Maintenance modeling and operation parameters optimization for complex production line under reliability constraints

  • Hongming Zhou
  • Sufen Wang
  • Faqun QiEmail author
  • Shun Gao
S.I.: Reliability Modeling with Applications Based on Big Data


An optimal preventive maintenance policy and optimization method of operation parameters for a production line consisting of multiple execution units is described herein. According to the characteristics of the production unit, the relationship between the reliability and operating parameters of the execution unit is established, as well as its relationship between the operating parameters and maintenance cost. The minimum maintenance cost and effective operating speed is selected as the objective, and the optimal parameters are derived by heuristic algorithm. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the proposed method.


Preventive maintenance Reliability constraints Bi-objective optimization Maintenance costs Complex production line 

List of symbols

\( U_{i} \)

The execution unit (where \( i = 1, \ldots , n \))

\( {\text{A}} \)

Minor repair

\( {\text{B}} \)

Preventive maintenance



\( T_{MA} \)

The repair time of minor repair

\( T_{MB} \)

The repair time of preventive maintenance

\( T_{MC} \)

The repair time of replacement

\( T_{order} \)

The order cycle

\( T_{j} \)

Maintenance cycle (where \( j = 1, \ldots , m \))

\( T_{P\left( j \right)} \)

The working period (where \( j = 1, \ldots , m \))

\( T_{M\left( j \right)} \)

The maintenance period (where \( j = 1, \ldots , m \))

\( R\left( t \right) \)

The system reliability

\( R_{{\left( {i,j + 1} \right)}}^{ + } \)

The system reliability of the initial value (where \( i = 1, \ldots , n \), \( j = 1, \ldots , m \))

\( N_{A} \)

The number of minor repair

\( N_{B} \)

The number of preventive maintenance

\( N_{C} \)

The number of replacement

\( N_{R} \)

The execution unit is replaced by new one when \( N_{B} \) is reached \( N_{R} \)

\( R_{B} \)

The reliability threshold for the execution unit to be moved to have preventive maintenance

\( v \)

The operating speed of the execution unit

\( \theta \)

The age-return factor

\( ME_{i} \)

The maintenance cost of the execution unit \( U_{i} \)

\( ME \)

The maintenance cost of the production line

\( V_{R} \)

The effective speed of the production line

\( W_{i} \left( t \right) \)

The wear and tear amount of the execution unit \( U_{i} \)

\( u \)

The wear and tear amount rate of the executive unit \( U_{i} \)

\( k_{i} \)

The factor of wear amount

\( p \)

The pressure in the unit area of the friction surface

\( v_{l} \)

The relative sliding speed of the friction surface

\( \alpha \)

The factor of friction

\( \beta \)

The factor of speed factor

\( l \)

The relative sliding distance

\( t_{l} \)

The time for the component to operating once

\( \overline{p} \)

The mean of \( p \)

\( s_{p} \)

The standard deviation of \( p \)

\( \overline{v} \)

The mean of \( v \)

\( s_{v} \)

The standard deviation of \( v \)

\( \overline{{W_{i} \left( t \right)}} \)

The mean of the wear and tear amount

\( S_{W} \)

The standard deviation of the wear and tear amount

\( W_{max} \)

The maximum allowable the wear and tear amount

\( {{\upsigma }} \)

The standard deviation

\( M_{A} \)

The cost of a minor repair

\( M_{B} \)

The cost of preventive maintenance

\( M_{C} \)

The cost of replacement

\( M_{D} \)

The downtime loss for a single maintenance

\( G\left( t \right) \)

The total optimization objective function



This work was supported by the National Natural Science Foundation of China (71271156) and the Natural Science Foundation of Zhejiang Province (LY19G010007).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Wenzhou UniversityWenzhouChina

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