SEMINAR: A model on the total number of defective items: A point process29-12-2020

Speaker: Hans Frenk

Title: A model on the total number of defective items: A point process approach

Date/Time: 30 December 2020/ 13:40 - 14:30

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Abstract: Based on the practical problem of estimating the total number of spare parts needed to repair defective products we propose in this talk a model describing the total number of defective items under warranty returned to a manufacturer over time. This model represents the sales process by means of a general point process and it also describes the total number of repairs applied to an arbitrary item of this product under warranty. Combining these two stochastic processes yields an exact representation of the stochastic process counting the total number of defective items to be repaired by the manufacturer. Within the sub-model describing the total number of repairs, we also consider different repair strategies which can be used by the manufacturer. Due to the detailed description of both the sales process and the repair process of a particular item and the used repair strategy we are able to derive all kinds of properties of the stochastic process counting the number of defective items over time. In particular, detailed expressions of moments, variances and covariances can be obtained under the simplifying assumption that the sales process is represented by a non-homogeneous Poisson process. It is assumed that the audience is familar with Poisson processes Although this talk mainly deals with the theory of stochastic point processes and the analysis of general counting processes the developed theoretical model and its derived properties will then be used as a parametric model to fit a large data set. If time permits also the statistical analysis of the proposed model will be discussed. As such the approach serves as an alternative to the approach of using time series in case item tracking information is available.

Bio:  Hans Frenk joined the Faculty of Engineering and Natural Sciences at Sabanci University in 2009. He obtained his master degree (1979) from the Mathematics Department of Utrecht University, the Netherlands and his Ph.D degree (1984) from Erasmus University Rotterdam. His Ph.D thesis was on the rate of convergence of the renewal measure to the Lebesgue measure (renewal theory and regenerative processes) for interarrival times having a subexponential distribution using the theory of Banach algebras. Next to this he also obtained a Bachelor degree in Econometrics (1982) from Erasmus University Rotterdam. Before joining Sabanci university he was working at IEOR department (UC Berkeley), Mathematics Department Technical University Eindhoven and Econometric Institute Erasmus University Rotterdam. Through the years his main research interest is in optimization, convex and quasiconvex analysis, stochastic processess and stochastic control problems. At the moment his research is in applications of those techniques to problems in Management Science and Engineering (maintenance, inventory control, revenue management and pricing). Recently his interests is also in statistical estimation problems related to stochastic processes. Three of his former master or Ph.D students received INFORMS awards for best master thesis or Ph.D thesis and he received the Wickham Skinner award for second best paper published in POMS 2012 on a topic in inventory control. Some of his papers jointly written with coauthors appeared in Production and Operations Management, Management Science, Operations Research, Transportation Science, Advances of Applied Probability, Journal of Applied Probability, Journal of Optimization Theory and Applications. Mathematics of Operations Research, Mathematical Programming and Discrete Applied Mathematics.