A multi-stage stochastic programming for condition-based maintenance with proportional hazards model

Document Type: Research Paper


Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


Condition-Based Maintenance (CBM) optimization using Proportional Hazards Model (PHM) is a kind of maintenance optimization problem in which inspections of a system relevant to its failure rate depending on the age and value of covariates are performed in time intervals. The general approach for constructing a CBM based on PHM for a system is to minimize a long run average cost per unit of time as an objective function in which the model is considered for an infinite span of time.  In this paper, a CBM model is presented based on two types of maintenance actions (minimal repair and replacement) to determine control limits to cope with the class of real-life problems in which a system would be planned for a specified planning horizon. An effective multi-stage stochastic programming approach is used to come up with the minimum expected cost given the state scenarios of the system in periods over a planning horizon. An extensive computational study is presented to demonstrate the efficiency of the proposed model through numerical instances solved by a novel hybrid meta-heuristic algorithm. A sensitivity is also performed on cost parameters to designate the effects of minimal repair cost and replacement cost in the proposed model.


Main Subjects

Ahmad R., Kamarruddin S. (2012). An overview of time-based and condition-based maintenance in industrial application. Computers and Industrial Engineering, 63(1): 135-149.

Alaswad, S., Xiang, Y. (2017). A review on condition-based maintenance optimization models for stochastically deteriorating system. Reliability Engineering and System Safety, 157: 54-63.

Banjevic D., Jardine A.K.S, Makis V. (2001). A control limit policy and software for condition-based maintenance optimization. INFOR, 39:32-50.

Bansal D., Evans D.J., Jones B. (2004). A real-time predictive maintenance system for machine systems. International Journal of Machine Tools and manufacture, 44(7-8): 759-766.

Birge, J. R. Introduction to stochastic programming. (2010). New York, Second edition, Springer.

Box, G.E.P. and Wilson, K.B. (1951). On the experimental attainment of optimum conditions". Journal of the Royal Statistical Society Series B, 13: 1-38.

Caballéa N.C., Castro I.T., Pérezb C.J., Lanza-Gutiérrezc J.M. (2015). A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes. Reliability Engineering and System Safety, 134: 98-109.

Campos, J. (2009). Development in the application of ICT in condition monitoring and maintenance. Computers in Industry, 60(1): 1-20. 

Cox, D.R. (1972). Regression Models and Life-tables. Journal of the Royal Statistical Society, Series B (Methodological), 34(2): 187-220.

Fu C., Ye L., Liu Y., Yu R., Iung B., Cheng Y. (2004). Predictive maintenance in intelligent control-maintenance-management system for hydro electronic generating unit. IEEE Transactions on Energy Conversion, 19(1): 179-186.

Ghasemi A., Yacout S., Ouali M.S. (2007). Optimal condition based maintenance with imperfect information and the proportional hazards model. International Journal of Production Research, 45(4):989-1012.

Golmakani H.R., Fattahipour F. (2011). Optimal replacement policy and inspection interval for condition-based maintenance. International Journal of production Research. 49(17):5153-5167.

Golmakani H.R., Fattahipour F. (2011). Age-based inspection scheme for condition-based maintenance. Journal of Quality in Maintenance Engineering, 17(1):93-110.

Golmakani H.R., Pouresmaeeli M. (2014). Optimal replacement policy for condition-based maintenance with non-decreasing failure cost and costly inspection. Journal of Quality in Maintenance Engineering, 20(1): 51-64.

Jafari, L., Naderkhani, F., Makis, V. (2015). An optimal maintenance policy for a two-unit production system using a proportional hazards model. IFAC-PapersOnline. 48(3):2170-2175.

Jardine A.K.S, Lin D.M, Banjevic D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 20(7): 1483-1510.

Jonge, B., D., Teunter, R., Tinga, T. (2017). The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance. Reliability Engineering and System Safety, 158: 21-30. 

Kasier K.A., Gebraeel N.Z. (2009). Predictive maintenance management using sensor-based degradation models, IEEE Transactions on Systems Manufacturing and Cybernetics Part A-Systems and Humans, 39(4): 840-849.

Koc M, Lee J. (2001). A system framework for next-generation E-maintenance systems. Transaction of Chinese Mechanical Engineer, 12-18. doi: 10.1109/.2001.992398.

Lam J.Y.J., Banjevic D. (2015). A myopic policy for optimal inspection scheduling for condition based maintenance. Reliability Engineering and System Safety, 144: 1-11.

Majumder, A., Singh, A. and Goyal, A. (2009). Application of response surface methodology for glucan production from Leuconostoc dextranicum and its structural characterization. Carbohydrate Polymers, 75(1): 150-156.

Makis V., Jardine A.K.S. (1992). Optimal replacement in the proportional hazards model. INFOR, 30:172-183.

Mehrabian A.R., Lucas C. (2006). A novel numerical optimization algorithm inspired from weed colonization. Ecological Informatics, 1(4), 355-366.

Mousavi S.M., Shams H., Ahmadi, S. (2014). Simultaneous optimization of repair and control-limit policy in condition-based maintenance. Journal of Intellectual Manufacturing, 28(1): 245-254.

Naderkhani, F.Z.C., Malik, V. (2015). Optimal condition-based maintenance policy for a partially observable system with two sampling intervals. International Journal of Advanced Technology, 78(5):795-805.

Nakagawa, T. (2005). Maintenance theory of reliability. London, Springer.

Prajapati A., Bechtel J., Ganesan S. (2012). Condition based maintenance: a survey. Journal of Quality in Maintenance Engineering, 18(4): 384-400.

Sharma A., Yadava G.S. (2011). A literature review and future perspectives on maintenance optimization. Journal of Quality in Maintenance Engineering, 17(1): 5-25.

Shin J.H., Jun H.B. (2015). On condition based maintenance policy. Journal of Computational Design and Engineering, 2(2):119-127.

Tian Z., Liao H. (2011). Condition-based maintenance optimization for multi-component systems using proportional hazards model. Reliability Engineering and System Safety, 96(5): 581-589.

Tian Z., Lin D., Wu B. (2009). Condition-based maintenance optimization considering multiple objectives. Journal of Intelligent Manufacturing, 23(2): 333-340.

Tian Z., Lin D., Wu B. (2012). Condition-based maintenance optimization considering multi objectives. Journal of Intellectual Manufacturing, 23(20): 333-340.

Yan J., Koc M., Lee J. (2004). A prognostic algorithm for machine performance assessment and its application, Production Planning and Control, 15(8):796-801.