Two single-unit inspection models with Markov deterioration are presented. The condition of the system is observable only through inspections except for failure states. Maintenance actions include inspection, repair and replacement. The system starts from new with an initial inspection interval. When the deterioration exceeds a certain level, the inspection interval is decreased to reduce failure risk. In Model I, we consider two deterioration states and two failure states. The condition immediately after a repair is unknown. Model II consists of three deterioration states and two failure states. We allow the result of a repair to be known. Each model is formulated as a Markov renewal process. Formulas for the long-run average cost are obtained using semi-regenerative reward theory. Numerical example and sensitivity analysis are presented for Model I to show the performance of the model and cost parameters. We find that replacement cost is dominant in this model.
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