General standby allocation in series and parallel systems

Stochastic orders are very useful tools to compare the lifetimes of two systems. Optimum lifetime of a series (resp. parallel) system with general standby component(s) depends on the allocation strategy of standby component(s) into the system. Here, we discuss three different models of one or more standby components. In each model, we compare different series (resp. parallel) systems (which are formed through different allocation strategies of standby component(s)) with respect to the usual stochastic order and the stochastic precedence order. The results related to the cold as well as the hot standby models are obtained as particular cases of the results discussed in this article because the model considered here is a general one.     

On some generalized ageing orderings

Some partial orderings that compare probability distributions with the exponential distribution are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which describe the same kind of phenomenon of some generalized ageing classes. We give some equivalent conditions for each of the orderings. Inter-relations among the generalized orderings have also been discussed.     

Capacity Allocation among Multiple Suppliers in an Electronic Market

An electronic marketplace typically provides industrial suppliers an alternative option for selling their capacity in addition to the traditional open market. However, suppliers face different sets of costs and risks in open market and in electronic market. Consequently, suppliers participating in an electronic market are likely to offer their capacity at a different price compared with traditional open market. We analyze this problem and derive the price‐capacity function for the supplier. We also derive a basis for allocating buyer's requirements among multiple suppliers so as to minimize his cost. Our model shows that suppliers with large capacities would quote a lower price in the electronic market. It also predicts that the unit bid price increases with bid quantity in the electronic market. Based on the price‐capacity curve, we model a scenario where the buyer announces, a priori, the number of suppliers to be selected for award of a contract that will minimize its costs.     

On some generalized orderings: In the spirit of relative ageing

ABSTRACT

We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing classes and also helpful to guide the practitioners when there are crossing hazard rates and/or crossing mean residual lives. We study some characterizations of these orderings. Inter-relations among these orderings have also been discussed.