Susceptibility sets and the final outcome of collective Reed–Frost epidemics

This paper is concerned with exact results for the final outcome of stochastic SIR (susceptible → infective → recovered) epidemics among a closed, finite and homogeneously mixing population. The factorial moments of the number of initial susceptibles who ultimately avoid infection by such an epidemic are shown to be intimately related to the concept of a susceptibility set. This connection leads to simple, probabilistically illuminating proofs of exact results concerning the total size and severity of collective Reed–Frost epidemic processes, in terms of Gontcharoff polynomials, first obtained in a series of papers by Claude Lef`evre and Philippe Picard. The proofs extend easily to include general final state random variables defined on SIR epidemics, and also to multitype epidemics

A review of multi-component maintenance models with economic dependence

In this paper we review the literature on multi-component maintenance models with economic dependence. The emphasis is on papers that appeared after 1991, but there is an overlap with Section 2 of the most recent review paper by Cho and Parlar (1991). We distinguish between stationary models, where a long-term stable situation is assumed, and dynamic models, which can take information into account that becomes available only on the short term. Within the stationary models we choose a classification scheme that is primarily based on the various options of grouping maintenance activities: grouping either corrective or preventive maintenance, or combining preventive-maintenance actions with corrective actions. As such, this classification links up with the possibilities for grouped maintenance activities that exist in practice

Discovery of hidden maintenance opportunities in automotive assembly lines: MOW and GMOW

In manufacturing systems, many maintenance tasks require equipment to be locked out for safety. However, such stoppage might directly cause short-term production losses although maintenance is performed to increase the long-term system reliability. In this paper, we investigate how long we can strategically stop equipment for maintenance during production operating without affecting system throughput. We extend the concept of maintenance opportunity windows (MOWs) to various system configurations and introduce a new concept of group maintenance opportunity windows (GMOWs). GMOW is the maximum time window that allows to perform a group maintenance without jeopardizing the flow of a production line. Moreover, we also provide how to calculate MOW and GMOW via simulations which can deal with uncertainties in production lines, such as random machine failures, starvations, blockages, etc.close