• International Journal of Reliability and Applications
• /
• v.4 no.1
• /
• pp.27-40
• /
• 2003

Maintenance models involving minimal imperfect repair frequently appear in the literature of reliability and operations research. Most of the literatures concerning the stochastic behavior of repairable systems assume that it takes negligible time to repair a failed system and so the length of repair time does not affect the maintenance strategy. It is more realistic to consider the length of repair times in developing maintenance model, however. In this paper, we consider an imperfect repair model with random repair time and investigate some stochastic properties of the number of perfect repairs and the number of minimal repairs. Also we derive the expressions for evaluating the expected numbers of perfect and minimal repairs in general and apply these formulas for certain parametric life distributions.

• Journal of the Korean Statistical Society
• /
• v.28 no.3
• /
• pp.389-398
• /
• 1999

We consider an imperfect repair model under which either a perfect repair or a minimal repair can be performed at each failure of a unit. Some stochastic properties of the number of perfect repairs and the number of minimal repairs under the imperfect repair model are investigated. We also derive the expressions for evaluating the expected numbers of perfect and minimal repairs in general and apply these formulas for certain parametric families of life distributions.

• Journal of Korean Institute of Industrial Engineers
• /
• v.39 no.4
• /
• pp.233-238
• /
• 2013

This article concerns a profit model in a repair limit replacement problem with imperfect repair. If a system fails, we should decide whether we repair the failed system (repair option) or replace it by new one (replacement option with a lead time). We assume that repair times are random variables and can be estimated before repair with estimation error. If the estimated repair time is less than the specified limit (repair time limit), the failed unit is repaired but the unit after repair is different from the new one (imperfect repair). Otherwise, we order a new unit to replace the failed unit. The long run average profit (expected profit rate) is used as an optimization criterion and the optimal repair time limit maximizes the expected profit rate. Some special cases are derived.

• International Journal of Reliability and Applications
• /
• v.15 no.1
• /
• pp.51-64
• /
• 2014

This paper develops a warranty cost model for complex systems with imperfect repair within a warranty period by addressing a practical case that the first inter-failure interval is longer than any other inter-failure intervals. The product is in its best condition before the first failure if repair is imperfect. After the imperfect repair, other inter-failure intervals which are explained by renewal processes, are stochastically smaller than the first inter-failure interval. Based on this idea, we suggest the failure-interval-failure-criterion model. In this model, we consider two random variables, X and Y where X represents failure intervals and Y represents failure criterion. We also obtain the distribution of the number of failures and conduct the warranty cost analysis. We investigate different types of warranty cost models, reliabilities and other measures for various systems including series-parallel configurations. Several numerical examples are discussed to demonstrate the applicability of the methodologies derived in the paper.

• Proceedings of the Korean Reliability Society Conference
• /
• 2001.06a
• /
• pp.301-310
• /
• 2001

Lim et al.(1998) proposed the Bayesian Imperfect Repair Model, in which a failed system is perfectly repaired with probability P and is minimally repaired with probability 1 - P, where P is not fixed but a random variable with a prior distribution II(p). In this note, the steady state availability of the model is derived and the measure is obtained for several particular prior distribution functions.

• 한국데이터정보과학회:학술대회논문집
• /
• 2001.10a
• /
• pp.43-43
• /
• 2001

• Communications for Statistical Applications and Methods
• /
• v.8 no.3
• /
• pp.711-717
• /
• 2001

Two imperfect repair models for system are considered, one introduced by Brown and Proschan(1983) and the other by Lee and Seoh(1999). We, in this paper, after assigning repair costs to the system, optimize both repair models, when the underlying life distributions of the system are exponential, uniform and Weibull.

• International Journal of Reliability and Applications
• /
• v.14 no.1
• /
• pp.41-54
• /
• 2013

In this paper, cost analysis is conducted using inter-failure interval under renewable warranty subject to imperfect repair for multi-component system. One way to model the imperfect repair is to use the quasi-renewal process (Wang and Pham 1996). Two alternative quasi-renewal processes were suggested by Park and Pham (2010) using quasi-renewal process; first is an altered quasi-renewal process with random variable parameter and second is a mixed quasi-renewal process considering replacement service and repair service, simultaneously. In this study, we use the altered and mixed quasi-renewal processes and develop the warranty cost model to obtain the expected value of warranty cost and to help company make important decisions regarding the warranty policy. Numerical examples are used to demonstrate the applicability of the methodology derived in the paper.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.23 no.4
• /
• pp.111-130
• /
• 1998

We propose an imperfect repair model which depends on external effects quantified by covariates. The model is based on the Brown-Proschan imperfect repair model wherefrom the probability of perfect repair is represented by a function of covariates. We are motivated by deficiency of the BP model whose stationarity prevents us from predicting dynamically the time to next failure according to external condition. Five types of function for the probability of perfect repair are proposed. This article also presents a procedure for estimating the parameter of the function for the probability of perfect repair, as well as the inherent lifetime distribution of the system, based on consecutive inter-failure times and the covariates. The estimation procedure is based on the expectation-maximization principle which is suitable to incomplete data problems. focusing on the maximization step, we derive some theorems which guarantee the existence of the solution. A Monte Carlo study is also performed to illustrate the prediction power of the model as well as to show reasonable properties of the estimates. The model reduces significantly the mean square error of the in-sample prediction. so it can be utilized in real fields for evaluating and maintaining repairable systems.

• Journal of the Korean Statistical Society
• /
• v.30 no.1
• /
• pp.89-98
• /
• 2001

Brown and Proschan(1983) introduced a model for imperfect repair. At each failure of a device, with probability p, it is repaired completely or replaced with a new device(perfect repair), and with probability 1-p, it is returned to the functioning state, but it is only recovered to its condition just prior to failure(imperfect repair or minimal repair). In this paper, we limit the number of consecutive minimal repairs by n. We find some useful properties about $\mu$$_{k}$, the expected time between the k-th and the (k+1)-st repair under he assumption that only minimal repairs are performed. Then, we assign cost to each repair and find the value of n which minimized the long-run average cost for a fixed p under the condition that the life distribution F os the device is DMRL.L.