diversity or environmental favorability better predicted multi-functionality. In grazed fallows, positive effects of plant diversity best explained the proportion above half-maximum and mean percentage excess, the former also declining with grazing intensity. In improved fallows, the proportion above half-maximum was not associated with soil carbon or plant diversity, while soil carbon predicted mean percentage excess better than diversity. Grazed fallows yielded stronger evidence for diversity effects on multi-functionality, while environmental conditions appeared more influential in improved fallows. The contrast in diversity-multi-functionality relationships among fallow types appears related to differences in management and associated factors including disturbance and species composition. Complementary effects of species with contrasting functional traits on different functions and multi-functional species may have contributed to diversity effects in grazed fallows. Biodiversity and environmental favorability may enhance the capacity of smallholder fallows to simultaneously provide multiple ecosystem services, yet their effects are likely to vary with fallow management.

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an 'elastic'' version of the statistical mechanical monomer-dimer problem on the $n$-dimensional integer lattice. Our setting includes the classical 'rigid'' formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for 'Manhattan'' EDM systems where the dimer potential is a weighted $l_1$-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.