Weighted attribute control charts for variable sample size

Abstract

Two new attribute control charts, a pchart and a uchart, are proposed. The fraction nonconformitiesp _i and numbers of nonconformitiesu _i of the subgroup samples are transformed so that their variances are equal for all samples of various sizes. Consequently, the control limits on a new chart remain constant throughout, and hence, nonrandom patterns and trends of the nonconformities can be more meaningfully interpreted and identified. After the transformation, the fraction nonconformingp_i★ (oru_i★) becomesp_i(oru_i) plus a weighted deviation ofp_i from the overall fraction nonconforming (so the charts are called weighted attribute control charts). In many practical applications, the transformation could be made so that the transformed nonconformities almost coincide with the original nonconformities for most of the samples. The new charts could also be readily constructed through making a few additions to the traditional and frequently used p and u control charts whose control limits are based on the average sample size.