A control scheme for autocorrelated bivariate binomial data

• We build an effective control chart for the autocorrelated bivariate binomial observations.
• The charting statistic is constructed by integrating the likelihood ratio test with the EWMA procedure.
• Comprehensive numerical simulation studies are performed.
• We use a motivating example to demonstrate how the proposed method is used.

The applications of attribute data cover a wide variety of manufacturing and service processes. Moreover, the need for attribute control charts suitable for multivariate and autocorrelated processes has been well recognized. However, there is a scarcity of methods for addressing the autocorrelation among the multivariate attribute data. This paper focuses on autocorrelated bivariate binomial data and proposes a control chart based on the bivariate binomial autoregressive model by integrating a log-likelihood-ratio statistic into Exponentially Weighted Moving Average (EWMA). The performance of the proposed chart in detecting sustained shifts in parameters is evaluated by the Average Number of Samples to Signal (ANSS). The simulation results show that the proposed chart is generally more robust and sensitive to small and moderate shifts compared with the existing charts. In addition, a real example from laser gyroscope manufacturing is used to illustrate the implementation of the proposed approach.