Optimal T² Control Chart with a Double Sampling Scheme – An Alternative to the MEWMA Chart

Abstract

Recent studies have shown that a double sampling (DS) scheme yields improvements in detection times of process shifts over variable ratio sampling (VRS) methods that have been extensively studied in the literature. Additionally, a DS scheme is more practical than some of the VRS methods since the sampling interval is fixed. In this paper, we investigate the effect of double sampling on cost, a criterion as important as detection rate. We study economic statistical design of the DS T2 chart (ESD DS T2) so that designs are found that are economically optimal but yet meet desired statistical properties such as having low probabilities of false searches and high probabilities of rapid detection of process shifts. Through an illustrative example, we show that relatively large benefits can be achieved in a comparison with the classical T2 chart and the statistical DS T2 charts with our ESD DS T2 approach. Furthermore, the economic performance of the ESD DS T2 charts is favorably compared to the MEWMA and other VRS T2 control charts in the literature. Copyright © 2011 John Wiley & Sons, Ltd.

Control Charts monitoring Product's Loss to Society

“…The implementation of these control charts to carry out target cost philosophy has been considered as well. Future research directions include the development of time weighted control charts monitoring the social loss, the implementation of run rules, and improving the power of the investigated charts in detecting process shifts according to specific adaptive sampling strategies, (see Faraz and Saniga 5 and Faraz et al 6 )…”

Robust economic-statistical design of X-bar control chart

“…The first constraint addresses the crisis that the solutions derived from EDs can be unwieldy in practice (Saniga 1989;Woodall 1986). For instance, solutions reported by Faraz, Heuchenne, and Saniga (2011) where an average time of five minutes needs to test and analyse a sample item (E s = 5/60 h) with sample size of n 2 = 17 and sampling interval of h = 1.21 h needs 1.417 h (nE s = 17 * 5/60 h) for taking and interpreting samples. This is not consistent with the plan that recommends sampling every 1.21 h. Thus, the constraint, nE s ≤ h, ensures that plans are meaningful and applicable in practice.…”

Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to bar and S2 Charts

“…Faraz et al concluded a that large population size, say 100, and lower crossover rate than is typically used, say 0.3, shows better performance in designing the ESD of control charts. In this article, we set the MOGA parameters to N pop = 100, r C = 0.3, and P f = 0.3 (see also, Faraz et al ).…”