Design of control charts for multivariate Poisson distribution using generalized multiple dependent state sampling

Abstract

In this paper, two attribute control charts under multiple dependent state sampling (MDS) and its modification are proposed to monitor the multivariate Poisson count data. The sensitivity of the MDS is increased by introducing an additional parameter. The new method is named as generalized multiple dependent state sampling (GMDS). The proposed charts are based on two pairs of limits i.e. inner and outer control limits that make use of the past samples information in addition to the current sample. The monitoring statistics of the proposed charts are the sum of non-conformities or flaws of each quality characteristics that make the charting structure relatively simple. The performance comparison of the proposed charts with the existing multivariate Poisson control chart is made by using out-of-control average run length (ARL). The comparison reveals that the ARLs of the proposed charts are considerably smaller than the existing scheme for all shift sizes and different values of parameters. Simulation study also showed the dominance of the proposed charts over other existing control charts in detecting the process shift. For practical application, an empirical illustration is provided to signify the performance evaluation of the proposed charts.

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