Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an application to Xbar and S2 charts

in Quality & Reliability Engineering International (2012)

Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, by a statistical criterion, an economic criterion or a joint ... [more ▼]

Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, by a statistical criterion, an economic criterion or a joint economic-statistical criterion. Each method has its strengths and weaknesses. One weakness of the methods of design listed above is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this paper, we explore multi objective models as an alternative for the methods listed above. These provide a set of optimal solutions rather than a single optimal solution and thus allow the user to tailor their solution to the temporal imperative of a specific industrial situation. We present a solution to a well known industrial problem and compare optimal multi objective designs to economic designs, statistical designs, economic statistical designs and heuristic designs. [less ▲]

Economic Statistical Design of a T2 Control Chart with Double Warning Lines

in Quality & Reliability Engineering International (2011), 27

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 ... [more ▼]

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. [less ▲]