Kronecker algebra for series-parallel multi-state systems reliability evaluation

Multi-state systems (MSS) are systems whose stochastic degradation process is characterised by several performance levels varying from nominal functioning to complete failure. MSS arise naturally in many application areas. MSS reliability evaluation and estimation has received much attention from researchers and a wide range of papers dealing with MSS have been published. In this paper, an approach based on Kronecker algebra combined with stochastic processes is proposed to evaluate the reliability of a series-parallel MSS. The main advantage of the proposed approach is that the mathematical expressions of the MSS reliability indices are derived from data of individual elementary components without generating the whole, possibly huge, MSS state space. Furthermore, the approach is well formalised and easy to implement thanks to Kronecker algebra operators. Examples are given to illustrate the proposed approach.