(273g) Modeling for Reliability Optimization of System Design and Maintenance Based on Markov Chain Theory

Ye, Y., Carnegie Mellon University
Grossmann, I. E., Carnegie Mellon University
Pinto, J. M., Linde plc
Ramaswamy, S., Praxair, Inc.
Plant availability has always been a critical consideration for the design and operation of chemical processes as it represents the expected fraction of normal operating time, which impacts directly the ability of meeting customer demands. The failure of a key unit is likely to cause the shut-down of the entire plant. Effective ways to reduce the impact of equipment breakdown on the entire plant include installing back-up units and carrying out regular inspections and maintenance. Currently, discrete event simulation tools are used to evaluate the reliability/availability of selected alternatives to simulate the behavior of every asset in a plant using historical maintenance data and statistical models (Sharda and Bury, 2008). However, this approach does not systematically consider all the alternatives as it would be the case in an optimization approach.

A number of works have been reported to optimize the reliability of chemical plants. Pistikopoulos et al. (2001) and Goel et al. (2003b) formulate an MILP model for the selection of units with different reliability and the corresponding production and maintenance planning for a fixed system configuration. Terrazas-Moreno et al. (2010) formulate an MILP model using Markov chains to optimize the expected stochastic flexibility of an integrated production site by the selection of pre-specified alternative plants and the design of intermediate storage. Lin et al. (2012) model a simple utility system using Markov chain and carry out RAM (reliability, availability & maintainability) analysis iteratively to decide the optimal reliability design.

While mixed-integer optimization models have been proposed to address the reliability problem from various aspects, there are virtually no systematic modeling approaches proposed to make decisions regarding the number and selection of parallel units, as well as maintenance policy for the optimal profitability of reliable chemical processes. In response to this gap, this work extends our recent mixed-integer framework (Ye et al., in press) and introduces a systematic approach to model the stochastic process of system failures and repairs as a continuous-time Markov chain.

Two decision levels are considered to increase the availability of the system. The first decision level is to install parallel units for certain processing stages, such that when the primary unit fails, the other units can fill in its place in order to reduce system downtime. The second decision level is to carry out periodic inspections, and conditional maintenance if the inspection result indicates that the equipment will fail shortly. By that strategy the system can avoid a number of repairs, which are more costly than maintenances in terms of both time and money. Thus, there are two types of trade-offs in the model. The first type is the trade-off between the costs incurred and the revenue gained from increasing system availability. The second type is the budget balance between the two decision levels and among the processing stages. A non-convex MINLP model based on Markov chain assumption is proposed accordingly. It is worth mentioning that when inspections and conditional maintenance are not considered, the model reduces to an MILP, and a small superstructure with two stages is solved directly with global optimization solvers to show that improved system availability and net profit can be obtained compared to the case when disregarding maintenance, although at the expense of longer computing time.

However, the size of the non-convex MINLP model grows geometrically with the number of processing stages in the system. In addition, the combination of the two decision levels creates a large number of bilinear and multilinear terms. In order to overcome these computational difficulties and make the model applicable to practical problems, a decomposition scheme is proposed to reduce the model complexity. Moreover, scenario reduction, i. e., preprocess the scenarios and eliminate those with consistently low probabilities, is also applied to reduce the size of the model. The non-convex MINLP model with the specialized solution methods is applied to the two-stage problem and reaches global optimum in significantly shorter time than the global solvers. It is then used to solve larger examples that are not directly solvable and is able to obtained solutions in acceptable time.


Pistikopoulos, E. N., Vassiliadis, C. G., Arvela, J., and Papageorgiou, L. G. (2001). Interactions of maintenance and production planning for multipurpose process plants a system effectiveness approach. Industrial & engineering chemistry research, 40(14):3195-3207.

Goel, H. D., Grievink, J., and Weijnen, M. P. (2003b). Integrated optimal reliable design, production, and maintenance planning for multipurpose process plants. Computers & chemical engineering, 27(11):1543-1555.

Sharda, B. and Bury, S. J. (2008). A discrete event simulation model for reliability modeling of a chemical plant. In Proceedings of the 40th Conference on Winter Simulation, pages 1736-1740. Winter Simulation Conference.

Terrazas-Moreno, S., Grossmann, I. E., Wassick, J. M., and Bury, S. J. (2010). Optimal design of reliable integrated chemical production sites. Computers & Chemical Engineering, 34(12):1919-1936.

Lin, Z., Zheng, Z., Smith, R., and Yin, Q. (2012). Reliability issues in the design and optimization of process utility systems. Theoretical Foundations of Chemical Engineering, 46(6):747-754.

Ye, Y., Grossmann, I. E., Pinto, J. M., (in press). Mixed-integer nonlinear programming models for optimal design of reliable chemical plants. Computers & chemical engineering, doi: 10.1016/j.compchemeng.2017.08.013.