An inspection strategy for randomly failing machine to guarantee robust schedules

This paper is motivated by the availability improvement of a single randomly failing machine whose state is only known through inspection. Jobs to be processed on the machine arrive according to a random distribution and the processing of each job induces a shock whose magnitude depends on the job´s desired operating characteristics. These shocks cumulatively aggravate the deterioration process and hasten machine failure. The machine is inspected at predetermined times T₁ , T₂, ... . If failure is detected then the machine is repaired as good as new, otherwise it is kept operating. Given a prespecified availability level for the machine, the corresponding inspection sequence is determined and the scheduler builds his schedule around the inspection points. The expression of the system time-stationary availability is presented and an algorithm has been developed to generate the inspection sequence which insures a certain machine availability level. In cases where the inspection period is predetermined due to limited resources, the computer program determines the maximum job arrival rate not to be exceeded in order to guarantee a minimum required machine availability level. Numerical results are provided for a test case