Cost comparisons of modified X¯ chart for autocorrelated observations

Abstract

This paper presents the economic design of modified X¯ chart for autocorrelated data and comparison with the economic design of Shewhart's X¯ chart. An attempt has been made to counter autocorrelation by designing the modified X¯ chart; as the cost of operating a process control system is an important element in the economic design of control charts. The economic designs of both modified and Shewhart X¯ charts for autocorrelated observations are presented; using Lorenzen-Vance [1] cost model. The modified X¯ chart is based upon sum of chi-squares and has simplicity like Shewhart X¯ chart but more efficient than standard chart. Two sets of parameters suggested by Montgomery [2] are used to determine the optimal sampling intervals (h) and expected costs per hour. It shows that sampling interval (h) and expected cost/hour (C) depend upon various parameters of chart, used in this model. The expected costs/hour (C) for both the charts are computed for sample sizes of 2 and 4 at the various levels of correlation and process shifts in mean. It is concluded that at each level of correlation and shift in the process mean, the expected costs/hour of the modified X¯ chart are lower than the Shewhart chart.