Monitoring Nonlinear Profiles in Phase II Using Wavelets

In many industrial processes, quality of a process can be characterized as a nonlinear relation between a response variable and explanatory variables. In several articles, use of nonlinear regression is suggested for monitoring nonlinear profiles. Such regression has two disadvantages. First the distribution of the regression coefficients cannot be specified for small samples and second with increased process complexity, number of regression parameters increases and this decreases power of the test and reduces performance of control charts. In this article, wavelets are used for monitoring nonlinear profiles in phase II. Two smoothing parameter, the threshold and decomposition level, determine form of the regression function in discrete wavelet transform. A method is proposed to determine decomposition level and mean and variation (within) of profile are monitored in that level. For monitoring variation within profile based on two estimator of variance in DWT, parametric and nonparametric control chart are proposed and the performance of them are compared. Results indicate that F/T2 control chart performs better than median/T2 in monitoring shift in the process mean. For small shifts in the variance, F/T2 perfoms better than median/T2 and for large shifts median/T2perfoms better.