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Maintenance cost minimization of manufacturing systems using PSO under reliability constraint

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Abstract

Profit is a main objective of production units, and minimization of its maintenance cost will help to achieve it. But with no compromise with plant machinery reliability constraints. Manufacturing systems do require maintenance, but deferring it due to production constraints may increase its requirements, resulting in the increased cost. The experience shows that carrying out of the preventive maintenance (PM) helps in avoidance of catastrophic failures, but this needs to be optimized. An optimal PM interval will minimize maintenance cost, while maintaining their lower bound reliability. Most existing optimization models do not address this issue especially in the context of real life industries. Particle swarm optimization is an effective meta-heuristic technique and is extensively applied to find optimal solution for various engineering problems. In this paper, this is proposed for maintenance cost minimization of manufacturing systems under reliability constraint. An example is illustrated to demonstrate it.

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Abbreviations

\({\text{a}}_{\text{m}}^{\text{i}}\) :

mth assembly of ith subsystem

C1, C2 :

Learning factors, i.e., cognitive and social constants of PSO

\({\text{C}}_{{{\text{AM}}_{{{\text{k}}^{\text{mi}} }} }}\) :

Average cost of major PM of kth component of mth assembly in ith subsystem

\({\text{C}}_{{{\text{AM}}_{{{\text{m}}^{\text{i}} }} }}\) :

Average cost of major PM of mth assembly in ith subsystem

\({\text{C}}_{{{\text{FM}}_{{^{\text{i}} }} }}\) :

Fixed cost of minimal PM for all assemblies of hydraulic subsystem of NC crankshaft balancing machine

\({\text{C}}_{{{\text{FM}}_{{{\text{m}}^{\text{i}} }} }}\) :

Fixed cost of minimal PM for all components of mth assembly in ith subsystem

\({\text{C}}_{{{\text{FRPL}}_{{{\text{k}}^{\text{mi}} }} }}\) :

Cost of failure–repair and production loss of kth component of mth assembly in ith subsystem

\({\text{C}}_{{{\text{FRPL}}_{{{\text{m}}^{\text{i}} }} }}\) :

Cost of failure–repair and production loss of mth assembly in ith subsystem

\({\text{C}}_{{{\text{RP}}_{{{\text{k}}^{\text{mi}} }} }}\) :

Cost of reduced production due to poor/irregular maintenance of kth component of mth assembly in ith subsystem

\({\text{C}}_{{{\text{RP}}_{{{\text{m}}^{\text{i}} }} }}\) :

Cost of reduced production due to poor/irregular maintenance of mth assembly in ith subsystem

\({\text{C}}_{{{\text{QD}}_{{{\text{k}}^{\text{mi}} }} }}\) :

Cost of product quality-deterioration due to poor/irregular maintenance of kth component of mth assembly in ith subsystem

\({\text{C}}_{{{\text{QD}}_{{{\text{m}}^{\text{i}} }} }}\) :

Cost of product quality-deterioration due to poor/irregular maintenance of mth assembly in ith subsystem

CMCC :

Total maintenance cost of the components of a manufacturing system

CMCHS :

Total maintenance cost of the assemblies of crankshaft balancing machine

\({\text{c}}_{\text{k}}^{\text{im}}\) :

kth component of mth assembly in ith subsystem

\({\text{F}}_{{{\text{k}}^{\text{mi}} }} \, ( {\text{T}}_{\text{PMC}} )\) :

Maximum allowable failure probability of kth component of mth assembly in ith subsystem

\({\text{F}}_{{{\text{m}}^{\text{i}} }} \,\left( {{\text{T}}_{\text{PMAHS}} } \right)\) :

Maximum allowable failure probability of mth assembly in ith subsystem

\({\text{g}}_{\text{best}}^{ ( {\hat{\text{n}})}}\) :

Global best position in iteration ‘\({\hat{n}}\)’ of PSO

\({\text{g}}_{\text{best}}^{{ ( {\hat{n}} - 1 )}}\) :

Global best position of the ĩth particle in iteration, ‘\({\hat{\text{n}}} - 1\)’

itermax :

Maximum number of iteration

n:

