General Repair Process Research Articles

General Repair Models for Maintained Systems

Any system when put on operation deteriorates over a period of time and fails on crossing a threshold. Maintenance is performed either on failure or for mitigating the effects of this deterioration. In general the system is either partially maintained or renewed to bring it back to its operating state. The general behaviour of the failure process of a maintained system is modelled by means of stochastic processes called general repair processes. In these processes the effect of the maintenance carried out on the system is captured by means of a variable called the maintenance indicator which indicates the degree to which the system has been maintained. Such a maintenance indicator acting on the system’s failure age or intensity post maintenance generalizes the modelling of the failure processes. The general repair process models based on the type of the maintenance indicator can be broadly classified into two categories based on age or intensity loss or recovery and two sub-categories based on whether these take place additively or multiplicatively. This paper focuses on such models, their inference, their uses, the physical reality they depict and their shortcomings when modelling the failure processes of maintained systems. DOI: http://dx.doi.org/10.4038/sljastats.v12i0.4971 Sri Lankan Journal of Applied Statistics Vol.12 2011 pp.117-143

On Some Ageing Properties of General Repair Processes

We consider ageing properties of a general repair process. Under certain assumptions we prove that the expectation of an age at the beginning of the next cycle in this process is smaller than the initial age of the previous cycle. Using this reasoning, we show that the sequence of random ages at the start (end) of consecutive cycles is stochastically increasing and is converging to a limiting distribution. We discuss possible applications and interpretations of our results.

On Some Ageing Properties of General Repair Processes

We consider ageing properties of a general repair process. Under certain assumptions we prove that the expectation of an age at the beginning of the next cycle in this process is smaller than the initial age of the previous cycle. Using this reasoning, we show that the sequence of random ages at the start (end) of consecutive cycles is stochastically increasing and is converging to a limiting distribution. We discuss possible applications and interpretations of our results.

On Some Ageing Properties of General Repair Processes

We consider ageing properties of a general repair process. Under certain assumptions we prove that the expectation of an age at the beginning of the next cycle in this process is smaller than the initial age of the previous cycle. Using this reasoning, we show that the sequence of random ages at the start (end) of consecutive cycles is stochastically increasing and is converging to a limiting distribution. We discuss possible applications and interpretations of our results.

A simple recursive Markov chain model to determine the optimal replacement policies under general repairs

A repairable system (machine) is subject to failure. At each failure epoch, a general repair is performed. Such repairs return the system to a working condition somewhere between ‘good-as-new’ (a perfect repair) and ‘bad-as-old’ (a minimal repair). An important question for such systems is at what time should a major overhaul be conducted to return the unit to a ‘good-as-new’ state. Two policies are investigated in this research: (1) overhaul at fixed intervals and (2) overall at variable intervals by conducting each overhaul on the first failure following a predetermined time. We show in this research that both of these policies can be analyzed using a simple recursive Markov model thereby permitting the best of these policies to be identified in any particular situation. The Markov model is quite general, permitting a wide variety of structures to be investigated. Scope and purpose Considerable research has been conducted on the issue of periodic replacement times for failing systems. Typically in such analysis, each random failure is assumed to be repaired minimally and the replacement (or major overhaul) is assumed to refresh the failure intensity of the system. More recently, there has been recognition that repairs often serve to improve the system by partially resetting its failure intensity. Such a repair effect is known as a general (or an imperfect) repair. Previous research has extended well-known renewal functions into generalized renewal functions in order to estimate the impact of these general repair processes. In this paper we propose an alternative approach based on Markov chains which yields a simpler, more flexible model.

