Design of Shewhart ratio control chart with variable sample size based on normalized transformation
To improve the efficiency of the Shewhart control chart for monitoring the ratio of bivariate normal varia-bles(denoted as Shewhart-RZ chart),a new control chart was proposed by combining the Shewhart-RZ chart with a variable sample size strategy(denoted as VSS Shewhart-RZ*chart).Based on the normalized transformation meth-od,a new statistic Z*was designed to eliminate the adverse effects of varying sample size on the design and use of the control chart.The Markov chain method was used to calculate the average run length and average sample size of the VSS Shewhart-RZ*chart,and the corresponding parameter optimization algorithm was given.The statistical performance of VSS Shewhart-RZ*chart was studied through simulation analysis and compared with the Shewhart-RZ chart.The results showed that the performance of VSS Shewhart-RZ*chart was significantly better than She-whart-RZ chart.
variable sample sizeratio distributionaverage run lengthnormalized transformation