Combining attribute and variable data to monitor process variability: MIX S2 control chart. Issue 9 (December 2016) - Ho, Linda; Costa Quinino, Roberto
Abstract The necessity to monitor process variability to maintain similar, but more economical, performance to that of theS 2 control chart in terms of ARL1 is the motivation of this paper. In general, a sample of four to six units is used to build anS 2 control chart. Reducing the sample size to two or three units is a possibility, but the performance will be poor (in terms of ARL1 ), and the project specification may not be met. Additional cost would be required to remove the nonconforming units before shipment to the customers. This would compromise the quality of products in an environment of high worldwide competitiveness. The aim of this paper is to present the MIXS 2 control chart, which employs a two-phase control chart to monitor the variability. At every interval of h hours, each unit is sequentially classified as approved or rejected by employing a Go/No Go ring gauge. A unit is approved if its dimension lies in [LDL; UDL], where L(U)DL is the lower(upper) discriminant limit; otherwise, it is rejected. IfA 1 -approved items are first observed, then the production continues. However, ifB 1 -rejected items are first observed, thenn (n  < 5) complementary units are taken, and the quality characteristics are measured to calculate the sample varianceS 2 . IfS 2 is greater than the control limit, then the process is stopped for adjustment; otherwise, the production continues. The MIXS 2 chart employs mixed control charts (attribute and variable) with the aim to find optimized parameters—LDL, UDL, A 1, B 1, and CL—such that similar values to ARL1 (and average sample size) are provided at a lower cost than theS 2 control chart.