Eliminating a Numerical Accuracy Problem in Mean Life Calculations

In applying the Markov approach to evaluating the mean life of repairable systems, the matrix of state equations is often badly conditioned for inversion. This is especially true for systems with 2-state weather models and/or a broad range of failure and repair rates. If the matrix is inverted by pivoting, accuracy is lost through subtractive cancellation. The paper describes a simple modification to the Gauss-Jordan method which avoids this accuracy loss. On test, this modified method has given fully accurate solutions, where other techniques have given very poor accuracy.