A periodic testing model for a preparedness system with a defective state

This paper considers the periodic testing of a preparednesssystem where in addition to working and failed state recognition,a working but defective state also exists. Based upon the delaytime model, an expected availability model is derived and evaluatedas a function of the constant inspection period. The model enablesthe range of inspection periods which satisfy a pre-set availabilitycriterion to be established, and the optimal availability inspectionperiod to be identified. Variants of the basic model are considered including: wherea delay time period exists, but the technology to detect a defectis not available; where the delay time is zero, so that onlyfailures are detected; and where the system is replaced on aregular basis without any state testing. These variants enablethe value and effectiveness of the ability to detect defectsand to detect failures to be identified and quantified. The models are demonstrated in the context of a missile buffersystem, where the numerical example clarifies the value of modellingand the insight into the potential effectiveness of defect andfailure detection.