2013
DOI: 10.4028/www.scientific.net/amr.837.116
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Estimation of Reliability Characteristics in a Production Scheduling Model with Failures and Time-Changing Parameters Described by Gamma and Exponential Distributions

Abstract: In the paper a classical model of failures is considered in that successive failure-free times are supposed to have Gamma distributions and are followed by exponentially distributed times of repairs. It is assumed that parameters of these distributions, in general, change with time. Basing on information about the number of failures and failure-free times in a number of periods of the same duration in the past, three different methods of estimation unknown parameters of the model are proposed. Next, prediction… Show more

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Cited by 25 publications
(25 citation statements)
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“…Examples using normal, exponential, triangular distributions to describe both failure and repair times are described in [28]. In the article [29], it is assumed that the parameters of distributions describing failure-free times, in general, change with time. Based on information about the number of failures and failure-free times in different periods of the same duration in the past, some methods for estimating unknown parameters for scheduling purposes can be proposed [30].…”
Section: Availability and Reliability Of Machinesmentioning
confidence: 99%
“…Examples using normal, exponential, triangular distributions to describe both failure and repair times are described in [28]. In the article [29], it is assumed that the parameters of distributions describing failure-free times, in general, change with time. Based on information about the number of failures and failure-free times in different periods of the same duration in the past, some methods for estimating unknown parameters for scheduling purposes can be proposed [30].…”
Section: Availability and Reliability Of Machinesmentioning
confidence: 99%
“…-b is estimated on the assumption that the probability of the failure-free time of the bottle_neck is less than b equalling 70% (Paprocka and Skołud 2013 (Paprocka and Kempa 2012;Skołud et al 2011;Kempa et al 2014). The MIDOS is computed if the operation can be executed on the bottleneck which is a parallel machine.…”
Section: Predictive Scheduling Methodsmentioning
confidence: 99%
“…The MTTR and the MTTF/MTTFF are described using probability density functions. Parameters of the functions are estimated using the Empirical Moments approach, the Renewal Theory based approach and the Maximum Likelihood approach (Skołud et al 2011;Kempa et al 2014). The mathematical description of the production model is presented by Paprocka and Kempa (2012).…”
Section: Problem Formulationmentioning
confidence: 99%
“…The examples of using normal, exponential, triangular distributions to describe both failure and repair times are described in [4]. In the article [5], it is assumed that parameters of distributions describing failure-free times, in general, change with time. Basing on information about the number of failures and failure-free times in a number of periods of the same duration in the past, some methods of estimation unknown parameters for scheduling purpose can be proposed [6].…”
Section: A Availability and Failuresmentioning
confidence: 99%
“…(5) In the case of repairable objects the parameters MTBF (mean time between failures), and the MTTR (mean time to repair) are used.…”
Section: A Availability and Failuresmentioning
confidence: 99%