Applied Stochastic Models in Business and Industry最新文献

In the development of devices for cutting Chinese yams into chunks for use as seeds, accurately measuring the yam's shape with a simple mechanism is crucial. In our prior study, we introduced a statistical approach for predicting the shape of a Chinese yam based on its key diameters. This method involves organizing sample data, estimating diameters at discrete points along the central axis, and constructing a predictive model based on these estimated diameters. However, the initial predictive model relied on separate regression models for each point, potentially leading to instability. In this article, we enhance our previous approach by incorporating a new step that refines the estimation of regression coefficients through Bayesian linear modeling methods. This modification allows for the simultaneous estimation of regression coefficients, ensuring greater stability in the reconstructed model. Additionally, we modify the method for locating key diameters. To validate the performance of the enhanced approach, we apply it to a set of samples and compare the output of the reconstructed model with that of our initial method. The results demonstrate improved stability and performance, highlighting the efficacy of the refined modeling technique.

Limited failure or cure rate models provide generalization of lifetime models which allow the possibility of subjects or units to be cured or be failure-free. While modeling and analysis of such models are extensively studied, we study the important question of identifiability of these models. We discuss the latent and hierarchical activation cure models and establish a series of results on stochastic ordering within these models. We also establish a series of results on identifiability of these models under various conditions. Further, we demonstrate multiple cases where there models are not identifiable and illustrate the potential difficulty with these models in a simulation study.

Negative probabilities arise primarily in physics, statistical quantum mechanics, and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link between these two viewpoints. Bartlett provides a definition of negative probabilities based on extraordinary random variables and properties of their characteristic function. A version of the Bayes rule is given with negative mixing weights. The classic half-coin distribution and Polya-Gamma mixing are discussed. Heisenberg's principle of uncertainty and the duality of scale mixtures of Normals is also discussed. A number of examples of dual densities with negative mixing measures are provided including the Linnik and Wigner distributions. Finally, we conclude with directions for future research.

Fatigue data arise in many research and applied areas, and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic-stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue-life and fatigue-strength distributions. Likelihood-based confidence bands can then be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue-life and fatigue-strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue-life cdf and the fatigue-life qf, (b) the equivalence of confidence bands for the fatigue-strength cdf and the fatigue-strength qf, and (c) the equivalence of confidence bands for the fatigue-life qf and the fatigue-strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.

Balancing consumer's and producer's risk is an important consideration when planning tests. Instead of focusing on finding a single best test plan, we introduce a general framework to systematically identify a set of binomial test plans by leveraging the inverse relationship between the two risks. The framework is applied to compare a variety of assurance testing frameworks, including classical tests, and Bayesian reliability assurance tests such as the Bayesian assurance test, the assurance reliability demonstration test, and the coverage criterion test. Efficient algorithms are presented to compute the set of test plans, providing practitioners with a comprehensive range of options to choose from. In addition, we include a comparison to the sequential probability ratio test. We also provide formal proofs for the inverse relationship between consumer's and producer's risk in Bayesian reliability assurance tests that underlie our algorithms. A case study is presented to illustrate the framework's application and compare the risks associated with different test plans.