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Incremental checkpoint mechanism was introduced to reduce high checkpoint overhead of regular (full) checkpointing, especially in high-performance computing systems. To gain an extra advantage from the incremental checkpoint technique, we propose an optimal checkpoint frequency function that globally minimizes the expected wasted time of the incremental checkpoint mechanism. Also, the re-computing time coefficient used to approximate the re-computing time is derived. Moreover, to reduce the complexity in the recovery state, full checkpoints are performed from time to time. In this paper we present an approach to evaluate the appropriate constant number of incremental checkpoints between two consecutive full checkpoints. Although the number of incremental checkpoints is constant, the checkpoint interval derived from the proposed model varies depending on the failure rate of the system. The checkpoint time is illustrated in the case of a Weibull distribution and can be easily simplified to the exponential case.

A study of the distribution of the value of traded goods under the Harmonized System is presented. The ramifications of this classification system are found to exhibit an approximate power law decay, indicating complexity and self-organization in the nomenclature of traded merchandises. For almost all countries with available data, log-values of annually imported and exported goods are well described by three-parameter Weibull distributions. This distribution commonly appears in particles size distributions, suggesting a connection between random fragmentation processes and the mechanisms behind the international trade of merchandises. Analysis of the resulting values for the fitting parameters from 1995 to 2018 shows a nearly constant linear relationship between the parameters of the Weibull distributions, so that, for each country, the distribution of log-values can be approximately characterized by a single shape parameter $\beta$. The empirical findings of this paper suggest that specialization on trading a constant set of goods prevents the values of all traded merchandises from growing/decreasing simultaneously.

A total of nine methods are compared and tables are presented for selecting the best performing estimator for a two-parameter Weibull distribution using randomly right censored data. The results indicate that a best performing method can be selected given a certain sample size, censoring level, and shape parameter range. Such a comparison of estimators is necessary as the best performing method is shown to vary across these values. The estimation methods tested include the Maximum Likelihood Estimator, Kaplan-Meier Estimator, Piecewise Exponential Estimator, Földes, Rejt, and Winter Estimator, Klein, Lee, and Moeschberger Partially Parametric Estimator, Ross Estimator, White Estimator, Bain and Engelhardt Estimator, and the Modified Profile Maximum Likelihood Estimator. Recommendations are provided for applying the studied approach to other types of data and distributions.

In this paper, we introduce an innovative Software Reliability Growth Model (SRGM) designed to tackle the pivotal challenges associated with software reliability in the contemporary digital landscape, where the prevalence of online systems is ubiquitous. This SRGM integrates Imperfect Debugging (ID), Testing Coverage (TC), Testing Effort (TE), and error generation into a cohesive framework. Employing a sigmoid function to encapsulate TE, it incorporates three distinct TC functions: Delayed S-shaped, Exponential, and Logistic. This model relies on foundational assumptions, including the proportionality of fault detection rates to remaining faults, the introduction of new faults during debugging, and the intricate connection between fault detection and code coverage. The Mean Value Function (MVF) is computed through these differential equations, and the resultant MVFs are systematically tabulated for all models. An examination of the sigmoid TE function and the Weibull TE function across diverse datasets, utilizing a range of goodness-of-fit criteria including Mean Square Error (MSE), Pham’s Criterion (PC), Predictive Risk Ratio (PRR), Bayesian Information Criterion (BIC), and Akaike’s Information Criterion (AIC), reveals the superior performance of the sigmoid TE function over the Weibull counterpart across various datasets and evaluation criteria. In conclusion, this paper introduces a groundbreaking SRGM that seamlessly integrates ID, TC, and TE, offering valuable insights for assessing software reliability in the dynamic landscape of modern digital systems.

This paper discusses stochastic models for the lifelength of non-repairable items under the influence of dominant failure mechanisms like fatigue, corrosion and wear. The Weibull, the lognormal, the inverse Gaussian, and the Birnbaum-Saunders distributions are discussed and compared. Model selection problems based on both field performance data and laboratory data are focused. The consequences of choosing a wrong life model are highlighted. It is concluded that model selection must be based on a thorough knowledge of actual failure mechanisms, and the associated time dependent deterioration. Current knowledge on the relation between some dominant failure mechanisms and the associated life distributions is presented.

Wind energy has been the focus of attention by governments over the past several decades because it is clean and renewable energy source that offers many advantages compared to others. This paper reports a particle swarm optimization based flowchart used to identify the most appropriate wind speed distribution function. In this procedure, the PSO algorithm modifies and estimates the parameters of the distribution functions examined. The distributions of Nakagami, Normal and Weibull are judged for right-skewed, non-skewed and left-skewed distributions, respectively. The outcomes showed that each function offers impressive performance compared to the others in its defined conditions. Despite the changes of one-component distribution’s parameters made by the PSO algorithm are not significant, the same changes will affect the function’s performance greatly. Because of the sufficient flexibility offered by the nominated functions, the proposed flowchart is applicable for all wind regimes.

In fatigue testing of railway vehicles' structure, stress is usually increased to accelerate the testing process, so that the fatigue failure mechanism can be manifested in a shorter time. For determining the stress, the accelerated life model is key. In this paper, the fatigue life test of typical welded joints of railway vehicles is first carried out. The Weibull distribution of accelerated life model of welded joints is then used to estimate the parameters. Accelerated life parameters under 50%, 95% and 99% reliability are obtained, and the results are compared with IIW standard. It was found that the dynamic stress amplitude of vehicle welded joints is generally lower than that corresponding to 1E+07 cycles, and that the slope parameter of the model is 3.70. In addition, the constant term under 95% is 8.402E+011. The parameters of the welded joints meet the IIW standard very well in terms of the fatigue performance of the welded structures in China. This study provides a reference for future designing and testing of railway vehicles.