The Trinomial ATTRIVAR control chart

Abstract

In this article, we propose the Trinomial - ATTRIVAR (T-ATTRIVAR) control chart where attribute and variable sample data are used to control the process mean. Firstly, two discriminating limits sort the sample items into three excluding categories; that is, items in categories A, B, or AB, are, respectively, items with X dimensions smaller than the lower discriminating limit, larger than the upper discriminating limit, or neither smaller than the lower discriminating limit nor larger than the upper discriminating limit. Depending on the number of sample items in each category, one of three decisions is made: the process is declared in-control, the process is declared out-of-control, or all sample items are also measured. In this last case, the sample mean of X is used to decide the state of the process. Aslam et al. (2015) worked with the particular case where the sample items are classified as defective (items in category - A plus items in category - B) or not-defective (items in category - AB). The strategy of splitting defectives into two excluding categories (A and B) enhances the performance of the ATTRIVAR chart. It is worth to emphasize that the previous attribute classification truncates the X distribution. Consequently, the mathematical development to obtain the ARLs is complex – the Average Run length (ARL) is the average number of samples the control chart requires to signal. With the density function of the sum of truncated X distributions, we obtained the exact ARLs. The exact minimum ARLs are lower than the minimum ARLs Ho and Aparisi (2016) obtained with the Genetic Algorithm.