The SPC Charts with Parameters Unknown

When the in-control process parameter（s） is unknown, Quensenberry （1991） proposed theQstatistic. Under the hypothesis that the process is in control （i.e. all observations are i.i.d.） theQ statistics are also i.i.d. standard normal variables. But if the hypothesis is not true, what does theQ statistics perform? We studied the case and proposed a new CUSUM statistic based on theQ statistics. The simulation results show that our new CUSUM statistics works well. In the other hand, if the in-control variance is unknown, theQ 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.