Bootstrap method approach in designing multi-attribute control charts

In a production process, when the quality of a product depends on more than one correlated characteristic, multivariate quality control techniques are used. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In monitoring the quality of a product or process in multi-attribute environments in which the attributes are correlated, several issues arise. For example, a high number of false alarms (type I error) occur and the probability of not detecting defects (type II error) increases when the process is monitored by a set of independent uni-attribute control charts. In this paper, to overcome these problems, first we develop a new methodology to derive control limits on the attributes based on the bootstrap method in which we build simultaneous confidence intervals on the attributes. Then, based upon the in-control and out-of-control average run length criteria we investigate the performance of the proposed method and compare it with the ones from the Bonferroni and Sidak's procedure using simulation. The results of the simulation study show that the proposed method performs better than the other two methods. At the end, we compare the bootstrap method with the T-2 control chart for attributes.