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In this paper we use Monte Carlo sampling experiments to examine the properties of pretest estimators in the random parameters logit (RPL) model. The pretests are for the presence of random parameters. We study the Lagrange multiplier (LM), likelihood ratio (LR), and Wald tests, using conditional logit as the restricted model. The LM test is the fastest test to implement among these three test procedures since it only uses restricted, conditional logit, estimates. However, the LM-based pretest estimator has poor risk properties. The ratio of LM-based pretest estimator root mean squared error (RMSE) to the random parameters logit model estimator RMSE diverges from one with increases in the standard deviation of the parameter distribution. The LR and Wald tests exhibit properties of consistent tests, with the power approaching one as the specification error increases, so that the pretest estimator is consistent. We explore the power of these three tests for the random parameters by calculating the empirical percentile values, size, and rejection rates of the test statistics. We find the power of LR and Wald tests decreases with increases in the mean of the coefficient distribution. The LM test has the weakest power for presence of the random coefficient in the RPL model.

This chapter investigates the performance of different dimension reduction approaches for large vector autoregressions in multi-step ahead forecasts. The authors consider factor augmented VAR models using principal components and partial least squares, random subset regression, random projection, random compression, and estimation via LASSO and Bayesian VAR. The authors compare the accuracy of iterated and direct multi-step point and density forecasts. The comparison is based on macroeconomic and financial variables from the FRED-MD data base. Our findings suggest that random subspace methods and LASSO estimation deliver the most precise forecasts.

This study aims to examine the value of the call option contract in hedging the risks in the supply chain. The decentralized supply chain without call option contract is first studied as the criterion model for evaluations. This paper addresses several questions: What will be the optimal manufacturer’s production quantity, retailer’s ordering and pricing policies in the presence of random demand and random yield by applying the downconversion approach? How will the call option contract influence the optimal decisions for the members of the supply chain? Can the risk from randomness be divided among the members in the supply chain through the call option contract?

This paper considers a two-level decentralized supply chain under random yield and random demand in which the manufacturer takes advantage of the downconversion approach with two scenarios, with and without option contract. To the best of the authors’ knowledge, no article or study uses the downconversion approach in a supply chain regarding random yield and random demand. Furthermore, the paper considers pricing with option contract in the supply chain, which makes this article stands out significantly from other articles in the literature.

This study shows that the downconversion approach would reduce the risk caused by the random yield, which appears to be the appropriate method for the environmental goal of the supply chains. Moreover, adopting a call option contract can increase flexibility and mitigate risks, resulting in more expected members’ profits.

To simplify the model, the authors assume one manufacturer and one retailer, so extending the model to consider multiple retailers instead of one retailer and inventory sharing between them would be interesting. Considering the option and exercise prices as decision variables would be important future research topics. Put option and bidirectional option contracts could be investigated in the future. Another extension is modeling asymmetry of information in supply chain.

This paper provides managerial insights on dealing with both demand and yield risks in a manufacturer–retailer supply chain. The manufacturer has a random yield production and produces two types of vertical products: low-end and high-end. To reduce waste caused by the random yield, the manufacturer uses a downconversion approach in which low-end products are made by converting the defective high-end products. The manufacturer purchased a shortage of high-end products from the secondary market (i.e. emergency sourcing). High-end products are sold through the retailer, and low-end products are sold directly by the manufacturer. The customer demand for high-end products in the end market is random and depends on the selling price, and the customer demand for the low-end products in the secondary market is independent and random. The retailer contracts the manufacturer with the call option to obtain high-end products to meet a random demand; in fact, by using the call option contract, the authors try to balance the risks between two members. Two scenarios of with and without call option contract are proposed. After the high-end product demand is observed, the retailer would exercise the option order quantity in the call option contract scenario and then place an instant order with the manufacturer if necessary. In each scenario, the manufacturer and the retailer make their decisions simultaneously (static game) to determine the retailer’s optimal ordering and pricing policies and the optimal production quantity of the manufacturer (Nash equilibrium) by maximizing their expected profits. Finally, the impact of the model parameters on the supply chain is expressed through numerical examples. The numerical analysis shows that the call option contract provides greater profit than the wholesale price contract.