Number of PM actions

\(( {\hat{\text{n}}} - 1 )\), \(\hat{\text{n}}\), \((\hat{\text{n}} + 1)\) :

Previous, current, following iterations in PSO

\(\dot{\text{p}}_{{\tilde{\text{i}}}}\) :

Position of ĩth particle

\(\dot{\text{p}}_{{\tilde{\text{i}}}}^{{ ( {\hat{\text{n}}} + 1 )}}\) :

Updated position vector of the ĩth particle in iteration ‘\({\hat{n}} + 1\)’

\(\dot{\text{p}}_{{\tilde{\text{i}}}}^{{ ( {\hat{\text{n}}} - 1 )}}\) :

Position of particle ‘ĩ’ at the end of \(({\hat{n}} - 1){\text{th}}\) iteration

\(\dot{\text{p}}_{{{\text{best}}\tilde{\text{i}}}}^{{ ( {\hat{\text{n}}} - 1 )}}\) :

Best position of ĩth particle in iteration, ‘\(( {\hat{n}} - 1 )\)’

\(\dot{\text{p}}_{{{\text{best}}\tilde{\text{i}}}}^{{ ( {{\hat{\text{n}})}}}}\) :

Best position of ĩth particle in iteration, ‘\({\hat{n}}\)’

\(\dot{\text{p}}_{{\tilde{\text{i}}}}^{{ ( {{\hat{\text{n}})}}}}\) :

Position of ĩth particle in iteration ‘\({\hat{\text{n}}}\)’

\({\text{R}}_{{{\text{k}}^{\text{mi}} }} \,\left( {{\text{T}}_{\text{PMC}} } \right)\) :

Lower bound reliability of kth component of mth assembly in ith subsystem

\({\text{R}}_{{{\text{m}}^{\text{i}} }} \, ( {\text{T}}_{\text{PMAHS}} )\) :

Lower bound reliability of mth assembly in ith subsystem

rand1, rand2:

Random functions in updating particle velocity

S:

Manufacturing system

Si :

ith subsystem of manufacturing system, S

TPMC :

PM Interval for components of a manufacturing system

TPMAHS :

PM interval of assemblies of hydraulic subsystem of crankshaft balancing machine

\({\text{v}}_{{{\tilde{\text{i}}}}}\) :

Velocity of ĩth particle

\(\bar{\text{v}}_{{\tilde{\text{i}}}}^{{ ( {{\hat{\text{n}})}}}}\) :

Velocity of ĩth particle in iteration ‘\({\hat{n}}\)’

\(\bar{\text{v}}_{{\tilde{\text{i}}}}^{{ ( {\hat{\text{n}}} + 1 )}}\) :

Updated velocity of the ĩth particle in iteration, ‘\({\hat{n}} + 1\)’

W:

Inertial weight

Wmax, Wmin :

Initial and final inertial weight

\(\upbeta_{{{\text{k}}^{\text{mi}} }}\) :

Shape factor of Weibull distribution for kth component of mth assembly in ith subsystem

\(\upbeta_{{{\text{m}}^{\text{i}} }}\) :

Shape factor of Weibull distribution for mth assembly in ith subsystem

\(\uptheta_{{{\text{k}}^{\text{mi}} }}\) :

Scale factor of Weibull distribution for kth component of mth assembly in ith subsystem

\(\uptheta_{{{\text{m}}^{\text{i}} }}\) :

Scale factor of Weibull distribution for mth assembly in ith subsystem

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Acknowledgments

The authors would like to acknowledge various people, especially Binu NG of General Motors Group, John P of Cummins Group and Kundaram N of Mahindra Group companies for their contribution to the analysis reported in this paper.

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  1. ITMMEC, Indian Institute of Technology Delhi, New Delhi, India

    M. K. Loganathan & O. P. Gandhi

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  1. M. K. Loganathan
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Correspondence to M. K. Loganathan.

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Loganathan, M.K., Gandhi, O.P. Maintenance cost minimization of manufacturing systems using PSO under reliability constraint. Int J Syst Assur Eng Manag 7, 47–61 (2016). https://doi.org/10.1007/s13198-015-0374-2

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