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Customer satisfaction data collected by a large cellular phone service provider are to be used to evaluate and improve the quality of their service. For this purpose, we propose a Bayesian treatment of a joint-response chain graph relating partial assessments of specific aspects of quality to an overall assessment of the service quality. The resulting Bayesian model can be used to render basic geographical and temporal differentiation, allowing the company to undertake direct corrective actions. Both normal and binary models are considered for our customer satisfaction data and are compared with other currently used methods in the study of customer satisfaction. Copyright © 2011 John Wiley & Sons, Ltd.

Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random number of components chosen from the first batch increases in increasing convex order. As a consequence, we establish a result analogous to the Parrondo’s paradox, which shows that randomness in the number of components extracted from the two batches improves the reliability of the series system.

We discuss suitable conditions such that the lifetime of a series or of a parallel system formed by two components having nonindependent lifetimes may be stochastically improved by replacing the lifetimes of each of the components by an independent mixture of the individual components' lifetimes. We also characterize the classes of bivariate distributions where this phenomenon arises through a new weak dependence notion. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Consider a general coherent system with independent or dependent components, and assume that the components are randomly chosen from two different stocks, with the components of the first stock having better reliability than the others. Then here we provide sufficient conditions on the component’s lifetimes and on the random numbers of components chosen from the two stocks in order to improve the reliability of the whole system according to different stochastic orders. We also discuss several examples in which such conditions are satisfied and an application to the study of the optimal random allocation of components in series and parallel systems. As a novelty, our study includes the case of coherent systems with dependent components by using basic mathematical tools (and copula theory).

Consider m counting processes @C"i,i=1,2,...,m, and a random vector of positive integers M=(M"1,M"2,...,M"m). Denote by X"i"j the jth interpoint interval in the process @C"i,i=1,2,...,m,j=1,2,..., and define Z"[email protected]?"j"="1^M^"^iX"i"j,i=1,2,...,m. It is assumed that M is independent of the @C"i's, however, the processes @C"i's are not necessarily mutually independent. In this paper we identify some situations in which the positive (negative) association of the M"i's implies the positive (negative) association of the Z"i's. Some applications in reliability theory and in insurance are indicated.

The geometric telegrapher's process is proposed as a model to describe the dynamics of the price of risky assets. When the underlying random inter-times have Erlang distribution we express the probability law of such process in terms of a suitable two-index pseudo-Bessel function. Stochastic comparisons of two geometric telegrapher's processes based on the usual stochastic order (FSD comparison) and on the stop-loss order are also performed. Various examples of application of such comparisons are then provided. Copyright © 2002 John Wiley & Sons, Ltd.

In this article, we identify conditions under which the epoch times and the interepoch intervals of a nonhomogeneous Poisson process have logconcave densities. The results are extended to relevation counting processes. We also study discrete-time counting processes and find conditions under which the epoch times and the interepoch intervals of these discrete-time processes have logconcave discrete probability densities. The results are interpreted in terms of minimal repair and record values. Several examples illustrate the theory.

New concepts of partial stochastic orderings are introduced, and the relations among them and the classical partial orderings are shown. Relevance of these partial orderings in aging properties classification is discussed, and new classes of life distributions, based on them, are proposed. An application to stochastic comparison between Poisson shock models is proposed. © 1993 John Wiley & Sons, Inc.

Let [NA(t), t≥0] and [NB(t), t≥0] be two counting processes with independent interarrivals Ai and Bi, respectively, i ∈ + ≡ [1,2,… ], and let [Xi, i ∈ +] and [Yi, i ∈ +] be two sequences of independent non-negative random variables. Consider the two compound processes [U(t), t ≥ 0] and [V(t), t ≥ 0] defined as U(t) = Xi, t ≥ 0, and V(t) = Yi, t ≥ 0. Then it is well known (and not hard to verify) that if the Ai's are independent of the Xi's, and if the Bi's are independent of the yi's, and if Ai ≥st Bi and Xi ≤st Yi, for all i ∈ +, then [U(t), t ≥ 0] ≤st [V(t), t ≥ 0]. In this paper we provide conditions under which this stochastic order relation holds even if Ai ≤st Bi and/or Xi ≥st Yi for all i ∈ +. In fact, we derive the stochastic order relationships among processes that are much more general than the cumulative ones described above. For example, it is not necessarily assumed that the Ai's are independent of the Xi's or that the Bi's are independent of the Yi's. Examples that illustrate the applications of the theory are included.

Recently, Belzunce, Ortega, Pellerey, and Ruiz [3] have obtained stochastic comparisons in increasing componentwise convex order sense for vectors of random sums when the summands and number of summands depend on a common random environment, which prove how the dependence among the random environmental parameters influences the variability of vectors of random sums. The main results presented here generalize the results in Belzunce et al. [3] by considering vectors of parameters instead of a couple of parameters and the increasing directionally convex order. Results on stochastic directional convexity of families of random sums under appropriate conditions on the families of summands and number of summands are obtained, which lead to the convex comparisons between random sums mentioned earlier. Different applications in actuarial science, reliability, and population growth are also provided to illustrate the main results.

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

For a component operating in random environment, whose hazard rate is assumed to be the realization of a suitable increasing stochastic process, conditions are found such that its lifetime is increasing in likelihood ratio (ILR). For the lifetimes of two components of the same kind some comparisons based on partial stochastic orders are presented. Some applications to the case of repairable components are finally provided.