Estimating step and linear drift change point in contingency tables

In many practical cases, product or process quality is defined by frequency table of two or more qualitative variables. This frequency table is called contingency table. Monitoring the contingency tables is an area in statistical process control with many applications in industrial and service units.
On the other hand, reducing quality costs is the most fundamental issue preoccupying the minds of managers. It is clear that a quicker diagnosis of the assignable causes can reduce the quality costs. Estimating change point by limiting the probable interval of change, reduces the cost and time of detecting assignable causes. In this research, using maximum likelihood approach, the step and linear drift change points estimators are proposed for multivariate multi-nominal contingency tables. After the change point, parameters are estimated with making the average in the proposed step estimator, and using the linear regression in the proposed linear drift estimator. Results of the simulations demonstrated that the proposed step change point estimator carries out very well in all shift types and shift magnitudes from small to large. Furthermore, the proposed estimator of the linear drift change point has relatively good performance in moderate changes. Finally, the proposed estimators’ performance is assessed by a numerical example.