Analysis of the performance of safety-critical systems with diagnosis and periodic inspection

This paper presents a method for analysis of performance indexes of safety-critical systems. It incorporates periodic inspection and repair which occurs just after each time interval into Markov model. This modeling technique is applied to the typical system structures regulated in the standard IEC 61508. Both perfect and imperfect inspections and repairs can be modeled. Through derivation, a variety of important system performance indexes can be obtained in closed form, that include MTTF, MTTFD, MTTFS, average availability, average probability of failure-dangerous, and average probability of failure on demand. The solutions are applied to 1-out-of-2 system structure to illustrate the usefulness of this method in analyzing the system performance, for example, choice of proof-test interval and evaluation on the average probability of failure on demand.