• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.2
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• pp.41-47
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• 2006

The Renewal process and the Non-homogeneous Poisson process (NHPP) process are probably the most popular models for describing the failure pattern of repairable systems. But both these models are based on too restrictive assumptions on the effect of the repair action. For these reasons, several authors have recently proposed point process models which incorporate both renewal type behavior and time trend. One of these models is the Modulated Power Law Process (MPLP). The Modulated Power Law Process is a suitable model for describing the failure pattern of repairable systems when both renewal-type behavior and time trend are present. In this paper we propose Bayes estimation of the next failure time after the system has experienced some failures, that is, Mean Time Between Failure for the MPLP model. Numerical examples illustrate the estimation procedure.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.55-65
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• 2002

In this paper we present a Bayesian approach for determining an optimal maintenance policy following the expiration of warranty for a repairable system. We consider two types of warranty policies : non-renewing free replacement warranty (NFRW) and non-renewing pro-rata warranty (NPRW). The mathematical formula of the expected cost rate per unit time is obtained for NFRW and NPRW, respectively. When the failure time is Weibull distribution with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal maintenance policy. We illustrate the use of our approach with simulated data.

• Journal of Korean Society for Quality Management
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• v.25 no.3
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• pp.86-95
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• 1997

This paper considers a repairable system, which is maintained preventively at periodic times and is minimally repaired at each failure. Most preventive maintenance policies for such repairable systems assume that the cost of minimal repair is constant regardless of its age at failure. However, it is more practical to consider the situations where the cost of minimal repair is dependent not only on its age at failue, but also on the number of preventive maintenance carried out prior to its failure. We consider the preventive maintenance carried out prior to its failure. We consider the preventive maintenance policy with age-dependent minimal repair cost. The optimal policies which minimize the expected cost rate over an infinite time span are discussed. We obtain the optimal period and number of preventive maintenance prior to replacement of the system.

• International Journal of Quality Innovation
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• v.5 no.1
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• pp.1-9
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• 2004

The nonhomogeneous poisson process (NHPP) is often used to model repairable systems that are subject to a minimal repair strategy, with negligible repair times. In this situation, the system can be characterized by its intensity function. There have been many NHPP models according to intensity functions. However, the intensity function of system in use can be changed because of repair or its aging. We consider the single change point model as the modification of the power law process. The shape parameter of its intensity function is changed before and after the change point. We detect the presence of the change point using Bayesian methodology. Some numerical results are also presented.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.133-145
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• 1995

This paper is concerned with the method of estimating lifetime distribution from field data for repairable products with multiple modes of failure, and is an extension of Bai et al.(1995). The log linear function is considered as a model for describing the relation between failure time of a product and covariates. Using the nonhomogeneous poisson process, general methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and specific formulas for Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extension to case-cohort design is also considered.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.3
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• pp.81-90
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• 1993

This article concerns the problem of determining the optimal spare inventory level for multiechelon repairable-item inventory system. The system we are concerned has several bases and a central depot. When an item fails, it is dispatched to a repair facility and, a spare, if available, is plugged in immediately. When the failed item is repaired, it is sent to the base and either used to fill a backorder or stored at a spare inventory point. We develop an optimal algorithm to find the spare inventory level at each base spareswhich minimizes the total expected cost and, simultaneously, satisfies a specified minimum service rate. The algorithm is applied to examples with good results.

• Journal of Korean Society for Quality Management
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• v.29 no.2
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• pp.46-53
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• 2001

In this paper, a preventive maintenance(PM) policy for a repairable system is considered. The failure rate model proposed by Park et at.(2000) is generalized by assuming that after each PM not only the PM slows down the degradation process of the system but also reduces down the system failure rate by a certain fixed amount. Long-run expected cost rate of the PM policy is derived and the properties of joint solution of the optimal PM period and optimal number of PM which minimizes the expected cost rate are obtained. Numerical examples for the case of a Weibull-type failure rate are given.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.15-23
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• 1998

This paper concerns the problem of determining the spare inventory level for multi-echelon repairable-item inventory system with finite number of operating items. We consider the system which has several bases and a central depot. When an item fails, it is dispatched to a repair facility and, a spare, if available, is plugged in immediately. When the failed item is repaired, it is sent to the base and either is used to fill a backorder or is stored at a spare inventory point. Using queueing network, we develop an algorithm to find the spare inventory level which minimizes the total expected cost and, simultaneously, satisfies a specified minimum fill rate. The results of the algorithm clearly indicate that the algorithm successfully generate output with optimal solution.

• Journal of Applied Reliability
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• v.5 no.3
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• pp.373-379
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• 2005

In many cases, it is more practical and economical to repair a system than to replace the whole system or to perform a complete overhaul when the system fails. Two basic replacement policies were proposed by Barlow and Hunter(1960) and Morimura (1970), in which the minimal repair times are identically distributed. But, as Lam(1988) pointed out, in many cases of deteriorating system, in view of ageing and cumulative wear, the repair time will tend to be longer and longer. In this note, the two basic replacement policies are considered for a repairable system with linearly increasing repair times. Optimal policies, which maximize the steady state availability of the system, are obtained for the Weibull failure rate case.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.99-111
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• 2015

In this paper, we study the reliability analysis of a repairable system with two types of failure in which switching failures and reboot delay are considered. Let units in this system be cold standby, and failure rate and repair rate of [type1, type2] components be exponentially distributed. The expressions of reliability characteristics - such as the system reliability and the mean time to system failure MTTF - are derived. We use several cases to graphically analyze the effect of various system parameters on the system reliability and MTTF. We also perform a sensitivity analysis of the reliability characteristics with changes in specific values of the system's parameters.