The problem of image retrieval and image description exists in various fields. In this paper, a model of content-based image retrieval and image content extraction based on the KD-Tree structure was proposed.

A Random Forest structure was built to classify the objects on each image on the basis of the balanced multibranch KD-Tree structure. From that purpose, a KD-Tree structure was generated by the Random Forest to retrieve a set of similar images for an input image. A KD-Tree structure is applied to determine a relationship word at leaves to extract the relationship between objects on an input image. An input image content is described based on class names and relationships between objects.

A model of image retrieval and image content extraction was proposed based on the proposed theoretical basis; simultaneously, the experiment was built on multi-object image datasets including Microsoft COCO and Flickr with an average image retrieval precision of 0.9028 and 0.9163, respectively. The experimental results were compared with those of other works on the same image dataset to demonstrate the effectiveness of the proposed method.

A balanced multibranch KD-Tree structure was built to apply to relationship classification on the basis of the original KD-Tree structure. Then, KD-Tree Random Forest was built to improve the classifier performance and retrieve a set of similar images for an input image. Concurrently, the image content was described in the process of combining class names and relationships between objects.

Under multiaxial random loading, the material stress–strain response is not periodic, which makes it difficult to determine the direction of the critical plane on the material. Meanwhile, existing methods of constant loading cannot be directly applied to multiaxial random loading; this problem can be solved when an equivalent stress transformation method is used.

First, the Liu-Mahadevan critical plane is introduced into multiaxial random fatigue, which is enabled to determine the material's critical plane position under random loading. Then, an equivalent stress transformation method is proposed which can convert random load to constant load. Meanwhile, the ratio of mean stress to yield strength is defined as the new mean stress influence factor, and a new non-proportional additional strengthening factor is proposed by considering the effect of phase differences.

The proposed model is validated using multiaxial random fatigue test data of TC4 titanium alloy specimens and the results of the proposed model are compared with that based on Miner's rule and BSW model, showing that the proposed method is more accurate.

In this work, a new multiaxial random fatigue life prediction model is proposed based on equivalent stress transformation method, which considers the mean stress effect and the additional strengthening effect. Results show that the predicted fatigue lives given by the proposed model are in well accordance with the tested data.

Engineering components/structures are usually subjected to complex and variable loads, which result in random multiaxial stress/strain states. However, fatigue analysis methods under constant loads cannot be directly applied to fatigue life prediction analysis under random loads. Therefore, the purpose of this study is how to effectively evaluate fatigue life under multiaxial random loading.

First, the average phase difference is characterized as the ratio of the number of shear strain cycles to the number of normal strain cycles, and the new non-proportional additional hardening factor is proposed. Then, the determined random typical load spectrum is processed into a simple variable amplitude load spectrum, and the damage in each plane is calculated according to the multiaxial fatigue life prediction model and Miner theory. Meanwhile, the cumulative damage can be calculated separately by projection method. Finally, the maximum projected cumulative damage plane is defined as the critical plane of multiaxial random fatigue.

The fatigue life prediction capability of the method is verified based on test data of TC4 titanium alloy under random multiaxial loading. Most of the predicting results are within double scatter bands.

The objective of this study is to provide a reference for the determination of critical plane and non-proportional additional hardening factor under multiaxial random loading, and to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

The purpose of this paper is to expose computational methods as applied to engineering systems and evolutionary processes with randomness in external actions and inherent parameters.

In total, two approaches are distinguished that rely on solvers from deterministic algorithms. Probabilistic analysis is referred to as the approximation of the response by a Taylor series expansion about the mean input. Alternatively, stochastic simulation implies random sampling of the input and statistical evaluation of the output.

Beyond the characterization of random response, methods of reliability assessment are discussed. Concepts of design improvement are presented. Optimization for robustness diminishes the sensitivity of the system to fluctuating parameters.

Deterministic algorithms available for the primary problem are utilized for stochastic analysis by statistical Monte Carlo sampling. The computational effort for the repeated solution of the primary problem depends on the variability of the system and is usually high. Alternatively, the analytic Taylor series expansion requires extension of the primary solver to the computation of derivatives of the response with respect to the random input. The method is restricted to the computation of output mean values and variances/covariances, with the effort determined by the amount of the random input. The results of the two methods are comparable within the domain of applicability.

