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We take Cumulative Prospect Theory (CPT) seriously by rigorously estimating structural models using the full set of CPT parameters. Much of the literature only estimates a subset of CPT parameters, or more simply assumes CPT parameter values from prior studies. Our data are from laboratory experiments with undergraduate students and MBA students facing substantial real incentives and losses. We also estimate structural models from Expected Utility Theory (EUT), Dual Theory (DT), Rank-Dependent Utility (RDU), and Disappointment Aversion (DA) for comparison. Our major finding is that a majority of individuals in our sample locally asset integrate. That is, they see a loss frame for what it is, a frame, and behave as if they evaluate the net payment rather than the gross loss when one is presented to them. This finding is devastating to the direct application of CPT to these data for those subjects. Support for CPT is greater when losses are covered out of an earned endowment rather than house money, but RDU is still the best single characterization of individual and pooled choices. Defenders of the CPT model claim, correctly, that the CPT model exists “because the data says it should.” In other words, the CPT model was borne from a wide range of stylized facts culled from parts of the cognitive psychology literature. If one is to take the CPT model seriously and rigorously then it needs to do a much better job of explaining the data than we see here.

The purpose of this paper is to provide a method to predict the situation of a loaded element in the compressive stress curve to prevent failure of crucial elements in load-bearing masonry walls and to propose a material model to simulate a compressive element successfully in Abaqus software to study the structural safety by using non-linear finite element analysis.

A Weibull distribution function was rewritten to relate between failure probability function and axial strain during uniaxial compressive loading. Weibull distribution parameters (shape and scale parameters) were defined by detected acoustic emission (AE) events with a linear regression. It was shown that the shape parameter of Weibull distribution was able to illustrate the effects of the added fibers on increasing or decreasing the specimens’ brittleness. Since both Weibull function and compressive stress are functions of compressive strain, a relation between compressive stress and normalized cumulative AE hits was calculated when the compressive strain was available. By suggested procedures, it was possible to monitor pretested plain or random distributed short fibers reinforced adobe elements (with AE sensor and strain detector) in a masonry building under uniaxial compression loading to predict the situation of element in the compressive stress‒strain curve, hence predicting the time to element collapse by an AE sensor and a strain detector. In the predicted compressive stress‒strain curve, the peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus were predicted successfully. With a proposed material model, it was illustrated that the needed parameters for simulating a specimen in Abaqus software with concrete damage plasticity were peak stress and its corresponding strain, the stress and strain point with maximum elastic modulus and the maximum elastic modulus.

The AE cumulative hits versus strain plots corresponding to the stress‒strain curves can be divided into four stages: inactivity period, discontinuous growth period, continuous growth period and constant period, which can predict the densifying, linear, non-linear and residual stress part of the stress‒strain relationship. By supposing that the relation between cumulative AE hits and compressive strain complies with a Weibull distribution function, a linear analysis was conducted to calibrate the parameters of Weibull distribution by AE cumulative hits for predicting the failure probability as a function of compressive strain. Parameters of m and θ were able to predict the brittleness of the plain and tire fibers reinforced adobe elements successfully. The calibrated failure probability function showed sufficient representation of the cumulative AE hit curve. A mathematical model for the stress–strain relationship prediction of the specimens after detecting the first AE hit was developed by the relationship between compressive stress versus the Weibull failure probability function, which was validated against the experimental data and gave good predictions for both plain and short fibers reinforced adobe specimens. Then, the authors were able to monitor and predict the situation of an element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression loading by an AE sensor and a strain detector. The proposed model was successfully able to predict the main mechanical properties of different adobe specimens which are necessary for material modeling with concrete damage plasticity in Abaqus. These properties include peak compressive strength and its corresponding axial strain, the compressive strength and its corresponding axial strain at the point with maximum compressive Young’s modulus and the maximum compressive Young’s modulus.

The authors were not able to decide about the effects of the specimens’ shape, as only cubic specimens were chosen; by testing different shape and different size specimens, the authors would be able to generalize the results.

The paper includes implications for monitoring techniques and predicting the time to the collapse of pretested elements (with AE sensor and strain detector) in a masonry structure.

This paper proposes a new method to monitor and predict the situation of a loaded element in the compressive stress‒strain curve, hence predicting the time to its collapse for pretested plain or random distributed short fibers reinforced adobe (with AE sensor and strain detector) in a masonry building under uniaxial compression load by an AE sensor and a strain detector.

This chapter of the book seeks to use famous mathematical functions (statistical distribution functions) in evaluating and analyzing supply chain network data related to supply chain management (SCM) elements in organizations. In other words, the main purpose of this chapter is to find the best-fitted statistical distribution functions for SCM data. Explaining how to best fit the statistical distribution function along with the explanation of all possible aspects of a function for selected components of SCM from this chapter will make a significant attraction for production and services experts who will lead their organization to the path of competitive excellence. The main core of the chapter is the reliability values related to the reliability function calculated by the relevant chart and extracting other information based on other aspects of statistical distribution functions such as probability density, cumulative distribution, and failure function. This chapter of the book will turn readers into professional users of statistical distribution functions in mathematics for analyzing supply chain element data.

