Non-homogeneous Poisson Process Models Research Articles

A Software Reliability Model Considering the Syntax Error in Uncertainty Environment, Optimal Release Time, and Sensitivity Analysis

The goal set by software developers is to develop high quality and reliable software products. During the past decades, software has become complex, and thus, it is difficult to develop stable software products. Software failures often cause serious social or economic losses, and therefore, software reliability is considered important. Software reliability growth models (SRGMs) have been used to estimate software reliability. In this work, we introduce a new software reliability model and compare it with several non-homogeneous Poisson process (NHPP) models. In addition, we compare the goodness of fit for existing SRGMs using actual data sets based on eight criteria. The results allow us to determine which model is optimal.

Reliability analysis of open source software systems considering the effect of previously released version

ABSTRACTIn this study, reliability analysis of open source software in an imperfect debugging environment has been discussed by considering the effect of detection rate and the remaining faults in successive releases. First, a modified non-homogeneous Poisson process model is developed in an imperfect debugging environment by assuming that new faults may be introduced in fault detection and correction process. Then, the detection rate and remaining faults of previous release are considered in the modeling and analysis of reliability of the current release. The optimal version-update time is computed using multi-attribute utility theory for these software systems, considering the two main utility factors, namely, rapid release strategy and level of reliability. The proposed models are verified on real data sets and are compared with other existing models. The proposed decision models may be helpful for the software developing management to decide the optimal version update time for open source software.

A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

AbstractTraditionally, in the studies of the optimal maintenance policies for repairable systems, the nonhomogeneous Poisson process model, which corresponds to the minimal repair process, has been intensively applied. However, in many practical situations, the repair type is not necessarily minimal. In this article, a new repair process based on a new counting process model (so‐called the generalized Polya process) is introduced. Then, the issue of the optimal replacement problem is discussed. A bivariate preventive replacement policy is developed and the properties of the optimal policy are studied. Illustrative examples are also presented. In addition, a comparison with a conventional replacement policy is performed.

Quantifying the relative effect of environmental contamination on surgical ward MRSA incidence: Anexploratory analysis.

To investigate and quantify the contribution of environmental contamination towards methicillin-resistant Staphylococcus aureus (MRSA) incidence observed in a hospital ward using stochastic modelling. A non-homogeneous Poisson process model was developed to investigate the relationship between environmental contamination and MRSA incidence in a UK surgical ward during a cleaning intervention study. The model quantified the fractional risks (FRs) from colonised patients, environmental contamination and a generic background source as a measure of their relative importance in describing the observed MRSA incidence. While the background source remained the most likely MRSA acquisition source for this ward (as measured by the FRs), environmental contamination was the second most likely source, ahead of colonised patients in the ward. The relative importance of environmental contamination was smaller in the enhanced cleaning period compared with the normal cleaning period, albeit with notable variability in the estimates. Accounting for environmental contamination in stochastic modelling of MRSA transmission within a hospital ward provides a richer interpretation of the FRs, and is particularly pertinent in quantitative investigations of hospital cleaning interventions to reduce MRSA acquisition.

Can Customer Arrival Rates Be Modelled by Sine Waves?

Customer arrival patterns observed in the real world typically exhibit strong seasonal effects. It is therefore natural to ask: Can a nonhomogeneous Poisson process (NHPP) with a rate function that is the simple sum of sinusoids provide an adequate description of reality? If so, how can the sinusoidal NHPP be used to improve the performance of service systems? We empirically investigate the first question in settings of interest to the operations community: Patient arrivals to an emergency department and customer calls to a bank call centre. We develop a statistical test based on recent advances in queuing data analytics to show that the model is consistent with arrivals data from both settings. Regarding the second question, we clarify how the same analytics techniques can be used to fit a sinusoidal NHPP model that can outperform standard NHPP models when the underlying arrival pattern is aperiodic (e.g., does not follow a weekly cycle). The performance gain is illustrated using a naturalistic staffing simulation based on the call centre. On the other hand, if the arrival pattern is periodic, we explain why both models should perform comparably. Even then, it is still useful to fit the sinusoidal NHPP in order to verify if the arrival pattern is indeed periodic in the first place, a step that is seldom performed in applications.

