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To improve the accuracy of parameter prediction for small-sample data, considering the existence of error in samples, the error circle is introduced to analyze original samples.

The influence of surface roughness on fatigue life is discussed. The error circle can treat the original samples and extend the single sample, which reduces the influence of the sample error.

The S-N curve obtained by the error circle method is more reliable; the S-N curve of the Bootstrap method is more reliable than that of the Maximum Likelihood Estimation (MLE) method.

The parameter distribution and characteristics are statistically obtained based on the surface roughness, surface roughness factor and intercept constant. The original sample is studied by an error circle and discussed using the Bootstrap and MLE methods to obtain corresponding S-N curves. It provides a more trustworthy basis for predicting the useful life of products.

Maintenance managers must often make preventive maintenance (PM) decisions based on limited historical failure data. These small data sets introduce significant uncertainties which can lead to selecting suboptimal (more costly) PM intervals. Examines the performance of two commonly used estimation techniques (MLE and rank regression), and develops a third hybrid technique which improves the PM interval accuracy for small data sets. In addition, characterizes the risks involved in making PM decisions based on small data sets for all three methods, to provide useful guidelines for the practising maintenance engineer.

In this paper, a mixture of exponential and Rayleigh distributions in the proportions α and 1 − α and all the parameters in the mixture distribution are estimated based on fuzzy data.

The methods such as maximum likelihood estimation (MLE) and method of moments (MOM) are applied for estimation. Fuzzy data of triangular fuzzy numbers and Gaussian fuzzy numbers for different sample sizes are considered to illustrate the resulting estimation and to compare these methods. In addition to this, the obtained results are compared with existing results for crisp data in the literature.

The application of fuzziness in the data will be very useful to obtain precise results in the presence of vagueness in data. Mean square errors (MSEs) of the resulting estimators are computed using crisp data and fuzzy data. On comparison, in terms of MSEs, it is observed that maximum likelihood estimators perform better than moment estimators.

Classical methods of obtaining estimators of unknown parameters fail to give realistic estimators since these methods assume the data collected to be crisp or exact. Normally, such case of precise data is not always feasible and realistic in practice. Most of them will be incomplete and sometimes expressed in linguistic variables. Such data can be handled by generalizing the classical inference methods using fuzzy set theory.

While there exist many surveys on the use stochastic frontier analysis (SFA), many important issues and techniques in SFA were not well elaborated in the previous surveys, namely, regular models, copula modeling, nonparametric estimation by Grenander’s method of sieves, empirical likelihood and causality issues in SFA using regression discontinuity design (RDD) (sharp and fuzzy RDD). The purpose of this paper is to encourage more research in these directions.

A literature survey.

While there are many useful applications of SFA to econometrics, there are also many important open problems.

This is the first survey of SFA in econometrics that emphasizes important issues and techniques such as copulas.

The purpose of this paper is to apply the concept of equivalent initial flaw size (EIFS) to the anisotropic nickel-based single crystal (SX) material, and to predict the fatigue life on this basis. The crack propagation law of SX material at different temperatures and the weak correlation of EIFS values verification under different loading conditions are also investigated.

A three-parameter time to crack initial (TTCI) method with multiple reference crack lengths under different loading conditions is established, which include the TTCI backstepping method and EIFS fitting method. Subsequently, the optimized EIFS distribution is obtained based on the random crack propagation rate and maximum likelihood estimation of median fatigue life. Then, an effective driving force based on anisotropic and mixed crack propagation mode is proposed to describe the crack propagation rate in the small crack stage. Finally, the fatigue life of three different temperature ESE(T) standard specimens is predicted based on the EIFS values under different survival rates.

The optimized EIFS distribution based on EIFS fitting - maximum likelihood estimation (MLE) method has the highest accuracy in predicting the total fatigue life, with the range of EIFS values being about [0.0028, 0.0875] (mm), and the mean value of EIFS being 0.0506 mm. The error between the predicted fatigue life based on the crack propagation rate and EIFS distribution for survival rates ranges from 5% to 95% and the experimental life is within two times dispersion band.

This paper systematically proposes a new anisotropic material EIFS prediction method, establishing a framework for predicting the fatigue life of SX material at different temperatures using fracture mechanics to avoid inaccurate anisotropic constitutive models and fatigue damage accumulation theory.

The purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit generalized Rayleigh (GR) distributions with common scale parameter.

The authors derive inference for the unknown parametric function using classical and Bayesian approaches. In sequel, (weighted) least square (LS) and maximum product of spacing methods are used to estimate the reliability. Bootstrapping is also considered for this purpose. Bayesian inference is derived under gamma prior distributions. In consequence credible intervals are constructed. For the known common scale, unbiased estimator is obtained and is compared with the corresponding exact Bayes estimate.

Different point and interval estimators of the reliability are examined using Monte Carlo simulations for different sample sizes. In summary, the authors observe that Bayes estimators obtained using gamma prior distributions perform well compared to the other studied estimators. The average length (AL) of highest posterior density (HPD) interval remains shorter than other proposed intervals. Further coverage probabilities of all the intervals are reasonably satisfactory. A data analysis is also presented in support of studied estimation methods. It is noted that proposed methods work good for the considered estimation problem.

