Classes of imperfect repair models based on reduction of failure intensity or virtual age

Doyen, Laurent; Gaudoin, Olivier

doi:10.1016/s0951-8320(03)00173-x

Cited by 394 publications

(302 citation statements)

References 9 publications

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“…In regard to the preventive maintenance strategy, we state that it rejuvenates the age of the machine of an amount proportional to its age before preventive maintenance, in line with the so-called Arithmetic Reduction of Age (ARA) presented in Doyen and Gaudoin (2004). Hence, we propose the following expression to model the benefit of preventive maintenance:…”

Section: Deterioration Modelingmentioning

confidence: 99%

Joint control of production, overhaul, and preventive maintenance for a production system subject to quality and reliability deteriorations

Rivera-Gómez

Gharbi

Kenné

2013

Int J Adv Manuf Technol

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This research investigates the case of an unreliable manufacturing system subject to quality and reliability deterioration. In particular, we conjecture that the deterioration of the system leads to a continuous increase in the intensity of failures and a decrease on the quality of the parts produced. As such, deterioration implies a twofold effect on the manufacturing system. When the machine fails, minimal repair is conducted, leaving the machine at the same level of deterioration before failure. Hence, the quality of the parts produced and the failure intensity remain unchanged with this repair. Meanwhile, an overhaul refers to a perfect repair that completely restores the quality of the parts and the failure intensity of the machine. This option completely counters all the effects of the deterioration. Preventive maintenance may also be conducted, but it reduces the level of deterioration only partially, improving the quality of the units produced and the failure intensity just in part. These set of characteristics yield to the formulation of a new control model that simultaneously determines the optimal production plan, the overhaul and preventive maintenance strategies. Such a joint control policy minimizes the total cost including the inventory holding, backlog, overhaul, preventive maintenance and defectives costs over an infinite planning horizon. Since the dynamics of the system change as a function of the level of deterioration, it is necessary to use its history for a proper formulation; therefore a Semi-Markov decision process is used. Numerical methods are applied to determine the control policy and numerical examples are conducted as illustrations. An extensive sensitivity analysis is presented in order to confirm the structure of the control policy obtained and examine the effect of several parameters.

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Section: Deterioration Modelingmentioning

confidence: 99%

Joint control of production, overhaul, and preventive maintenance for a production system subject to quality and reliability deteriorations

Rivera-Gómez

Gharbi

Kenné

2013

Int J Adv Manuf Technol

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“…Many models, including the geometric process (GP) and its variants (Lam, 1988;Wang & Pham, 1996;Wu & Clements-Croome, 2006), the generalised renewal process models (GRP) (Kijima & Sumita, 1986;Kijima, 1989;Doyen & Gaudoin, 2004), and the reduction of failure hazard models (Doyen & Gaudoin, 2004), have been developed for modelling imperfect repair. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 The particular models themselves are defined as follows.…”

Section: Definitionsmentioning

confidence: 99%

“…There exist many papers that attempt to develop statistical models for characterising the failure process of a system (see, Duane, 1964;Cox & Lewis, 1966;Lam, 1988;Kijima & Sumita, 1986;Baxter, Kijima, & Tortorella, 1996;Dorado, Hollander, & Sethuraman, 1997;Doyen & Gaudoin, 2004;Wu & Zuo, 2010;Doyen & Gaudoin, 2011, for example). However, much of this existing research assumes that the systems are equivalent to one-component systems.…”

