A discrete semi-Markov decision model to determine the optimal repair/replacement policy under general repairs

Love, C. E.; Zhang, Zhe George; Zitron, M.A.; Guo, R.

doi:10.1016/s0377-2217(99)00009-0

Cited by 66 publications

(37 citation statements)

References 8 publications

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“…At first glance, it appears that productive systems are subject to deterioration because of several factors, including usage, wear, aging, and so forth. Some authors have dealt with this matter, for example, Love et al (2000) proposed that the failure rate depends on the age of the machine, and so they used that age to determine repair activities that reset the failure rate of the system. In the same direction, Dehayem et al (2011) suggested that the deterioration of the machine is denoted by its age and number of failures, and the effect of deterioration is reflected at increasing several transitions rates.…”

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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“…With the aim to determine the optimal joint control policy, i.e., the optimal value of the production rate, and the optimal repair/major maintenance scheduling, we use a numerical technique called Kushner´s approach to solve the HJB Equation (16). Such technique was proposed by Kushner and Dupuis [19] and Gharbi et al [20], and the idea behind this procedure is to approximate the value function v(α, x, a) by a discrete function v h (α, x, a), and the first-order partial derivatives of the value function ∂v(·)/∂x and ∂v(·)/∂a are approximated by:…”

Section: Optimization Methods Descriptionmentioning

confidence: 99%

“…Furthermore, bearing in mind that the deterioration process also has an effect on the reliability of the machine, in particular in its failure rate λ 12 (·). Then the lifetime distribution of a new machine follows an increasing function, as in Love et al [16]:…”

Section: Problem Formulationmentioning

confidence: 99%

Production and Maintenance Planning for a Deteriorating System with Operation-Dependent Defectives

et al. 2018

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This paper provides new insights to the area of sustainable manufacturing systems at analyzing the novel paradigm of integrated production logistics, quality, and maintenance design. For this purpose, we investigate the optimal production and repair/major maintenance switching strategy of an unreliable deteriorating manufacturing system. The effects of the deterioration process are mainly observed on the failure intensity and on the quality of the parts produced, where the rate of defectives depends on the production rate. When unplanned failures occur, either a minimal repair or a major maintenance could be conducted. The integration of availability and quality deterioration led us to propose a new stochastic dynamic programming model where optimality conditions are derived through the Hamilton-Jacobi-Bellman equations. The model defined the joint production and repair/major maintenance switching strategies minimizing the total cost over an infinite planning horizon. In the results, the influence of the deterioration process were evident in both the production and maintenances control parameters. A numerical example and an extensive sensitivity analysis were conducted to illustrate the usefulness of the results. Finally, the proposed control policy was compared with alternative strategies based on common assumptions of the literature in order to illustrate its efficiency.

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“…For example, in the series of works presented by Love et al (1998Love et al ( , 2000, it is considered that at failure, the machine may undergo a repair that partially resets its failure intensity, or be put through a second option, which is to conduct a major repair that restores the machine to an as-good-as-new condition. This model was extended by Dehayem et al (2011a), who included production planning in the repair/replacement problem.…”

Section: Introductionmentioning

confidence: 99%

Production and quality control policies for deteriorating manufacturing system

Rivera-Gómez¹,

Gharbi²,

Kenné³

2013

International Journal of Production Research

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In this paper, a novel model for a deteriorating manufacturing system is analyzed, considering repairs and overhauls of random durations. The machine manufactures one product and the model is further complicated because the quality of the parts' produced deteriorates according to the wear of the machine and human interventions. When a breakdown occurs, either a repair or an overhaul is performed. The machine is restored to as-good-as-new conditions if the overhaul is selected, and conversely, its condition deteriorates following repairs. Multiple operational states are considered to define an aging process. The decision variables of the model are the production rate and the repair/overhaul switching strategy. This paper provides new insights to this research area by considering the simultaneous production and repair/overhaul control policy under the effect of deteriorations. The optimal decision policy minimizes the total incurred cost comprising the inventory, backlog, repair and overhaul costs over an infinite planning horizon. Our paper differs from other research projects in its consideration of the machine's history, defined by the number of repairs and multiple operational states. A numerical example is given to illustrate the proposed approach and a sensitivity analysis has been conducted to confirm the structure of the obtained control policies.

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A discrete semi-Markov decision model to determine the optimal repair/replacement policy under general repairs

Cited by 66 publications

References 8 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

Production and Maintenance Planning for a Deteriorating System with Operation-Dependent Defectives

Production and quality control policies for deteriorating manufacturing system

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