Inflated beta control chart for monitoring double bounded processes

This study proposes a new control chart for monitoring double bounded processes in the intervals (0,1], [0,1) or [0,1], such as fractions and proportions, which commonly contain zeros and/or ones in practical applications. The proposed chart, called inflated beta control chart, presents the control limits based on the inflated beta probability distribution. This distribution allows the modeling of double bounded processes that assume values in the unit interval containing zeros and/or ones. For control limits determination, we consider two approaches based on the suppositions of known and unknown parameters. When the parameters are unknown, usually in empirical applications, the control limits are determined by maximum likelihood estimators. In this case, the performance of the proposed control chart and of the well-known beta control chart is evaluated by Monte Carlo simulations. The inflated beta control chart outperforms the beta control chart in terms of run length analysis. In addition, three illustrative examples are presented to demonstrate the applicability of the proposed control chart.