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

Abstract

Recent studies have shown that enhancing the common T 2 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 T 2 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.

Statistical Merits and Economic Evaluation of T2 Control Charts with the VSSC Scheme

“…Faraz et al [8] and Faraz and Saniga [31] studied economic statistical design of VSS T 2 and DWL T 2 control charts based on the cost model proposed by Lorenzen and Vance [12]. The significant contribution of the present paper is the combination of the Costa and Rahim [1] cost model and the ESD of the VSSC scheme that is currently absent in the literature.…”

Considering Taguchi loss function on statistically constrained economic sum of squares exponentially weighted moving average charts

“…Therefore, the use of a GA is an effective optimization methodology, and it has been successfully applied in the design optimization problem of quality control charts. [24,25,30] The steps in the GA optimization approach are briefly described as follows:…”

“…Chen and Pao [29] considered the joint economic-statistical design ofX and R control charts under assumption that the quality characteristic follows a non-normal distribution. Faraz and Saniga [30] investigated the economic-statistical design of a T 2 control chart with double warning lines. Concerning the use of employing an EWMA statistic on an economic-statistical model, Montgomery et al [31] presented a economicstatistical design of EWMA control charts to monitor the process mean.…”

Economic‐Statistical Design of Acceptance Control Chart

“…developed the economic‐statistical design model for the chart when in‐control times follow a Gamma ( λ ,2) distribution. Some recent works an economic‐statistical design of control charts are as follows: Kim et al ., Torng et al ., Chen et al ., Celano, Faraz, and Yin et al …”