A 2‐Stage Attribute‐Variable Control Chart to Monitor a Vector of Process Means. (19th February 2017) - Melo, Moizes S.; Ho, Linda Lee; Medeiros, Pledson G.
Abstract : The aim of this paper is to propose a combined attribute‐variable control chart, namely M a x D  −  T 2, to monitor a vector of process means μ  = [ μ 1, …, μ q ] in a multivariate process control. The procedure consists of splitting a sample of size n into two sub‐samples of sizes n 1 and n 2 ( n  =  n 2  +  n 2 ), determined by an optimized process. Units of the first sub‐sample are evaluated by an attribute inspection. Using a device like a gauge ring, each unit of the first sub sample is considered approved related to the quality characteristic i if X i ∈[ w L i ; w U i ]; otherwise, it is disapproved in the characteristic i, where w L i and w U i (obtained by an optimization) are respectively the lower and upper discriminating limits of the quality dimension X i . If the number of disapproved items in any quality characteristic is higher than a control limit, then the measurement of the q quality characteristics is taken on each unit of the second sub‐sample and the statistic T 2 is calculated. If T 2  <  L ( L, the control limit) the process is judged as in control. The process will suffer intervention if both charts signal. The procedure has an advantage to not inspect the units of the second sub‐sample if the first sub‐sample indicates that the process is in control. This proposal shows a better performance than T 2 control chart for a large number of scenarios. The two control limits and discriminant limits are optimized to reach a desired value of A R L 0 and to minimize A R L 1 . Copyright © 2017 John Wiley & Sons, Ltd.