Applied Stochastic Models in Business and Industry最新文献

The model of extended sequential order statistics (ESOS) comprises of two valuable characteristics making the model powerful when modelling multi-component systems. First, components can be assumed to be heterogeneous and second, component lifetime distributions can change upon failure of other components. This degree of flexibility comes at the cost of a large number of parameters. The exact number depends on the system size and the observation depth and can quickly exceed the number of observations available. Consequently, the model would benefit from a reduction in the dimension of the parameter space to make it more readily applicable to real-world problems. In this article, we introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model. These functions model the relation between model parameters of a component across levels. By construction the proposed ‘link estimates’ conveniently yield ordered model estimates. We demonstrate how those ordered estimates lead to better results compared to their unordered counterparts, particularly when sample sizes are small.

Recently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal-Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one-shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence-based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald-type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi-criteria-based optimal design. Population-based heuristic algorithm nondominated sorting-based multiobjective Genetic algorithm is exploited to solve this optimization problem.

In this article, we consider the censored $��\delta �-�\text{shock}�$ model in which the distribution of intershock times do not have the same distribution, but it is assumed that a change occurs in the distribution of the intershock times due to an environmental effect and hence this distribution changes after a random number of shocks. For this shock model, several reliability characteristics are evaluated by assuming that the random change point has a discrete phase-type distribution. Analytical results for evaluating the reliability function of the system for several continuous as well discrete distributions of the interarrival times, are also given. Also, the optimal replacement policy that is based on a control limit is proposed for a mixed censored $��\delta �$-shock model in which both the distributions of the magnitudes of shocks and the distributions of the interarrival times of shocks change after a random number of shocks. Finally, several numerical examples are given to illustrate our results.

The 13th spring meeting of the ENBIS society was held in Grenoble, France, on May 19–20 2022. ENBIS is the European Network for Business and Industrial Statistics. Its objective is to connect people and organisations throughout Europe to improve statistical methods and their applications in the field of business and industry. ENBIS organizes each year a one-week congress and a 2- or 3-days spring meeting.

The topic of the 13th spring meeting in Grenoble has been “Degradation and Maintenance, Modelling and Analysis”. In fact, in the field of reliability studies, the multiplication of equipment control and monitoring systems implies that degradation models become more and more prominent over lifetime models. The modelling of degradation processes, the statistical analysis of the corresponding data and their use for the predictive maintenance of industrial systems are important and challenging issues.

The aim of this Special Issue of ASMBI is not only to publish selected extended versions of papers presented during ENBIS 2022 spring meeting, but also to promote high-quality, innovative, and original works relevant to the application of statistical methods and probability models to the field of degradation and maintenance and more generally reliability analysis.

After an exhaustive peer review process, this Special Issue includes nine papers that contribute significantly to advance of the knowledge in the reliability and maintenance field. Here we introduce this collection of papers which cover both mathematical developments and practical applications.

Another modelling framework discussed in this special issue, is Phase type distributions. Any lifetime distribution can be approximated arbitrarily close by a phase type distribution. This fact makes this distribution very attractive as parametric model to failure time data with degradation trend. In this sense, Lindqvist⁶ shows how phase-type distributions can be used for modelling the effect of degradation and maintenance. The paper focuses on Phase-type models used in competing risks framework who consider multiple absorbing states on their continuous time Markov chain. Instantaneous transitions are added at certain stages to model repair actions bringing failed system into working conditions. Two different approaches are proposed, and their long run properties are studied in term of measure of reliability and maintenance efficiency.

The guest editors of this Special Issue thank all the persons who helped to make this issue possible. They are thankful to Fabrizio Ruggeri, the Editor in Chief of ASMBI, for giving them the opportunity of editing this Special Issue and for his support and guidance during the editorial process. They are also grateful to the reviewers for their careful work and constructive revisions that contribute to improve the papers. At last, they are very grateful to the authors, and more generally to all the participants of

One primary objective of reliability engineering is to achieve optimal maintenance of technical systems, which ensures they remain in good operating condition. This paper proposes an age-based preventive optimal maintenance policy for $��n�$-component coherent systems. Under this proposed strategy, the system begins operating at $��t�=�0�$ and undergoes preventative maintenance (PM) at a time $��{�T�}_{�p�}�$. If the system fails before $��{�T�}_{�p�}�$, it will be replaced with a new one. If the system is still functioning at time $��{�T�}_{�p�}�$, an assessment is made based on the number of failed components to determine whether the system should be replaced or allowed to continue operating. If the number of failures at $��{�T�}_{�p�}�$ is below a predetermined threshold $��m�$, the PM time

This article considers a condition-based maintenance for a system subject to deterioration. The deterioration is modeled by a non-homogeneous gamma process, more precisely the gamma process and the preventive maintenance are imperfect or worse than old. The corrective maintenance actions are as good as new. The maintenance efficiency or non-efficiency parameters as well as the deterioration parameters are considered to be unknown. The monitoring data under consideration give indirect information on the maintenance parameters. Therefore, an expected maximum algorithm is applied for parameter estimation.

Two key features of airline departure delays are that they cascade and that there can be exceptional peaks. We model these features using an intensity-based Hawkes process. Our application to all KLM departure delays at Amsterdam Schiphol airport in January 2015 shows that volatility in departure delays is endogenous. We correlate the key parameters of the estimated Hawkes process with daily weather conditions and find that these conditions amplify the self-exciting feature of departure delays.

We consider testing for trend in recurrent event data. More precisely, for such data we consider testing of the null hypothesis of data coming from a renewal process. The new tests are essentially obtained by considering appropriate integrated versions of classical trend tests. Moreover, adaptive versions of earlier considered tests versus non-monotonic alternatives, like bathtub trend, are suggested. A simulation study shows that the new tests have favorable properties and sometimes outperform classical tests. Examples with real data are also considered.