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

Abstract

Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, 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 is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this article, we explore multiobjective models as an alternative for the methods listed. 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 multiobjective designs with economic designs, statistical designs, economic statistical designs, and heuristic designs.

Monitoring the process mean based on attribute inspection when a small sample is available

“…Some contributions have employed genetic algorithms to plan x-bar charts. For example, Noorossana and Toosheghanian (2012) used a genetic algorithm to plan variable sampling interval (VSI) X-bar control charts; Faraz and Saniga (2013), to design X-bar and S 2 charts; and Costa and Machado (2012), to plan a wandering process mean.…”

Joint X- and S2 Control Charts Optimal Design Using Genetic Algorithm

“…References [1][2][3][4][5] among other references designed their control charts based on the SD. The drawback of this design is that it does not account for the economic consequences of the design because the main focus of this design is to enhance the statistical properties of the SPC and this usually happens at the expense of the economic aspect.…”

The guaranteed adaptive c‐charts with estimated parameter

“…The traditional method for implementation of control charts is to apply a fixed ratio sampling scheme in which samples of fixed size are obtained at constant intervals to monitor a process. The control limits are designed such that a desired in‐control performance is obtained (Faraz and Saniga). With respect to the significance of control charts in improving the quality of products and processes, over the past few decades, different methods have been proposed to improve their performance, such as variable sampling intervals (VSI), variable sample sizes (VSS), variable sample sizes and sampling intervals (VSSI), variable parameters (VP), and double sampling.…”