An Nonparametric Control Chart Based On Sign Test

In current statistical control process,control chart is the most common method.In general,the traditional control charts assume the sample distributions are normal.But in practice,this assumption cannot always be satisfied,and we should monitor whether the data streams have shifts when the sample distributions are unknown.In addition,many methods also need pairwise independent data stream,which can not be satisfied absolutely in practical applications.This paper presents a multivariate nonparametric SPC method T_newto monitor data streams online.It combines the multivariate sign test,proposed by Randles?2000?^[19]and the control chart,proposed by Mei?2010?^[13],based on the sum of local CUSUM statistics from each individual data stream.It extends normal distribution hypothesis to distribution-free,so it can monitor the unnormal distribution samples effectively.In order to eliminate the hypothesis that the data streams are independent,we combine correlative data streams into a single high-dimensional data stream and name this method T_nd.The two methods are affine invariant,and only use the direction of an observation from the origin but not the distance.In addition,they are distribution-free for the class of distribution with elliptical directions.We can see that the two control charts can both monitor shifts,especially for the small and moderate shifts,effectively.Even when the distributions are skewed,they can also alarm the shifts as early as possible.