The demerit‐based control chart for trinomial distribution

Purpose – The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X2, G2, GM2, and NM2 in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with dip null hypothesis based on demerit control chart.Design/methodology/approach – The research involves the linear form of the test statistics, the linear function of counts since the marginal distribution of the counts in any category is binomial or approximated Poisson, in which the uniformly minimum variance unbiased estimator is the linear function of counts. A control chart is used for monitoring student characteristics in Thailand. The control chart statistics based on an average of the demerit value computed for each student as a weighted average lead to a uniformly most powerful unbiased test marginally. The two‐sided control limits were obtained using percentile estimates of the empirical distribution...

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