Cost comparisons of modified X̅ chart for autocorrelated observations

Abstract

This paper presents the economic design of modified X̅ chart for autocorrelated data and comparison with the economic design of Shewhart’s X̅ chart. An attempt has been made to counter autocorrelation by designing the modified X̅ 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 X̅ charts for autocorrelated observations are presented; using Lorenzen-Vance [1] cost model. The modified X̅ chart is based upon sum of chi-squares and has simplicity like Shewhart X̅ 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 X̅ chart are lower than the Shewhart chart.

Keywords

• Level of autocorrelation
• modified X̅ chart
• Lorenzen-Vance (1986) cost model
• sample size
• sampling intervals