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

This paper considers the periodic testing of a preparedness system where in addition to working and failed state recognition, a working but defective state also exists. Based upon the delay time model, an expected availability model is derived and evaluated as a function of the constant inspection period. The model enables the range of inspection periods which satisfy a pre-set availability criterion to be established, and the optimal availability inspection period to be identified. Variants of the basic model are considered including: where a delay time period exists, but the technology to detect a defect is not available; where the delay time is zero, so that only failures are detected; and where the system is replaced on a regular basis without any state testing. These variants enable the value and effectiveness of the ability to detect defects and to detect failures to be identified and quantified. The models are demonstrated in the context of a missile buffer system, where the numerical example clarifies the value of modelling and the insight into the potential effectiveness of defect and failure detection.