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.