ORIGINAL ARTICLE An algorithm for performance evaluation of resilience engineering culture based on graph theory and matrix approach Masoud Rabbani 1 • Reza Yazdanparast 1 • Mahdi Mobini 2 Received: 11 November 2017 / Revised: 14 October 2018 Ó The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019 Abstract While strengths can be improved, when weak- nesses are not addressed, the desired improvements are not achievable. Determining weaknesses and strengths is much more important when it comes to safety issues in critical industrial units. Oil, gas and petrochemical industry is the main pillar of the economy in Iran. Not only most of the oil, gas and petrochemical infrastructure in Iran are old and worn-out, but also the safety man- agement practices are not adequate. Resilience engineer- ing is a growing concept toward proactive and preventive safety and performance improvement in critical industrial units. This study presents a new algorithm for perfor- mance evaluation of resilience engineering culture in critical industrial units. A petrochemical plant is consid- ered as a real-life case study to demonstrate the applica- tion of the proposed methodology. The presented algorithm is based on graph theory, statistical methods, and matrix algebra which offer some desirable properties for modeling and solving complex decision-making problems and considers the interactions between factors. To the best of our knowledge, this is the first study that proposes a performance evaluation algorithm based on graph theory and matrix approach. Keywords Performance optimization Á Resilience engineering Á Graph theory Á Matrix approach Á Statistical methods 1 Introduction Intense global competition has forced organizations and companies to constantly look for improvement opportuni- ties in all aspect of their business to survive and/or to get ahead of the competition. There are various important concepts that management needs to evaluate the system to find the weaknesses and strengths. Determining the most efficient open spots for optimization is of utmost impor- tance. Strengths can be improved, but when weaknesses are not addressed, the desired improvements are not achiev- able. Therefore, performance evaluation and optimization is a very significant concern for managers in any organi- zation (Braunger et al. 2015). Safety is one of the most important aspects of any critical industrial unit. Besides the human injuries and loss, any accident in critical industrial units can result in a catastrophic scope (Nejad et al. 2017). Oil, gas and petrochemical industry is the main pillar of the economy in Iran. Not only most of the oil, gas and petrochemical infrastructure in Iran are old and worn-out (Azadeh et al. 2017b), but also the safety management practices are not adequate. Currently, more than seventeen million employees are working in oil, gas and petrochemical industry in Iran which highlights the need for health and safety practices. Although the Ministry of Labour and & Masoud Rabbani mrabani@ut.ac.ir Reza Yazdanparast r.yazdanparast@ut.ac.ir Mahdi Mobini mobini@mail.ubc.ca 1 School of Industrial Engineering, University of Tehran, Tehran, Iran 2 Department of Mechanical Engineering, The University of British Columbia, Vancouver, Canada 123 Int J Syst Assur Eng Manag https://doi.org/10.1007/s13198-019-00774-0