A Parrondo Paradox in Reliability Theory

Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version of Parrondo's paradox in reliability theory involving two systems in series, the units of the first system being less reliable than those of the second. If the first system is modified so that the distributions of its new units are mixtures of the previous distributions with equal probabilities, then under suitable conditions the new system is shown to be more reliable than the second in the "usual stochastic order" sense.Comment: 6 page

On jump-diffusion processes with regime switching: martingale approach

We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these processes by means of the relative entropy. The minimal entropy approach is also developed. It is shown that in contrast to the case of L\'evy processes, for this model an Esscher transformation does not produce the minimal relative entropy.Comment: 23 pages, 2 figure

A review on symmetry properties of birth-death processes

In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the transition rates such that the transition probabilities satisfy a spatial symmetry relation. The latter leads to simple expressions for first-passage-time densities and avoiding transition probabilities. This approach is thus thoroughly extended to the case of bilateral birth-death processes, even in the presence of catastrophes, and to the case of a two-dimensional birth-death process with constant rates.Comment: 16 pages, 4 figure

On the Effect of Random Alternating Perturbations on Hazard Rates

We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability distribution, mean and variance. An application to survival analysis and reliability data sets based on confidence bands for estimated hazard rate functions is also provided.Comment: 14 pages, 6 figure

Extension of the past lifetime and its connection to the cumulative entropy

Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and series systems under suitably proportionality assumptions on the hazards rates. Furthermore, we prove that the (reversed) relevation transform is commutative if and only if the proportional (reversed) hazard rate model holds. By repeated application of the reversed relevation transform we construct a decreasing sequence of random variables which leads to new weighted probability densities. We obtain various relations involving ageing notions and stochastic orders. We also exploit the connection of such a sequence to the cumulative entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative formulae for computing the mean and the cumulative entropy of the random variables of the sequence are finally investigated

Service Implementation Framework in Manufacturing Firms: A Case Study

The culture and the operational methods of service management have become a formidable competitive weapon even for manufacturing firms. The term "service factory" has been proposed for identifying that particular integration of products and services, achieved by the excellent manufacturing firm, where "service is a multidimensional concept". The creation of a service factory necessarily implies a radical change in the operational and organizational characteristics of the firm. In order to support manufacturing firms in adopting a service strategy, it is relevant on the one hand to identify the bundle of services which have to be provided for the customers and, on the other hand, to understand the implications for firm management model. As regards the first point, the paper proposes a framework which classifies the services along with two dimensions: Timedimension and target-dimension. The proposed framework is of interest for manufacturing firms because it allows a better recognition of services that are more perceptible for the customers. In the second part of the paper, authors discuss the implications of a service strategy adoption on the management model of manufacturing firms. In order to carry out this analysis, authors propose a model that combines four service dimensions with three decision-making categories (Organization, Methodologies and Technologies). In the end, the proposed framework has been applied in a sample of Italian hot water heater manufacturers and a case study analysis has been carried out