Statistically Constrained Economic Design of a VSSI X-bar Control Chart Considering Taguchi Loss Function

In the economic design of control charts, traditional approaches often assume that quality loss remains constant once the quality characteristic surpasses the specification limits. This simplification overlooks the nuanced relationship between deviation magnitude and associated costs. With the increasing adoption of Taguchi’s quality loss function in product design, which quantifies loss as a continuous function of deviation from target values, there is a compelling need to integrate this perspective into control chart methodologies. This paper addresses this gap by developing an economic design framework for control charts that incorporates variable sample sizes and sampling intervals, guided by Taguchi’s quality loss function. The objective is to optimize control chart parameters to minimize the total quality-related costs, including sampling and quality loss costs. To efficiently determine the optimal parameters, a genetic algorithm is employed, with its settings fine-tuned using Taguchi’s orthogonal arrays to enhance convergence and solution quality. The proposed model is rigorously evaluated against traditional fixed sampling interval approaches. Results demonstrate that the variable sampling strategy, informed by Taguchi’s loss function, significantly improves cost efficiency and quality control effectiveness. This integration offers a more realistic and economically sound approach to control chart design, accommodating the continuous nature of quality loss and enabling dynamic sampling adjustments. The findings underscore the potential of combining advanced optimization techniques with robust quality loss modeling to advance statistical process control practices in manufacturing and service industries.

Keywords:

Genetic algorithm , Markov chain , Taguchi loss function , Variable sample size and sampling interval (VSSI) , X-bar control chart