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An integrated strategy for efficient business plan and maintenance plan for systems with a dynamic failure distribution

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Abstract

The purpose of this study is to propose an integrated strategy to determine jointly efficient business and maintenance plans. The studied system is subject to random failures with a dynamic failure law. It must perform a set of missions (among M possible missions) over a finite planning horizon. Each mission may have different characteristics that depend on operational and environmental conditions. The determination of a business plan consists in choosing and scheduling the missions to be performed. To maximize the net profit (profits generated by the achievement of missions minus maintenance costs), two meta-heuristics based on genetic algorithms are developed. The first genetic algorithm is used to determine the business plan and the second one generates an efficient maintenance plan. Two maintenance policies are studied: a minimalist policy which involves only corrective maintenance actions and another policy, called sequential, which involves several imperfect preventive maintenance activities performed at predetermined times. Two cases are studied for the latter strategy. The first one considers the maintenance effectiveness factor as being the same for all preventive maintenance actions and we search for the best factor. In the second case, we consider maintenance actions with different efficiency factors and we look for the optimal value of each factor. Finally, a numerical example illustrates the proposed approach and the difference between the maintenance policies.

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Abbreviations

\({\delta_{x_m}}\) :

Duration of mission x m

\({\sigma_{x_m}\left(n \right)}\) :

Duration of mission x m in the preventive maintenance interval n

\({\psi_{x_m}}\) :

Profit of mission m

Z xm :

Vector of the conditions under which mission x m takes place

\({g\left({Z_{x_m}}\right)}\) :

Risk function of mission x m

B:

Vector of weights associated to the conditions of mission x m

λ0 (t):

System’s hazard rate for nominal conditions

\({\lambda_{x_m}\left(t \right)}\) :

System’s hazard rate representing the instantaneous failure rate at t under the conditions of the mission x m

H :

Available time for the business plan i.e. the planning horizon

M = {1, 2, . . . M}:

Set of M proposed missions

X = {x 1, x 2, . . . x k }:

Vector of k variables x j characterizing the business plan

\({x_j \left({\in M}\right)}\) :

Variable indicating the jth mission to achieve in the business plan

P:

Vector of variables \({\rho_j\;\left({j=1,\ldots ,\dim \left(\fancyscript{N}\right)-1}\right)}\)

\({\rho_j \in]0,\ldots, 1[:}\) :

Factor representing the maintence effectiveness for the j th preventive maintenance action

ρ max :

the maximum maintenance effectiveness factor

ρ inc :

the step increment of the maintenance effectiveness factor

N:

Vector of preventive maintenance intervals

Δ j :

Duration of the jth preventive maintenance interval (j = 1, . . . , dim (N))

s(n):

First mission of the interval n

e(n):

Last mission of the interval n

\({\tau_{x_{i-1}}}\) :

Virtual age associated to the mission x i

dim (·):

Dimension of the vector (·)

M C :

Corrective maintenance action cost

M P (ρ):

Preventive maintenance action cost corresponding to effectiveness factor ρ

\({M_P^f}\) :

Preventive maintenance action fixed cost

\({M_P^v}\) :

Preventive maintenance action variable cost

μ P (ρ):

Preventive maintenance action duration corresponding to effectiveness factor ρ

\({\mu_P^f}\) :

Preventive maintenance action fixed duration

\({\mu_P^v}\) :

Preventive maintenance action variable duration

\({\Gamma_{Min}\left({\chi,\fancyscript{N},{P}}\right)}\) :

Total cost of maintenance activities under the minimalist policy

\({\phi_{Min}\left({\chi,\fancyscript{N},{P}}\right)}\) :

Average number of failures under the minimalist policy

\({\Gamma_{Seq}\left({\chi,\fancyscript{N},{P}}\right)}\) :

Total cost of maintenance activities under the sequential policy

\({\phi_{Seq}\left({\chi,\fancyscript{N},{P}}\right)}\) :

Average number of failures under the sequential policy

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Authors and Affiliations

  1. LGIPM/COSTEAM-INRIA, University Paul Verlaine, Metz, France

    J. Schutz & N. Rezg

  2. PREDICT, Nancy, France

    J.-B. Léger

Authors
  1. J. Schutz
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  2. N. Rezg
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  3. J.-B. Léger
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Correspondence to J. Schutz.

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Schutz, J., Rezg, N. & Léger, JB. An integrated strategy for efficient business plan and maintenance plan for systems with a dynamic failure distribution. J Intell Manuf 24, 87–97 (2013). https://doi.org/10.1007/s10845-011-0543-3

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  • DOI: https://doi.org/10.1007/s10845-011-0543-3

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