Matrix Approach to Computing MTTF of a System

This paper proposes a new method to compute the mean time to failure (MTTF) of a system that can be expressed with a combinatorial model whose components fail with i. i. d. The key idea is to use a matrix approach that replaces every component reliability with a specific matrix and replaces every operation (addition, subtraction, multiplication, and division) with its corresponding matrix operation in the system reliability computation. We can determine all coefficients of the polynomial expressing the system reliability by replacing each component reliability with a special matrix and thereby easily compute the MTTF by taking the integral of this polynomial. We assume two assumptions, where the first is i. i. d. component failure and the second is that the computational complexity of integral of the j ‐th power of reliability of each component is polynomial order for any natural number j not more than the number of components (like when component fails with exponential distribution). We can compute the MTTF of the system with polynomial order complexity when we can compute the system reliability with polynomial order complexity, under the above two conditions. © 2026 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.