Effect of non-normality on the monitoring of simple linear profiles in two-stage processes: a remedial measure for gamma-distributed responses

The relationship between the response variable and one or more independent variables refers to the quality characteristic in some statistical quality control applications, which is called profile. Most research dealt with the monitoring of profiles in single-stage processes considering a basic assumption of normality. However, some processes are made up of several sub-processes; thus, the effect of cascade property in multistage processes should be considered. Moreover, sometimes in practice, the assumption of normally distributed data does not hold. This paper first examines the effect of non-normal data to monitor simple linear profiles in two-stage processes in Phase II. We study non-normal distributions such as the skewed gamma distribution and the heavy-tailed symmetric t-distribution to measure the non-normality effect using the average run length criterion. Next, generalized linear models have been used and a monitoring approach based on generalized likelihood ratio (GLR) has been developed for gamma-distributed responses as a remedial measure to reduce the detrimental effects of non-normality. The results of simulation studies reveal that the performance of the GLR procedure is satisfactory for the multistage non-normal linear profiles. Finally, the simulated and real case studies with gamma-distributed data have been provided to show the application of the competing monitoring approaches.