Suchergebnisse

AbstractIn this work we consider spread of information which motivates the hearer to perform some specified action. The time to completion of an action is assumed to be a random variable and the main focus is on the number of completed actions by time t, X(t). Some models, which reflect different degree of centralization in the spread process, are analyzed and the distribution of X(t), as well as that of some other stochastic processes of interest, are obtained. The relevance to propagation of epidemics is pointed out.All models are solved by employing two interrelated concepts, namely, the order statistics property of stochastic processes and the binomial closure property of collections of distributions. In this respect, the work also serves as an illustration of the application of these useful concepts.

AbstractA trigger‐off replacement policy, suggested and analyzed in [1], for two‐unit systems composed of identical units, is generalized and extended in this work in several ways. In the first part of the paper we obtain the appropriate integral equations for nonidentical units and then use them for a complete solution of the case of two units, whose lifetimes are distributed according to general Erlang distributions. In the second part of the paper we extend the trigger‐off policy itself by allowing preventive replacements of units which reach a certain critical age. The system stops working if either one of the two units fails or reaches its critical age. Both cases present natural replacement possibilities for the remaining unit, provided that its age exceeds a predetermined critical age.Finally, we consider the question of which policy parameters, i.e. control limits and critical ages, to choose when facing a real‐life situation. Using the criterion of expected costs per unit time in the long run, we show how to find the optimal parameters which minimize this objective function. The fact that a restricted optimization, within the class of trigger‐off replacement policies, leads to the global optimal policy has been proved in [2] by a different approach.

ABSTRACTThis study presents a framework for choosing between depreciation methods when future cash flows from operations are not assumed known with certainty but only in probabilistic terms. Specifically, the accelerated depreciation method and the straight‐line depreciation method are compared and mathematical conditions are derived for the depreciation method that should be adopted in different circumstances and under different tax systems. It is shown that, contrary to conventional wisdom, the straight‐line depreciation method is the preferred method for lowering the company's present value of tax liability in various realistic situations.

AbstractThe model for a modified block replacement policy (MBRP) is extended to include running costs. An illustrative example is worked out for the case when item life is exponentially distributed and marginal running cost per unit time increases linearly with the age of the item.

AbstractA well known preventive replacement policy is the block replacement policy (BRP). In such a policy the item undergoes a planned replacement at a sequence of equally spaced time points independent of failure history. The main advantage of a BRP is its simplicity, because under this policy it is unnecessary to keep detailed records about times of failures or ages of items. The main drawback of a BRP is that at planned replacement times we may be replacing practically new items. In this paper we study a modified BRP which is free of this drawback. We calculate the expected cost of following a modified BRP for lifetime distributions possessing a special structure and illustrate it for the case of an Erlang distribution. A numerical comparison is made between a modified BRP and a standard BRP for the special case of a two stage Erlang distribution.