This thesis is concerned with economic designs of $\bar{X}$ and np control charts with variable sampling intervals. Variable sampling interval control chart is based on the notion that the time interval until the next sample should be short if a point is close to the control limits and long if it is close to the target value.
Two models of production are considered depending on whether the process is kept running or is shut down during the search for the assignable causes. For the two models, the total average loss cost per unit time is derived which involve the cost of sampling, the cost of searching for false alarm, the cost of detecting and removing an assignable cause, and the cost of producing nonconforming items. The optimum values of sample size, warning limits, short interval, long interval, and control limits are determined by minimizing the total average loss cost. Numerical studies are performed to compare variable sampling interval control chart with fixed sampling interval control chart.
