Statistical Performance Analysis of a VP X Control Chart with B&L Switching Rule by Using a Markov Chain Model

In statistical process control, variable parameter (VP)X chart is widely used. To improve the performance of the VP X chart, Bai & Lee (B&L) switching rules are applied to design the VP X chart. By this method, a Markov chain model is developed to obtain the expressions of Average Time to Signal (ATS), Adjusted Average Time to Signal (AATS), and average number of switches (ANSW). To evaluate the performance of the proposed method, comparison is done between the chart designed by the proposed method and the existing VP X chart by using two samples. Results show that, with the same average run-time, the proposed method outperforms the existing VP X chart in both shortening the alarm time and in reducing the number of switch times. The larger the parameter L is, the better the performance of the proposed method is.