Monitoring linear profiles using an adaptive control chart

We propose a model for the statistical design of a variable sample size chi-squared control chart (VSS chi(2) control chart) for monitoring linear profiles. Performance measures of the proposed adaptive control chart are obtained through a Markov chain approach. Through a numerical example, which consists of a calibration application in a production process of semiconductors, the proposed chart is compared to the fixed parameter chi-squared control chart (FP chi(2) chart) to monitor the intercept and slope of the linear profile. From this example, it is possible to assess the potential benefits provided by the proposed chart. Also, considering simultaneous shifts in the intercept, the slope, and the standard deviation, a sensitivity analysis of the proposed chart for monitoring linear profiles is presented.