An inspection model for automatic trips and warning instruments

Automatic trips and warning instruments (TWI) protect important machines by shutting them down or warning the operators of impending serious failure. They are subject to hidden faults which must be discovered and corrected at frequent inspections, and spurious trips when the machine is stopped unnecessarily because of a fault in the TWI spurious trips may also be reduced by inspections. A Markov model is used to optimize the inspection rate with respect to costs on the assumption that inspection is a Poisson event. This simplifies the mathematics compared to a model with periodic inspections and is often just as close to the truth. An example is given involving gas-turbines in the off-shore oil industry. An extension of the model covers the case of 2-out-of-3 voting systems which are increasingly used to reduce the risks of both types of TWI failure. The optimizations are usually rather flat around the optimum, and inspections often have to fit in with operational needs, so approximate methods such as this are potentially very useful as the example illustrates.