Inspection model for the replacement of critical units exhibiting delay time

System like Flexible Automated Manufacturing is designed to work effectively without continuous attention. However failures in such system can not be totally eliminated and there is a necessity for timely detection of failures of some of its critical units which may cause serious degradation of performance of the whole system. Even if such units fail, the fault can be detected only by inspection. There is a delay time between the time the fault is first detectable and the occurrence of failure of the system. In this paper a model has been presented which would help in deciding optimum number of inspections and the optimal sequence in which these inspections are to be carried out in order to minimize the total cost of inspections, inspection replacements and failure replacements per cycle. An example showing the application of the model is also provided in the paper