Multi-stage mixed system optimal redundancy allocation problem via random-fuzzy credibility measure

In this paper, an Optimal Redundancy Allocation Problem (OPAP), modelled as a non‐linear integer‐programming problem is formulated and solved. Here, costs and resources are random fuzzy in nature. The OPAP is formulated as a decision‐making model optimising Possibilistic Value at Risk (pVaR) by incorporating the concept of Value at Risk (VaR) into possibility and necessity measure theory. The reduced deterministic constrained problem is solved using Generalised Reduced Gradient (GRG) method (LINGO‐14). Some particular models are presented. The models are illustrated with numerical examples and some sensitivity analysis is made on damageability.