Bayesian Predictive Analyses for Logarithmic Non-Homogeneous Poisson Process in Software Reliability

This paper discusses the Bayesian approach to estimation and prediction of the reliability of software systems during the testing process. A Non-Homogeneous Poisson Process (NHPP) arising from the Musa-Okumoto (1984) software reliability model is proposed for the software failures. The Musa-Okumoto NHPP reliability model consists of two components—the execution time component and the calendar time component, and is a popular model in software reliability analysis. The predictive analyses of software reliability model are of great importance for modifying, debugging and determining when to terminate software development testing process. However, Bayesian and Classical predictive analyses on the Musa-Okumoto (1984) NHPP model is missing on the literature. This paper addresses four software reliability issues in single-sample prediction associated closely with development testing program. Bayesian approach based on non-informative prior was adopted to develop explicit solutions to these problems. Examples based on both real and simulated data are presented to illustrate the developed theoretical prediction results.

Small-ScaleWind Turbine Recurrence and Cost Modeling as a Function of Operational Covariates from Supervisory Control and Data Acquisition Systems

Small-scale wind turbine (SWT) installations saw a dramatic increase between 2008 and 2012. Recently, the trend within industry has shifted towards installing larger wind turbines, leaving little attention for installed SWT reliability. Unfortunately, multiple downtime events raise concerns about thereliability and availability of the large number of installed SWTs. SWTs are repairable systems that can return to an operational state after a downtime or repair event. When a SWT experiences multiple events over time, these are known as recurrent events. The reliability of SWTs is examined in this paper using data from 21 individual 100 kW wind turbines. SWTs periodically record dynamic covariate data in the form of a vector time series using supervisory control and data acquisition (SCADA) systems. One type of event experienced by SWTs is known as a “service event,” which is a time when a SWT is put into service mode for a repair or false alarm. Due to the proprietary nature of the data used in this paper,different kinds of service events are combined, even though different failure modes and event types exist. We explore recurring service events and the associated cost of each “service event” and propose methodologies to link dynamic covariate data to downtime costs to assist in quantifying the variation of downtime across wind turbines. Data used in this work was provided from a power systems company in the United States. We outline a nonhomogenous Poisson process (NHPP) model with a Bayesian hierarchical power law structure for the count process and an autoregressive time series use rate model with a Bayesian framework to describe posterior parameter distributions. Using the posterior results, we develop a conditional and unconditional method to predict downtime mean cumulative functions (MCFs) for wind turbines.

A Software Reliability Model with a Weibull Fault Detection Rate Function Subject to Operating Environments

When software systems are introduced, these systems are used in field environments that are the same as or close to those used in the development-testing environments; however, they may also be used in many different locations that may differ from the environment in which they were developed and tested. As such, it is difficult to improve software reliability for a variety of reasons, such as a given environment, or a bug location in code. In this paper, we propose a new software reliability model that takes into account the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness of fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models and confidence intervals of all models based on two sets of failure data collected from software applications. The results show that the proposed model fits the data more closely than other existing NHPP models to a significant extent.

Performance Optimized Expectation Conditional Maximization Algorithms for Nonhomogeneous Poisson Process Software Reliability Models

Nonhomogeneous Poisson process (NHPP) and software reliability growth models (SRGM) are a popular approach to estimate useful metrics such as the number of faults remaining, failure rate, and reliability, which is defined as the probability of failure free operation in a specified environment for a specified period of time. We propose performance-optimized expectation conditional maximization (ECM) algorithms for NHPP SRGM. In contrast to the expectation maximization (EM) algorithm, the ECM algorithm reduces the maximum-likelihood estimation process to multiple simpler conditional maximization (CM)-steps. The advantage of these CM-steps is that they only need to consider one variable at a time, enabling implicit solutions to update rules when a closed form equation is not available for a model parameter. We compare the performance of our ECM algorithms to previous EM and ECM algorithms on many datasets from the research literature. Our results indicate that our ECM algorithms achieve two orders of magnitude speed up over the EM and ECM algorithms of [1] when their experimental methodology is considered and three orders of magnitude when knowledge of the maximum-likelihood estimation is removed, whereas our approach is as much as 60 times faster than the EM algorithms of [2] . We subsequently propose a two-stage algorithm to further accelerate performance.

The Nonhomogeneous Poisson Process for Fast Radio Burst Rates

Abstract This paper presents the nonhomogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model the dependence of the rate on both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power-law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 587 events per sky per day above a flux of 1 Jy (95% CI: 272, 924) and a flux power-law index of (95% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al.