The present account addresses the main issues related to the presence of randomness in engineering systems and processes. They comprise the analysis of stochastic systems, reliability, design improvement, optimization and robustness against randomness of the data. The analytical Taylor approach is contrasted to the statistical Monte Carlo sampling throughout. In both cases, algorithms known from the primary, deterministic problem are the starting point of stochastic treatment. The reader benefits from the comprehensive presentation of the matter in a concise manner.

One of the biggest problems in an R&D process is the acquisition of information about the structure dynamic loads, which are needed to reliably prove the structure's durability. This paper aims to present an innovative method for simulating stationary Gaussian random processes, which is based on the conditional probability density function (PDF) approach.

The basic information on the structure dynamic loads is first obtained by short‐duration measurements on prototypes or the structure itself. These data are then used to simulate the expected structure load states during operations. A theoretical background is presented first, which is followed by the application of the method.

The results show that the spectral characteristics of the original and simulated Gaussian random processes are very similar, if the influential range of the conditional PDF is properly chosen.

The method can be applied for simulating random loads of structures, and excitations of dynamic systems, for example.

The innovative simulation approach could be helpful to engineers in the early phases of the new product development process.

The study aims to design the limited number of random working cycle as a warranty term and propose two types of warranties, which can help manufacturers to ensure the product reliability during the warranty period. By extending the proposed warranty to the consumer's post-warranty maintenance model, besides the authors investigate two kinds of random maintenance policies to sustain the post-warranty reliability, i.e. random replacement first and random replacement last. By integrating depreciation expense depending on working time, the cost rate is constructed for each random maintenance policy and some special cases are provided by discussing parameters in cost rates. Finally, sensitivities on both the proposed warranty and random maintenance policies are analyzed in numerical experiments.

The working cycle of products can be monitored by advanced sensors and measuring technologies. By monitoring the working cycle, manufacturers can design warranty policies to ensure product reliability performance and consumers can model the post-warranty maintenance to sustain the post-warranty reliability. In this article, the authors design a limited number of random working cycles as a warranty term and propose two types of warranties, which can help manufacturers to ensure the product reliability performance during the warranty period. By extending a proposed warranty to the consumer's post-warranty maintenance model, the authors investigate two kinds of random replacement policies to sustain the post-warranty reliability, i.e. random replacement first and random replacement last. By integrating a depreciation expense depending on working time, the cost rate is constructed for each random replacement and some special cases are provided by discussing parameters in the cost rate. Finally, sensitivities to both the proposed warranties and random replacements are analyzed in numerical experiments.

It is shown that the manufacturer can control the warranty cost by limiting number of random working cycle. For the consumer, when the number of random working cycle is designed as a greater warranty limit, the cost rate can be reduced while the post-warranty period can't be lengthened.

The contribution of this article can be highlighted in two key aspects: (1) the authors investigate early warranties to ensure reliability performance of the product which executes successively projects at random working cycles; (2) by integrating random working cycles into the post-warranty period, the authors is the first to investigate random maintenance policy to sustain the post-warranty reliability from the consumer's perspective, which seldom appears in the existing literature.

The purpose of this study is to develop a stochastic finite element method (FEM) to solve the calculation precision deficiency caused by spatial variability of dam compaction quality.

The Choleski decomposition method was applied to generate constraint random field of porosity. Large-scale laboratory triaxial tests were conducted to determine the quantitative relationship between the dam compaction quality and Duncan–Chang constitutive model parameters. Based on this developed relationship, the constraint random fields of the mechanical parameters were generated. The stochastic FEM could be conducted.

When the fully random field was simulated without the restriction effect of experimental data on test pits, the spatial variabilities of both displacement and stress results were all overestimated; however, when the stochastic FEM was performed disregarding the correlation between mechanical parameters, the variabilities of vertical displacement and stress results were underestimated and variation pattern for horizontal displacement also changed. In addition, the method could produce results that are closer to the actual situation.

Although only concrete-faced rockfill dam was tested in the numerical examples, the proposed method is applicable for arbitrary types of rockfill dams.

The value of this study is that the proposed method allowed for the spatial variability of constitutive model parameters and that the applicability was confirmed by the actual project.