A trinomial chart for monitoring the process variance

• Published in: Computers & industrial engineering 2021-07, Vol.157, p.107332, Article 107332
• Main Author: Costa, Antonio Fernando Branco
• Format: Article
• Language: English
• Subjects: Multiple-step gauge; Range chart; Trinomial chart; Variance control
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2021.107332

•Shewhart chart based on attribute inspections to control variability.•An attribute chart more efficient than the Range chart.•Multiple-step gauges. In this article we propose an attribute chart to control the process variability. A multiple-step gauge is used to classify the sample items in three excluding categories; that is, items in categories 1, 3, and 2, are, respectively, items with the X dimension in one of the two tails, in the central part, and in between the tails and the central part of the X distribution. After determining (n1, n2) – the number of items in the first and in the second categories, the monitoring statistic of the Trinomial chart, calculated as an1 + bn2, is compared with a control limit CLT; If an1 + bn2 > CLT, then the chart signals an increase in the process variance. The coefficients a and b are the weights assigned to the items according to their categories; for instance, if a = 2 and b = 1, then an item in the first category has the weight of two items in the second category. The Trinomial chart signals variance increases faster than the Range chart. The Trinomial chart is also more sensitive than its competitor even when the X distribution is no longer normally distributed. In comparison with the S2 chart, if the sample is small (n = 3 or 4), then the Trinomial chart signals faster, if the sample is large (n > 5), then the Trinomial chart requires samples of size (n + 1) to defeat its competitor; it is worthy to note that the use of larger samples is highly compensated by the fact that the Trinomial chart is an attribute chart, free of measurements and calculations to obtain the sample variances.