Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.2362pmid: N/A

No abstract is available for this article.

Gaudoin, Olivier; Lindqvist, Bo H.

doi: 10.1002/asmb.2448pmid: N/A

Spizzichino, Fabio L.

doi: 10.1002/asmb.2397pmid: N/A

For a coherent binary system made of binary components, we consider the assumption that the components' lifetimes are distributed according to a time‐homogeneous, load‐sharing model. Such models are characterized in terms of the so‐called multivariate conditional hazard rate functions. We aim to point out some related properties of the notions of signature, relative quality functions, and reliability functions. On this purpose, we preliminarily collect all the necessary background and review some related literature. This paper concludes with a discussion, also containing some hints for future work.

Yera, Yoel G.; Lillo, Rosa E.; Ramírez‐Cobo, Pepa

doi: 10.1002/asmb.2327pmid: N/A

The batch Markov‐modulated Poisson process (BMMPP) is a subclass of the versatile batch Markovian arrival process (BMAP), which has been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures, or risk events). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPPm(K ) is proven, where K is the maximum batch size and m is the number of states of the underlying Markov chain. This is a powerful result for inferential issues. On the other hand, some novelties related to the correlation and autocorrelation structures are provided.

Rykov, Vladimir; Kozyrev, Dmitry

doi: 10.1002/asmb.2368pmid: N/A

The reliability function is considered for a hot double redundant repairable heterogeneous system with exponentially distributed lifetimes and generally distributed repair times of its components. The problem of its sensitivity to the repair time distribution is discussed.

Giorgio, Massimiliano; Mele, Agostino; Pulcini, Gianpaolo

doi: 10.1002/asmb.2377pmid: N/A

This paper proposes and illustrates a new perturbed gamma degradation process where the measurement error is modeled as a non‐Gaussian random variable that depends stochastically on the actual degradation level. The expression of the likelihood function for a generic set of noisy degradation measurements is derived, and the expression of the remaining useful life distribution of a degrading unit that fails when its degradation level exceeds a given threshold limit is formulated. A particle filter method is suggested, which allows one to compute the likelihood function and to estimate the remaining useful life distribution in a quick yet efficient manner. In addition, a closed‐form approximation of the perturbed gamma process is proposed to use in the special, yet meaningful, case where the standard deviation of the measurement error depends linearly on the actual degradation level. Finally, an applicative example is discussed, where the parameters of the perturbed gamma process, the remaining useful life distribution, and the mean remaining useful life of the degrading units are estimated from a set of noisy real degradation data.

Kahle, Waltraud

doi: 10.1002/asmb.2438pmid: N/A

We consider a Wiener process with linear drift for degradation modeling. Regularly, maintenance actions are carried out which produce a reduction of the degradation level. In this paper, we consider the influence of such maintenance actions to the further development of the degradation process and the resulting lifetime distribution. A connection between virtual age in Kijima‐type models and degradation level in the underlying degradation process is developed. Furthermore, estimators for the process parameters as well as for the degree of repair are developed.

Corset, F.; Fouladirad, M.; Paroissin, C.; Remy, E.

doi: 10.1002/asmb.2449pmid: N/A

In this paper, we consider a system made of n components displayed on a structure (eg, a steel plate). We define a parametric model for the hazard function, which includes covariates and spatial interaction between components. The state (nonfailed or failed) of each component is observed at some inspection times. From these data, we consider the problem of model parameter estimation. To achieve this, we suggest to use the SEM algorithm based on a pseudo‐likelihood function. A definition for the time‐to‐failure of the system is given, generalizing the classical cases. A study based on numerical simulations is provided to illustrate the proposed approach.

Kohl, Christian; Kateri, Maria

doi: 10.1002/asmb.2435pmid: N/A

A step‐stress accelerated life testing model is considered for progressive type‐I censored experiments when the tested items are not monitored continuously but inspected at prespecified time points, producing thus grouped data. The underlying lifetime distributions belong to a general scale family of distributions. The points of stress‐level change are simultaneously inspection points as well while there is the option of assigning additional inspection points in between the stress‐level change points. In a Bayesian framework, the posterior distributions of the parameters of the model are derived for characteristic choices of prior distributions, as conjugate‐like and normal priors; vague or noninformative. The developed approach is illustrated on a simulated example and on a real data set, both known from the literature. The results are compared to previous analyses; frequentist or Bayes.

Deshpande, JV; Dewan, Isha; Lam, KF; Naik‐Nimbalkar, UV

doi: 10.1002/asmb.2375pmid: N/A

Let (X,Y) be a random vector and let G and H be the marginal distributions of X and Y, respectively. In this paper, we propose two tests, one of Kolmogorov‐Smirnov type and the other of Wilcoxon type, for the null hypothesis Ψ(G) = H against the alternative Ψ(G) < H, where Ψ() is a function such that Ψ(G) is a distribution function. The tests are based on the empirical distribution functions of the observations on X and Y, which are dependent. We obtain their asymptotic null distributions. A suspected relationship between the distribution functions of two dependent outcomes can be specified as a hypothesis to be tested in examples like the load sharing models, record values, and auction bidding models. As an application, we consider in detail the problem of testing the effect of load sharing in two component parallel systems.