Evolving parameters of Shewhart’s X¯ chart from present-day industrial engineering perspective

Sandeep and Arup Ranjan Mukhopadhyay

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5257-5283

Abstract: The implementation of control charts for controlling processes based on statistical principles often requires answering questions like what should be the sample size (n), the sampling interval (h), and the control limits’ multiplier (k). This work, inspired by Duncan and other authors like Gibra, I.N. and Saniga, E.M., etc., has evolved from certain practical considerations in an industry. Duncan in his economic design considered parameters like loss due to false alarm, the average cost of finding an assignable cause, the hourly cost of process control, and average income from in-control and out-of-control processes. However, the proposed model has considered additional parameters like production rate, sampling cost, sample preparation cost, testing cost, energy cost, consumables cost, and reporting cost from the perspective of production engineering. The economic model thus developed has been tailored to encapsulate the journey from Duncan to the contemporary period. The model has been appropriately optimized to determine n, h, and k. The effectiveness of the procedure has been demonstrated through numerical examples, comparative enumeration, and sensitivity analysis. The iterative algorithmic approach, adopted in this article, had yielded results in the context of real-life data. However, Duncan’s partial derivatives approach failed to do so. Considering the fact that the sample size (n) is an integer, the iterative algorithmic approach is the right methodological approach to be adopted. The work is expected to transcend the much-hyped divide between theory and practice in the parlance of statistical process control and Six Sigma.

Date: 2025
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DOI: 10.1080/03610926.2024.2435580

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