The step-stress accelerated test is the most appropriate statistical method to obtain information about the reliability of new products faster than would be possible if the product was left to fail in normal use. This paper presents the multiple step-stress accelerated life test using type-II censored data and assuming a cumulative exposure model. The authors propose a Bayesian inference with the lifetimes of test item under gamma distribution. The choice of the loss function is an essential part in the Bayesian estimation problems. Therefore, the Bayesian estimators for the parameters are obtained based on different loss functions and a comparison with the usual maximum likelihood (MLE) approach is carried out. Finally, an example is presented to illustrate the proposed procedure in this paper.

A Bayesian inference is performed and the parameter estimators are obtained under symmetric and asymmetric loss functions. A sensitivity analysis of these Bayes and MLE estimators are presented by Monte Carlo simulation to verify if the Bayesian analysis is performed better.

The authors demonstrated that Bayesian estimators give better results than MLE with respect to MSE and bias. The authors also consider three types of loss functions and they show that the most dominant estimator that had the smallest MSE and bias is the Bayesian under general entropy loss function followed closely by the Linex loss function. In this case, the use of a symmetric loss function as the SELF is inappropriate for the SSALT mainly with small data.

Most of papers proposed in the literature present the estimation of SSALT through the MLE. In this paper, the authors developed a Bayesian analysis for the SSALT and discuss the procedures to obtain the Bayes estimators under symmetric and asymmetric loss functions. The choice of the loss function is an essential part in the Bayesian estimation problems.

This study evaluates the impacts on gross revenue distributions of the use of alternative crop insurance products across different coverage levels and across locations with differing yield risks. Results are presented in terms of net costs, values‐at‐risk, and certainty equivalent returns associated with five types of multi‐peril crop insurance across different coverage levels. Findings show that the group policies often result in average payments exceeding their premium costs. Individual revenue products reduce risk in the tails more than group policies, but result in greater reductions in mean revenues. Rankings based on certainty equivalent returns and low frequency VaRs generally favor revenue products. As expected, crop insurance is associated with greater relative risk reduction in locations with greater underlying yield variability.

This paper aims to prevent gasket sealing failure in engineering, accurately predict gasket life, extend system life and improve sealing reliability. The accelerated life test method of flexible graphite composite–reinforced gaskets is established, the life distribution law of flexible graphite composite–reinforced gaskets is revealed, and the life prediction method of flexible graphite composite–reinforced gaskets with different allowable leakage rates is proposed, which can provide a reference for the life prediction of other types of gaskets.

In this study, flexible graphite composite–reinforced gaskets were tested for long-term high-temperature sealing performance on a multi-sample gasket accelerated life test rig. The data were also analyzed using the least squares method and the K-S hypothesis calibration method. A gasket time-dependent leakage model and an accelerated life model were also developed. Constant stress-accelerated life tests were conducted on flexible graphite composite–reinforced gaskets. On this basis, a gasket life prediction method at different allowable leakage rates was proposed.

The life distribution law of flexible graphite composite–reinforced gaskets is revealed. The results show that the life of the gasket obeys the Weibull distribution. The time-correlated leakage model and accelerated life model of the gasket were established. And the accelerated life test method of the flexible graphite composite–reinforced gasket was established. The life distribution parameters, accelerated life model parameters and life estimates of gaskets were obtained through tests. On this basis, a gasket life prediction method under different leakage rates was proposed, which can be used as a reference for other types of gaskets.

The research in this paper can better provide guidance for the use and replacement of gaskets in the project, which is also very meaningful for predicting the leakage condition of gaskets in the bolted flange connection system and taking corresponding control measures to reduce energy waste and pollution and ensure the safe operation of industrial equipment.

A multi-specimen gasket-accelerated life test device has been developed, and the design parameters of the device have reached the international advanced level. The life distribution law of the flexible graphite composite–reinforced gasket was revealed. The accelerated life test method for the flexible graphite composite–reinforced gasket was established. The life prediction method of the flexible graphite composite–reinforced gasket under different allowable leakage rates was proposed.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2023-0254/

The purpose of this paper is to present a new cumulant-based method, based on the properties of saddle-point approximation (SPA), to solve the probabilistic load flow (PLF) problem for distribution networks with wind generation.

This technique combines cumulant properties with the SPA to improve the analytical approach of PLF calculation. The proposed approach takes into account the load demand and wind generation uncertainties in distribution networks, where a suitable probabilistic model of wind turbine (WT) is used.

The proposed procedure is applied to IEEE 33-bus distribution test system, and the results are discussed. The output variables, with and without WT connection, are presented for normal and gamma random variables (RVs). The case studies demonstrate that the proposed method gives accurate results with relatively low computational burden even for non-Gaussian probability density functions.

The main contribution of this paper is the use of SPA for the reconstruction of probability density function or cumulative distribution function in the PLF problem. To confirm the validity of the method, results are compared with Monte Carlo simulation and Gram–Charlier expansion results. From the viewpoint of accuracy and computational cost, SPA almost surpasses other approximations for obtaining the cumulative distribution function of the output RVs.