Techniques for controlling bivariate grouped observations

The term grouped data refers to the case where the exact value of the characteristic of interest is either unknown or difficult to register. In the present article we study a model that can be used for the simultaneous control of two (possibly correlated) variables whose values have been registered in the form of grouped data. The exact distribution of the waiting time for an out of control signal through the suggested scheme and its ARL are investigated by using a Markov Chain embedding methodology and by establishing a recurrence scheme for the respective tail probabilities. A detailed study of the performance of the scheme is also carried out when the characteristics of interest follow the Marsall–Olkin’s bivariate Exponential Distribution.