Applied Stochastic Models in Business and Industry最新文献

If Francis Bacon were born today, he might have said “data is power” instead of his original saying, “knowledge is power.” In modern society, data is everywhere. In memory of Deming (a guru in quality), this paper attempts to address the fundamental issue of data quality and how Deming would handle it. Specifically, we attempt to explain what data quality really means, and the critical impact that it has on data science. Statisticians, who understand how to collect high quality data, have much more to contribute to both the intellectual vitality and the practical utility of data science. At the same time, data science challenges statisticians to move out of some familiar habits to engage less structured problems, to become more comfortable with ambiguity, and to engage more scientists in a fruitful discussion on what various parties can bring to this new mode of investigation. Some potential avenues for future research in the collection of high-quality data will be proposed.

Industrial processes generate a massive amount of monitoring data that can be exploited to uncover hidden time losses in the system. This can be used to enhance the accuracy of maintenance policies and increase the effectiveness of the equipment. In this work, we propose a method for one-step probabilistic multivariate forecasting of time variables involved in a production process. The method is based on an Input-Output Hidden Markov Model (IO-HMM), in which the parameters of interest are the state transition probabilities and the parameters of the observations' joint density. The ultimate goal of the method is to predict operational process times in the near future, which enables the identification of hidden losses and the location of improvement areas in the process. The input stream in the IO-HMM model includes past values of the response variables and other process features, such as calendar variables, that can have an impact on the model's parameters. The discrete part of the IO-HMM models the operational mode of the process. The state transition probabilities are supposed to change over time and are updated using Bayesian principles. The continuous part of the IO-HMM models the joint density of the response variables. The estimate of the continuous model parameters is recursively computed through an adaptive algorithm that also admits a Bayesian interpretation. The adaptive algorithm allows for efficient updating of the current parameter estimates as soon as new information is available. We evaluate the method's performance using a real data set obtained from a company in a particular sector, and the results are compared with a collection of benchmark models.

Stochastic orders have been widely used in reliability literature to compare the performances of coherent systems, and various criteria have been provided on this purpose. In particular, sufficient conditions have been found for the lifetime of a system to be stochastically larger than that of another system having the same components with identically distributed lifetimes but a different structure function. Known results of this kind concern some of the most relevant stochastic orders, but in the literature no conditions have been provided for the well-known increasing convex order (icx). Here we describe conditions such that two lifetimes of coherent systems are comparable in this stochastic sense when conditions for other stronger orders do not apply. Illustrative examples are also given.

This article presents a real-time predictive maintenance model of vehicle suspensions based on vibration signal analysis. The study is grounded in the observation that suspension wear and failure are primarily driven by cumulative stresses and external shocks encountered during vehicle operation. We use a wavelet-based technique integrated with stochastic modeling and lifetime data analysis to predict the remaining useful life (RUL) of the suspension. The proposed framework provides a decision-making tool for determining whether and when suspension systems should be subjected to inspection, replacement, or overhaul. An empirical application, using vibration data from a uniaxial accelerometer mounted on a vehicle suspension under varying road conditions, validates the theoretical model and estimation procedure.

The gamma process is a natural model for monotonic degradation processes. In practice, it is desirable to extend the single gamma process to incorporate measurement error and to construct models for the degradation of several nominally identical units. In this paper, we show how these extensions are easily facilitated through the Bayesian hierarchical modeling framework. Following the precepts of the Bayesian statistical workflow, we show the principled construction of a noisy gamma process model. We also reparameterise the gamma process to simplify the specification of priors and make it obvious how the single gamma process model can be extended to include unit-to-unit variability or covariates. We first fit the noisy gamma process model to a single simulated degradation trace. In doing so, we find an identifiability problem between the volatility of the gamma process and the measurement error when there are only a few noisy degradation observations. However, this lack of identifiability can be resolved by including extra information in the analysis through a stronger prior or extra data that informs one of the non-identifiable parameters, or by borrowing information from multiple units. We then explore extensions of the model to account for unit-to-unit variability and demonstrate them using a crack-propagation data set with added measurement error. Lastly, we perform model selection in a fully Bayesian framework by using cross-validation to approximate the expected log probability density of a new observation. We also show how failure time distributions with uncertainty intervals can be calculated for new units or units that are currently under test but have yet to fail.