Discrete hazard rate functions

Shaked, Moshe; Shanthikumar, J. George; Valdez-Torres, José Benigno

doi:10.1016/0305-0548(94)00048-d

Cited by 59 publications

(14 citation statements)

References 9 publications

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“…This is the case when an equipment operates in cycles and the number of cycles successfully completed prior to failure is observed. This is also the case when a device is monitored only once per time period and the observation then is the number of time periods successfully completed prior to the failure of the device (Shaked et al, 1995). Discrete lifetimes also occur through grouping or finite precision measurement of continuous time phenomena.…”

Section: Some Results For Discrete Random Variablesmentioning

confidence: 99%

Some distributional results through past entropy

Kundu

Nanda

Maiti

2010

Journal of Statistical Planning and Inference

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Section: Some Results For Discrete Random Variablesmentioning

confidence: 99%

Some distributional results through past entropy

Kundu

Nanda

Maiti

2010

Journal of Statistical Planning and Inference

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“…Part of this lemma was used for proving (2) and (3). In this work, it will be needed for proving Theorem 2.1 and, later, for studying a generalization of the memoryless property of geometric and exponential distributions.…”

Section: The Modelmentioning

confidence: 98%

“…ı ınez and Shaked [1]. This strategy can be seen as a generalization of a discrete model of failure and repair studied in Shaked et al [3] which can be regarded as a discrete analog of the imperfect repair model of Brown and Proschan [4]. And the other one is a combination of the previous two.…”

Section: Introductionmentioning

confidence: 97%

Three repair strategies

Rocha-Martínez

2001

Appl Stoch Models Bus & Ind

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Three repair strategiesJos! e e M. Rocha-Mart! ı ınez* E.S.F.M. del I.P.N., Edificio 9, U. P. ''Adolfo L ! o opez Mateos'', Col. Zacatenco, 07738 M ! e exico, D.F., Mexico SUMMARYThree imperfect repair strategies, derived from a discrete-time model of failure and repair, are implemented on items brand A (car, computer, washer, etc.), which are low quality with respect to equivalent items brand B (the leading brand in the market) in the sense that items brand A usually fail faster than items brand B do, in order to increase their lifetimes so that they have a chance to compete in durability against items brand B. The implementation of those strategies is performed by probabilistic simulations of the model. The effectiveness of these strategies is measured by comparing the expected 'output' lifetimes of items brand A under each strategy with respect to the expected lifetime of items brand B and the mean value of the total number of repair actions required on items brand A under one strategy with respect to the other two. The algorithm for designing a computer program for simulating those strategies is included. Some results concerning a relationship between a generalized memoryless property of geometric (exponential) distributions and the convolution property of probability (moment) generating functions are detected and also included.

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“…This is called the hazard rate (HR) of the distribution p [19]. Without further information, (1) is the best possible estimate of the job arrival probability.…”

Section: Estimating Arriving Loadmentioning

confidence: 99%

Exploiting per user information for supercomputing workload prediction requires care

Dinh

Andrew

Branch

2013

2013 13th IEEE/ACM International Symposium on Cluster, Cloud, and Grid Computing

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Abstract-Efficient management of supercomputing facilities requires estimates of future workload based on past user behaviour. For supercomputers with large numbers of users, aggregate user behaviour is commonly assumed to be best in prediction of future workloads, however for systems with smaller numbers of users the question arises as to whether it is still suitable or if benefits can be derived from monitoring individual user behaviour to predict future workload. We compare using individual user behaviour, aggregate user behaviour and a hybrid approach where we track heavy users individually and cluster aggregate light users into a small number of clusters. We find that the hybrid approach produces the best results in both mean absolute error and mean squared error. However, treating all users separately provides slightly worse predictions. We also introduce a new approach to prediction based on the hazard function which is a significant improvement on previously used schemes based on autoregressive models. The schemes are investigated numerically using a two-year workload trace from a supercomputer with a population of 136 users.

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Discrete hazard rate functions

Cited by 59 publications

References 9 publications

Some distributional results through past entropy

Some distributional results through past entropy

Three repair strategies

Exploiting per user information for supercomputing workload prediction requires care

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