Some properties and computational results for a general repair process

We consider a general repair process where the virtual age Vi after the ith repair is given by Vi = ϕ(Vi−1 + Xi), ϕ(·) is a specified repair functional, and Xi is the time between the (i − 1)th and ith repair. Some monotonicity and dominance properties are derived, and an equilibrium process is considered. A computational method for evaluating the expected number/density of repairs is described together with an approximation method for obtaining some parameters of the equilibrium process. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 391–405, 1998

Some properties and computational results for a general repair process

Some properties and computational results for a general repair process

Renewal-type equations for a general repair process

We consider a component which undergoes instantaneous general repairs on failure. Suppose that V i = Φ(V i-l + Y i ), where V i is the virtual age immediately after the ith failure, Y i is the time between the (i - 1)th and ith failures, Φ(.) is a specified repair functional, and V 0 =s. We derive integral equations for the repair density, and also for the joint density of repairs with respect to chronological age and virtual age on failure. In the asymptotic case, approximations are obtained for the mean and variance of virtual age on failure, virtual age after repair, and time between failures. Two policies are then considered. The first, an upgraded repair strategy employs minimal repairs until the component reaches a specified age, thereafter repairs restore the virtual age to that prescribed level. The second policy considered is the Kijima Type 2 model which is not amenable to the usual g-renewal analysis that is used in the Type 1 model. The repair density is obtained by numerical solution of the relevant integral equation. Finally, approximations for the asymptotic moments are found to be in close agreement with simulated results.

Heteroduplex repair in extracts of human HeLa cells

A general repair process for DNA heteroduplexes has been detected in HeLa cell extracts. Using a variety of M13mp2 DNA substrates containing single-base mismatches and extra nucleotides, extensive repair is observed after incubation with HeLa cell cytoplasmic extracts and subsequent transfection of bacterial cells with the treated DNA. Most, but not all, mispairs as well as two frameshift heteroduplexes are repaired efficiently. Parallel measurements of repair in HeLa extracts and in Escherichia coli suggest that repair specificities are similar for the two systems. The presence of a nick in the molecule is required for efficient repair in HeLa cell extracts, and the strand containing the nick is the predominantly repaired strand. Mismatch-dependent DNA synthesis is observed when radiolabeled restriction fragments, produced by reaction of the extract with heteroduplex and homoduplex molecules, are compared. Specific labeling of fragments, representing a region of approximately 1,000 base pairs and containing the nick and the mismatch, is detected for the heteroduplex substrate but not the homoduplex. The repair reaction is complete after 20 min and requires added Mg2+, ATP, and an ATP-regenerating system, but not dNTPs, which are present at sufficient levels in the extract. An inhibitor of DNA polymerase beta, dideoxythimidine 5'-triphosphate, does not inhibit mismatch-specific DNA synthesis. Aphidicolin, an inhibitor of DNA polymerases alpha, delta, and epsilom, inhibits both semiconservative replication and repair synthesis in the extract. Butylphenyl-dGTP also inhibits both replicative and repair synthesis but at a concentration known to inhibit DNA polymerase alpha preferentially rather than delta or epsilon. This suggests that DNA polymerase alpha may function in mismatch repair.

Basic physiology of wound healing in the horse.

Wound healing is part of the normal general repair process of the body. Its efficient completion depends on many factors, some physical, eg, pH, oxygen tension and tissue tension, and some biological, eg, cell-cell interaction and feedback of extracellular matrix on to the cells which produce it. The factors which affect healing are discussed and failures and anomalies in the process described. New techniques which may improve the quality of healing in specialised tissues are explained. Recent research on wound healing has concentrated on the role of the different cell types in the process and also on the effects of micro-environment on the enhancement or inhibition of cellular activity. The wound is a situation in which cells are apparently operating at the limits of their powers of survival and very slight modification of the micro-environment can render the tissue either unduly hostile to the cell or can enhance cellular activity. While it is not possible to increase the rate of healing of a clean surgical wound to any useful degree, an understanding of the mechanics of wound healing is essential to a rational treatment of simple or indolent wounds. It is especially important that surgical or medical treatment should complement, rather than compete with, the natural process. Tight bandages, which compress circulation, or excessive washing, which may remove macrophages and dilute bacteriostatic or chemotaxic agents, should be avoided.