In the literature various probability distributions which are often analyzed in life test studies are mostly unbounded in nature, that is, their support of positive probabilities lie in infinite interval. This class of distributions includes generalized exponential, Burr family, gamma, lognormal and Weibull models, among others. In many situations the authors need to analyze data which lie in bounded interval like average height of individual, survival time from a disease, income per-capita etc. Thus use of probability models with support on finite intervals becomes inevitable. The authors have investigated stress-strength reliability based on unit GR distribution. Useful comments are obtained based on the numerical study.

For repairable systems (RSs), reliability estimation is generally performed using virtual age models. Virtual age models consider the effect of maintenance actions by reducing system age using restoration factor (RF). RF is generally estimated from system failure data using various statistical methods. However, RSs such as railway systems experience various types of maintenance actions at different times during their life cycle. To consider all these different types of actions, we need multiple RFs in the virtual age model. As failure data are limited, the estimation of so many parameters becomes a complex problem and it can lead to erroneous inferences. These RFs are representative of effects of maintenance activities on the system. Therefore, these can be predicted from the information about the maintenance actions performed on the system. The paper aims to discuss these issues.

The paper considers different types of maintenance actions to predict RF of the system. These maintenance actions involve the replacement of components at some level of assembly. Each component in an assembly has its own impact on assembly restoration. RF for assembly/systems can be obtained by aggregating effects of multiple component replacement using analytical hierarchy process . The RF values obtained for different types of maintenance actions are then used to calculate the virtual age of the system at different failure points. Using these virtual age failure points, suitable distribution is fitted and parameters are estimated. The distribution and parameters provide information about reliability of the system at any point of time.

This paper provides an easier approach that gives different RFs for different types of PM and CM. To calculate RFs, it considers the impact of maintenance actions performed as well as the impact of the component on which they are performed. It is simpler and gives more consistent results than other approaches, which estimate RF using different statistical methods.

This paper provides an alternative approach to predict RF parameters instead of estimating these parameters using statistical methods. Estimation of parameters using different statistical methods is complex in nature and gives erroneous and inconsistent results. The approach given in this paper is simpler and gives more reliable results. This approach can be useful in estimating parameters for RSs when failure data are limited.

The purpose of this paper is to investigate how to incorporate the exponentiated Weibull (EW) testing‐effort function (TEF) into inflection S‐shaped software reliability growth models (SRGMs) based on non‐homogeneous Poisson process (NHPP). The aim is also to present a more flexible SRGM with imperfect debugging.

This paper reviews the EW TEFs and discusses inflection S‐shaped SRGM with EW testing‐effort to get a better description of the software fault detection phenomenon. The SRGM parameters are estimated by weighted least square estimation (WLSE) and maximum‐likelihood estimation (MLE) methods. Furthermore, the proposed models are also discussed under imperfect debugging environment.

Experimental results from three actual data applications are analyzed and compared with the other existing models. The findings reveal that the proposed SRGM has better performance and prediction capability. Results also confirm that the EW TEF is suitable for incorporating into inflection S‐shaped NHPP growth models.

This paper presents the WLSE results with equal weight. Future research may be carried out for unequal weights.

Software reliability modeling and estimation are a major concern in the software development process, particularly during the software testing phase, as unreliable software can cause a failure in the computer system that can be hazardous. The results obtained in this paper may facilitate the software engineers, scientists, and managers in improving the software testing process.

The proposed SRGM has a flexible structure and may capture features of both exponential and S‐shaped NHPP growth models for failure phenomenon.

During rush hours, many passengers find it difficult to board the first train due to the insufficient capacity of metro vehicles, namely, left behind phenomenon. In this paper, a data-driven approach is presented to estimate left-behind patterns using automatic fare collection (AFC) data and train timetable data.

First, a data preprocessing method is introduced to obtain the waiting time of passengers at the target station. Second, a hierarchical Bayesian (HB) model is proposed to describe the left behind phenomenon, in which the waiting time is expressed as a Gaussian mixture model. Then a sampling algorithm based on Markov Chain Monte Carlo (MCMC) is developed to estimate the parameters in the model. Third, a case of Beijing metro system is taken as an application of the proposed method.

The comparison result shows that the proposed method performs better in estimating left behind patterns than the existing Maximum Likelihood Estimation. Finally, three main reasons for left behind phenomenon are summarized to make relevant strategies for metro managers.

First, an HB model is constructed to describe the left behind phenomenon in a target station and in the target direction on the basis of AFC data and train timetable data. Second, a MCMC-based sampling method Metropolis–Hasting algorithm is proposed to estimate the model parameters and obtain the quantitative results of left behind patterns. Third, a case of Beijing metro is presented as an application to test the applicability and accuracy of the proposed method.

The purpose of this study was to examine whether the use of financial derivatives by business enterprises can avoid taxes and whether tax authorities can detect and effectively enforce measures regarding this emerging tax avoidance method.

Using panel data from the Shanghai and Shenzhen Stock Exchange listed companies from 2008 to 2019, this study used the Heckman self-selection two-stage model and a cross-sectional analysis to test a total of 22,578 samples. Moreover, propensity score matching (PSM), instrumental variable and Heckman MLE methods were conducted in the robustness test.

The results showed that enterprises could use financial derivatives to avoid taxation. The greater the tax effort is, the more obvious the effect of the company's use of financial derivatives for tax avoidance, which proves challenging for tax authorities to identify and manage.

This study expands on research on corporate tax avoidance and provides a new perspective for the study of financial derivatives. Moreover, it improves relevant research in the field of tax regulation, offering practical guidance for tax authorities to govern the use of financial instruments to prevent potential risks effectively.