Graduate Students Seminar

Speaker 1: Vahid Andalib

Title

A Repairable System Supported by Two Spare Units and Serviced by Two Types of Repairers

Abstract

We study a one-unit repairable system, supported by two identical spare units on cold standby, and serviced by two types of repairers. The model applies, for instance, to hydraulic systems in the aviation industry. The failed unit undergoes repair either by an in-house repairer within a random or deterministic patience time, or else by a visiting expert repairer. The expert repairs one or all failed units before leaving, and does so faster but at a higher cost rate than the regular repairer. Four models arise depending on the number of repairs done by the expert and the nature of the patience time. We compare these models based on the limiting availability, and the limiting profit per unit time, using semi-Markov processes, when all distributions are exponential. As anticipated, to maximize the limiting availability, the expert should repair all failed units. To maximize the limiting profit, a suitably chosen deterministic patience time is better than a random patience time.  Furthermore, given all cost parameters, we determine the optimum number of repairs the expert should complete, and the optimum patience time given to the regular repairer in order to maximize the limiting profit.

Speaker 2: Ellie Gurvich

Title

Degenerate Evolution Equations in Poroelasticity

Abstract

Existence and uniqueness results are presented for the quasi-static Biot system, a system of partial differential equations describing the coupled dynamics of structural deformation and fluid flow through a poroelastic medium. To simplify the discussion, homogeneous Dirichlet boundary conditions are used with a general initial condition.  The investigation proceeds via the theory of linear degenerate evolution equations in Hilbert space of the form B p_t(t) + A p(t) = f(t), as developed by Showalter. Notably, B need not be an isomorphism. To conclude, the existence and uniqueness results for such equations are constructed, following a non-trivial application of the Lumer-Phillips theorem to an abstract Cauchy problem.