Abstract:
When the in-control process parameter(s) is unknown, Quensenberry (1991) proposed the
Qstatistic. Under the hypothesis that the process is in control (i.e. all observations are i.i.d.) the
Q statistics are also i.i.d. standard normal variables. But if the hypothesis is not true, what does the
Q statistics perform? We studied the case and proposed a new CUSUM statistic based on the
Q statistics. The simulation results show that our new CUSUM statistics works well. In the other hand, if the in-control variance is unknown, the
Q statistics are difficult to compute (and so it can’t be used in the practice). We proposed a statistic, whose exact distribution is not normal but close to the normal, to detect the change instead of the
Q statistics. The simulation results also show that the new statistics act very well.