Monotonicity and aging properties of random sums

Cai, Jun; Willmot, Gordon E.

doi:10.1016/j.spl.2005.04.013

Cited by 16 publications

(10 citation statements)

References 33 publications

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“…It is well known (Shanthikumar ), that geometric sums with DFR summands are also DFR (see also , p. 588, for a recent alternative proof of this fact in the discrete case). Results concerning the DRHR property of random sums appear in , in which this property is shown for a random sum in which the summands have a concave cdf and where the random number of terms is Binomial or Poisson (note that this fact is also implicit in the proof of , Prop. 1‐3(iii)).…”

Section: The Periodic Review‐periodic Demand Modelmentioning

confidence: 99%

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

Badía

Sangüesa

2015

Naval Research Logistics

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Abstract:In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797-809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log-concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log-concavity properties of compound distributions.

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Section: The Periodic Review‐periodic Demand Modelmentioning

confidence: 99%

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

Badía

Sangüesa

2015

Naval Research Logistics

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“…Ageing concept for discrete distributions were studied by various authors. See for example, Barlow and Proschan, 1 Cai and Kalashnikov, 2 Cai and Willmot, 3 Lai and Xie, 4 Shaked and Shanthikumar, 5 Shaked et al, 6 Willmot and Cai, 7 Willmot and Lin, 8 Willmot et al, 9 and references therein. Using Laplace transform, various reliability classes have been characterized by different researches.…”

Section: Introductionmentioning

confidence: 99%

Shock models leading to G* class of lifetime distributions

Jayamol¹,

Jose²

2020

BBIJ

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In this paper we study a stochastic ordering namely alternate probability generating function (a.p.g.f .... ) ordering and its properties. The life distribution H(t) of a device subject to shocks governed by a Poisson process is considered as a function of the probabilities Pk of surviving the first k shocks. Various properties of the discrete failure distribution Pk are shown to be reflected in corresponding properties of the continuous life distribution H(t). A certain cumulative damage model and various applications of these models in reliability modeling are also considered.

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“…These classes of discrete distribution aging have been used extensively in different fields of statistics and probability such insurance, finance, reliability, survival analysis, and others. See, for example, [5,8,10,11,13,14,[16][17][18]. Some commonly used classes of discrete distributions include the classes of discrete decreasing failure rate (D-DFR), discrete decreasing failure rate average (D-DFRA), discrete new worse than used (D-NWU), discrete increasing mean residual life (D-IMRL), discrete harmonic new worse than used in expectation (D-HNWUE), and their dual ones including the classes of discrete increasing failure rate(D-IFR), discrete increasing failure rate average (D-IFRA), discrete new better than used (D-NBU), discrete decreasing mean residual life (D-DMRL), and discrete harmonic new better than used in expectation (D-HNBUE).…”

Section: Introductionmentioning

confidence: 99%