Reliability growth analysis of k-out-of-N systems using matrix-based system reliability method

The advent of ever more complex systems in extensive areas of industries hampers efficient and accurate analysis of reliability and effective reliability-based decision making. Such difficulties may arise from the intricate formulation of system failure events, statistical dependence between component failure events, and the convoluted quantification of underlying probabilities of basic events. So-called k-out-of-N systems, which survive or succeed when at least k components are available among the total of N components, give rise to a high level of complexity. This type of systems are commonly introduced to secure a proper level of redundancy in operating engineering systems, but the intricate definition of the system events may elude the system reliability analysis. It is noted that such k-out-of-N systems are often tested and corrected over a certain period of time before their official usage or release in order to assure the target reliability of the system. For the purpose of reliability prognosis based on the data collected from the test period, reliability growth models (RGMs) have been widely used in software and hardware engineering. However, RGMs have been applied mostly to individual components, not at the system level. Furthermore, in complex systems such as k-out-of-N system, it is challenging to relate the reliability growth of components with that of the system. To address this need, in this paper, the matrix-based system reliability (MSR) method is extended to k-out-of-N systems by modifying the formulations of event and probability vectors. The proposed methods can incorporate statistical dependence between component failures for both homogeneous and non-homogeneous k-out-of-N systems, and can compute measures related to parameter sensitivity and relative importance of components. The reliability growths of components represented by RGMs are incorporated into the proposed system reliability method, so that the trend of system reliability growth can be effortlessly evaluated and predicted. Two numerical examples are introduced in this paper to demonstrate the proposed method and its applications: (1) hypothetical systems each consisting of series, parallel and k-out-of-N subsystems, and (2) a simplified high speed train system modeled by multiple k-out-of-N subsystems. Two types of RGMs, i.e. non-homogeneous Poisson process (NHPP) and Duane models are employed in these examples.

Enhance non-homogeneous Poisson process models incorporating testing effort with coverage function

In this paper, we studied the software reliability models for evaluating the reliability growth of a product. We discussed improve enhance NHPP model which differs from previously reported NHPP based models it explain categorically the time changing test coverage function. Which provide its analytical formulation and defect detection during the testing and operational mode. Parameters estimation have been carried out to estimate the various foil rate with test coverage function

Reliability prediction for corroding natural gas pipelines

This paper aims to evaluate time-dependent reliability of a corroding onshore underground natural gas pipeline system over its lifetime. The reliability analysis is segment-based, as opposed to defect-based and the pipe segment is examined with respect to external metal loss corrosion. The non-homogeneous Poisson process (NHPP) and an empirical power law model are employed for generation of corrosion defects over time and for defect growth, respectively. The time-dependent probability of failure is evaluated by employing the limit state function for burst under internal pressure. Internal pressure is modelled using a Poisson square wave process-based method (PSWP). Thereinafter, the study uses the aforementioned analysis, in conjunction with a heuristic model, in order to investigate the influence of imperfect repairs on the reliability prediction of the pipeline system. The heuristic method is known as split system approach and it is used to describe the changes in reliability of the pipeline system over its lifetime with the consideration of multiple maintenance actions. A numerical example of the described methodology is presented based on a chosen maintenance policy. A parametric study is conducted to examine the impact of instantaneous generation rate of NHPP model, PSWP model and reliability control limit on the results of the numerical application. The proposed methodology aims to assist engineers in the decision making with regard to corrosion maintenance strategies.

A three-parameter fault-detection software reliability model with the uncertainty of operating environments

As requirements for system quality have increased, the need for high system reliability is also increasing. Software systems are extremely important, in terms of enhanced reliability and stability, for providing high quality services to customers. However, because of the complexity of software systems, software development can be time-consuming and expensive. Many statistical models have been developed in the past years to estimate software reliability. In this paper, we propose a new three-parameter fault-detection software reliability model with the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models based on three sets of failure data collected from software applications. The results show that the proposed model fits significantly better than other existing NHPP models based on three criteria such as mean squared error (MSE), predictive ratio risk (PRR), and predictive power (PP).

Finding the best bug fixing rate and bug fixing time using software reliability modelling

This article is mainly focused on finding the best possible way to rectify bug fixing rate (BFR) and bug fixing time (BFT). Further, versatile software projects have been verified when materialising the bug fixing rate. To increase the bug fixing rate, bug traceability is reduced by virtue of version tag in each and every component of a software deliverable. Software build release time is optimised by using mathematical optimisation techniques such as software reliability growth and non-homogeneous Poisson process models. This is very much essential in the present market scenario. The build inconsistency and automation are also rectified in this erudite research work. The developed software is free from defects and improves the software quality by increasing bug fixing rate.

Finding the best bug fixing rate and bug fixing time using software reliability modelling

This article is mainly focused on finding the best possible way to rectify bug fixing rate (BFR) and bug fixing time (BFT). Further, versatile software projects have been verified when materialising the bug fixing rate. To increase the bug fixing rate, bug traceability is reduced by virtue of version tag in each and every component of a software deliverable. Software build release time is optimised by using mathematical optimisation techniques such as software reliability growth and non-homogeneous Poisson process models. This is very much essential in the present market scenario. The build inconsistency and automation are also rectified in this erudite research work. The developed software is free from defects and improves the software quality by increasing bug fixing rate.

