In the real world applications nowadays, the situation of low defect level in process often e[x.sub.i]sts, and it results that the performances of classical attribute control charts become bad. Historically, classical attribute control charts have been developed by using the normal appro[x.sub.i]mation. However, the normal appro[x.sub.i]mations are far from adequate for the situation of low defect level and the sample size is not large enough, mainly due to skewness in the exact distribution. In this paper, an improved square root transformation, named ISRT, is used to construct the ISRT p-chart, np-chart and c-chart for charting the binomial data and Poisson data. Comparing the ISRT p-chart with several known p-charts, the minimum sample sizes required for obtaining positive lower control limits for the ISRT p-chart are small. Numerical results also indicate that the ISRT control charts can match any specific percentile point of run length distribution of the true limits when the parameter is unknown.
Tamsui Oxford Journal of Mathematical Sciences 22(1), pp.61-72