Section: Introductionmentioning

confidence: 99%

Two new stochastic models of the failure process of a series system

Scarf

2017

European Journal of Operational Research

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Consider a series system consisting of sockets into each of which a component is inserted: if a component fails, it is replaced with a new identical one immediately and system operation resumes. An interesting question is: how to model the failure process of the system as a whole when the lifetime distribution of each component is unknown? This paper attempts to answer this question by developing two new models, for the cases of a specified and an unspecified number of sockets, respectively. It introduces the concept of a virtual component, and in this sense, we suppose that the effect of repair corresponds to replacement of the most reliable component in the system. It then discusses the probabilistic properties of the models and methods for parameter estimation. Based on six datasets of artificially generated system failures and a real-world dataset, the paper compares the performance of the proposed models with four other commonly used models: the renewal process, the geometric process, Kijima's generalised renewal process, and the power law process. The results show that the proposed models outperform these comparators on the datasets, based on the Akaike information criterion.Our responses are shown below, taking the reviewer comments one by one.In the revised paper, new text is coloured blue, deletions are indicated, and text we wish to emphasise to address a review comment is coloured red.Reviewer #1: This revised version significantly improves the first paper. I have still some comments that should be taken into account before acceptation.1. Throughout the paper, the components of the series systems are supposed to be independent. This assumption should be stated clearly. Response: We now state this clearly at the beginning of Proposition 1. Also, please note that the first sentence immediately under the heading of Section 2 says: "Consider a series system with a number of statistically independent components." (See the sentence in red on page 6).2. Answer to my comment 9. The proof (d) of the additivity of the CRIF is not really a proof. The additivity comes from the facts that the counting process of system failures is the sum of the counting processes of components failures, and that the probability of having more than one failure in an infinitesimal interval is zero because of the independence of the components. See considerations of that kind in reference 1. Response: Yes, we agree, and we have rewritten the text in part (d) there on page 8. In addition, the sentence starting with "Alternatively, …" shortly after is introduced to outline the idea of the proof and is in response to comment 1 of reviewer 3.3. Answer to my comment 15. You say that the sentence "and the oldest VC in the VSS will be renewed" has been removed. But in fact, it is still in the paper. You should explain this part more clearly. The fact that one component in the VSS is renewed seems contradictory with the initial assumption that the VSS is not maintained or minimally repaired. Response: We agree the explanation was ...

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“…The age t(t) to be considered to evaluate the failure probability is the effective age of the unit. This effective age is different from the calendar working time of the unit and depends on its past and on the maintenance interventions it has undergone [9][10][11][12]. In particular, we consider that the different possible interventions affect this effective age by a rejuvenation factor, depending on the intervention type, as explicated below.…”

Section: Unit Modelmentioning

confidence: 99%

“…If e m ¼ 0, the maintenance is perfect (as good as new) and if e m ¼ 1 the maintenance has no effect (as bad as old). This model is equivalent to the model of Arithmetic Reduction of Age with infinite memory (ARA N , [11]) and to the Kijima II model, [12]. Before any intervention, the effective age of a unit is identical to the time spent since it was first operated (calendar time).…”

Section: Unit Modelmentioning

confidence: 99%

A Petri net-based modelling of replacement strategies under technological obsolescence

Clavareau

Labeau

2009

Reliability Engineering & System Safety

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a b s t r a c tThe technological obsolescence of a unit is characterised by the existence of challenger units displaying identical functionalities, but with higher performances. Though this issue is commonly encountered in practice, it has received little consideration in the literature. Previous exploratory works have treated the problem of replacing old-technology items by new ones, for identical components facing a unique new generation of items. This paper aims to define, in a realistic way, possible replacement policies when several types of challenger units are available and when the performances of these newly available units improve with time.Since no fully generic model can exist in maintenance optimisation, a modular modelling of the problem, allowing easy adaptations to features corresponding to specific applications is highly desirable. This work therefore proposes a modular Petri net model for this problem, underlying a Monte Carlo (MC) estimation of the costs incurred by the different possible replacement strategies under consideration.

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Classes of imperfect repair models based on reduction of failure intensity or virtual age

Cited by 394 publications

References 9 publications

Joint control of production, overhaul, and preventive maintenance for a production system subject to quality and reliability deteriorations

Joint control of production, overhaul, and preventive maintenance for a production system subject to quality and reliability deteriorations

Two new stochastic models of the failure process of a series system

A Petri net-based modelling of replacement strategies under technological obsolescence

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