Machine Learning Approach for Software Reliability Growth Modeling with Infinite Testing Effort Function

Reliability is one of the quantifiable software quality attributes. Software Reliability Growth Models (SRGMs) are used to assess the reliability achieved at different times of testing. Traditional time-based SRGMs may not be accurate enough in all situations where test effort varies with time. To overcome this lacuna, test effort was used instead of time in SRGMs. In the past, finite test effort functions were proposed, which may not be realistic as, at infinite testing time, test effort will be infinite. Hence in this paper, we propose an infinite test effort function in conjunction with a classical Nonhomogeneous Poisson Process (NHPP) model. We use Artificial Neural Network (ANN) for training the proposed model with software failure data. Here it is possible to get a large set of weights for the same model to describe the past failure data equally well. We use machine learning approach to select the appropriate set of weights for the model which will describe both the past and the future data well. We compare the performance of the proposed model with existing model using practical software failure data sets. The proposed log-power TEF based SRGM describes all types of failure data equally well and also improves the accuracy of parameter estimation more than existing TEF and can be used for software release time determination as well.

Dynamically Weighted Combination Model for Describing Inconsistent Failure Data of Software Projects

Background/Objective: The Software Reliability Engineering discipline is witnessing continued research in the field of Software Reliability Growth Models (SRGMs), in order to develop suitable models so as to match with the phenomenal developments in the software sector. The objective of this paper is to propose a combined dynamically weighed model for reliability analysis. Methods: In general, the ability of a model to describe a dataset adequately is assessed by Goodness of Fit (GoF) measures that a model achieves. We used one of the difficult data sets for evaluation of the GoF performance and the non-linear regression was carried out using Curve fitting application of the MATLABTM software tool. The coefficients of determination R-Square (R2), Sum of Squared Error (SSE), Root Mean Square Error (RMSE) are the different GoF metrics used. Findings: The major challenge for the software projects today, is to measure, analyze and control the level of quality of the delivered software. Undesirably long testing cycles adversely influence time to market and hence software development organizations are very keen on having a good control on the testing cycle. In the last few years many reliability models have been identified and recommended. However, no single model can be considered suitable for all situations. Some models assume the growth of mean value function to be exponential, while other models assume it to follow S-type growth. This poses a challenge to the reliability modeling. The dynamically weighted combination model that we propose in this paper helps to address both the phenomena. The superposition and time transformation property of Non-Homogenous Poisson Process (NHPP) model was considered to derive the proposed model. Application: Using SRGM helps to improve the reliability performance. We have derived a powerful model by combining two well-known models. The proposed model gives excellent GoF performance and provides more confidence both for the customer and for the software development organizations.

Lomax 분포의 형상모수에 근거한 소프트웨어 신뢰성 비용모형에 관한 연구

Software reliability in the software development process is an important issue. Software process improvement helps in finishing with reliable software product. Infinite failure NHPP software reliability models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this study, reliability software cost model considering shape parameter based on life distribution from the process of software product testing was studied. The cost comparison problem of the Lomax distribution reliability growth model that is widely used in the field of reliability presented. The software failure model was used the infinite failure non-homogeneous Poisson process model. The parameters estimation using maximum likelihood estimation was conducted. For analysis of software cost model considering shape parameter. In the process of change and large software fix this situation can scarcely avoid the occurrence of defects is reality. The conditions that meet the reliability requirements and to minimize the total cost of the optimal release time. Studies comparing emissions when analyzing the problem to help kurtosis So why Kappa efficient distribution, exponential distribution, etc. updated in terms of the case is considered as also worthwhile. In this research, software developers to identify software development cost some extent be able to help is considered.

A generalized fault-detection software reliability model subject to random operating environments

Many software reliability growth models (SRGMs) have been developed in the past three decades to estimate software reliability measures such as the number of remaining faults and software reliability. The underlying common assumption of many existing models is that the operating environment and the developing environment are the same. This is often not the case in practice because the operating environments are usually unknown due to the uncertainty of environments in the field. In this paper, we develop a generalized software reliability model incorporating the uncertainty of fault-detection rate per unit of time in the operating environments. A logistic fault-detection software reliability model is derived. Examples are included to illustrate the goodness of fit of the proposed model and existing nonhomogeneous Poisson process (NHPP) models based on a set of failure data. Three goodness-of-fit criteria, such as mean square error, predictive power, and predictive ratio risk are used as an example to illustrate model comparisons. The results show that the proposed logistic fault-detection model fit significantly better than other existing NHPP models based on all three goodness-of-fit criteria.