TY - JOUR

T1 - Economic statistical design of a T2 control chart with double warning lines

AU - Faraz, Alireza

PY - 2011/3

Y1 - 2011/3

N2 - Recent studies have shown that enhancing the common T2 control chart by using variable sample sizes (VSS) and variable sample intervals (VSI) sampling policies with a double warning line scheme (DWL) yields improvements in shift detection times over either pure VSI or VSS schemes in detecting almost all shifts in the process mean. In this paper, we look at this problem from an economical perspective, certainly at least as an important criterion as shift detection time if one considers what occurs in the industry today. Our method is to first construct a cost model to find the economic statistical design (ESD) of the DWL T2 control chart using the general model of Lorenzen and Vance (Technometrics 1986; 28:3-11). Subsequently, we find the values of the chart parameters which minimize the cost model using a genetic algorithm optimization method. Cost comparisons of Fixed ratio sampling, VSI, VSS, VSIVSS with DWL, and multivariate exponentially weighted moving average (MEWMA) charts are made, which indicate the economic efficacy of using either VSIVSS with DWL or MEWMA charts in practice if cost minimization is of interest to the control chart user.

AB - Recent studies have shown that enhancing the common T2 control chart by using variable sample sizes (VSS) and variable sample intervals (VSI) sampling policies with a double warning line scheme (DWL) yields improvements in shift detection times over either pure VSI or VSS schemes in detecting almost all shifts in the process mean. In this paper, we look at this problem from an economical perspective, certainly at least as an important criterion as shift detection time if one considers what occurs in the industry today. Our method is to first construct a cost model to find the economic statistical design (ESD) of the DWL T2 control chart using the general model of Lorenzen and Vance (Technometrics 1986; 28:3-11). Subsequently, we find the values of the chart parameters which minimize the cost model using a genetic algorithm optimization method. Cost comparisons of Fixed ratio sampling, VSI, VSS, VSIVSS with DWL, and multivariate exponentially weighted moving average (MEWMA) charts are made, which indicate the economic efficacy of using either VSIVSS with DWL or MEWMA charts in practice if cost minimization is of interest to the control chart user.

KW - Hotelling's T control chart

KW - Markov chain

KW - adjusted average time to signal (AATS)

KW - economic statistical design (ESD)

KW - genetic algorithm (GA)

KW - variable sample size and sampling interval (VSSVSI) scheme

UR - http://www.scopus.com/inward/record.url?scp=79951883854&partnerID=8YFLogxK

U2 - 10.1002/qre.1095

DO - 10.1002/qre.1095

M3 - Article

VL - 27

SP - 125

EP - 139

JO - Quality and Reliability Engineering International

JF - Quality and Reliability Engineering International

SN - 0748-8017

IS - 2

ER -