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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.

AbstractThis paper proposes a new model of consideration set sizes, which relies on a stochastic modelling approach to better understand data patterns. The paper combines the Poisson distribution with the lognormal distribution proposed by Hauser and Wernerfelt (1990) to create the Poisson lognormal (PLN) model of consideration set sizes. An advantage of PLN is that it allows variance within a given individual consumer. This is a crucial factor for brand managers who wish to choose a particular market to promote their brand, as a higher within‐individual variance suggests that there is more chance for a consumer to change their consideration set size, whereas a lower within‐individual variance indicates that a consumer tends to stick to his/her consideration set size. The paper then uses 10 datasets including service, durable and fast‐moving consumer goods across four countries to validate the new model and compare it with the lognormal model. The results show that PLN gives a good fit to these data. It outperforms the lognormal model. The average mean absolute percentage error of the PLN model is 12 per cent, whereas that of the lognormal model is 26 per cent. For managerial implications, the paper proposes a better tool to help brand managers analyse the nature and intensity of competition that is facing their brands. Also, relying on its stochastic element, the proposed model can help brand managers predict future brand consideration by their consumers, as well as evaluate any change in brand consideration, caused by marketing activity such as sales promotion and advertising. Copyright © 2014 John Wiley & Sons, Ltd.

The United States Air Force is developing its next generation aircraft and is seeking to reduce the risk of catastrophic failures, maintenance activities, and the logistics footprint while improving its sortie generation rate through a process called autonomic logistics. Vital to the successful implementation of this process is remaining lifetime prognosis of critical aircraft components. Complicating this problem is the absence of failure time information; however, sensors located on the aircraft are providing degradation measures. This research has provided a method to address at least a portion of this problem by uniting analytical lifetime distribution models with environment and/or degradation measures to obtain the remaining lifetime distribution.