Design Of The S~2 Control Charts With Unknown Parameter

In the production process,it is common to monitor the process mean,while ignoring the monitoring of the process variance.But it is important to monitor the process variance.In the manufacturing industry,such as problems of using inferior raw materials,employing unskilled workers,parts wear may lead to the shift in the process variance,and its mean has no effect.The S~2 control chart is commonly used to monitor process variance,and it is assumed that the process variance is known,in practice,the parameter is usually unknown.In this paper,the new metrics are used to evaluate the influences of parameter estimation on the S~2 control charts,meanwhile,the new S~2 control charts are developed to improve the ability of control chart to monitor the shift in the process variance.The main work and contributions in this paper are summarized as follows:(1)Based on the conditional distribution of ARL,we evaluate the influences of parameter estimation on upper-sided S~2 chart,lower-sided S~2 chart and two-sided 52 Cchart.(2)Because parameter estimation has serious effects on the S~2 control charts,the new S~2 control charts are designed to improve the conditional performance.