This thesis is concerned with economic designs of variable sampling interval $\bar{X}$ control charts for production systems with increasing failure rate(IFR) and minimal repairs.
Three minimal repair policy models are considered; one is to replace the system at a fixed time T, another is to replace it at the first failure after T, and the other is to replace it at a fixed number of failures. For each model, the expected cost per unit time is derived which involves the cost of sampling, the cost of detecting and removing assignable causes, and the cost of producing nonconforming items. The optimum values of sample size, control limits, length of the first sampling interval, and number of samples are obtained by minimizing the expected cost per unit time. Numerical studies are performed to compare the three models and the effects of using fixed sampling interval are also investigated.
