An economic design for variable sampling interval MA control charts

Most of the studies done on the economic design of control charts focus on a fixed-sampling interval (FSI); however, it has been discovered that variable-sampling-interval (VSI) control charts are substantially quicker in detecting shifts in the process than FSI control charts due to a higher frequency in the sampling rate when a sample statistic shows some indication of a process change. In this paper, an economic design for a VSI moving average (MA) control chart is proposed. The results of a numerical example adopted from an actual case indicate that the loss cost of VSI MA control charts is consistently lower than that of the FSI scheme.Design variables n Sampling size for each moving plot - h_a Subsequent sampling interval when preceding sample mean is located at sub-control regionI_a,a=1,2,..., - Number of different sampling-interval lengths, 2 - k_a Threshold limit expressed in units of - k₁ Control limit expressed in units of Parameters related to assignable cause µ₀ Target mean - True-process standard deviation - Magnitude of an assignable cause expressed in units of - Occurrence rate of an assignable cause per unit timeCost and technical parameters D Average time taken to find and repair an assignable cause after detection - e Time for a sample to be taken, transmitted to laboratory, and results phoned back to process control room - M Income reduction when=₀+ - T Average cost of looking for an assignable cause when a false alarm occurs - W Average cost of looking for and repairing an assignable cause when one does exist - F_c Fixed cost per subgroup of sampling, inspecting, evaluating and plotting - V_c Variable cost per subgroup of sampling, inspecting, evaluating and plotting