Development of X¯ control chart for non – normal variables with Additive Exponential shocks – a cost perspective

• Published in: Results in engineering Vol. 25; p. 103986
• Main Authors: Kalisetti, Yogendra, Kraleti, Srinivasa Rao, Katneni, Nirupama Devi
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2025
• Subjects: Additive exponential distribution; Design of X̄ control chart; Industrial experimentation; Non-normal variates; Sensitivity analysis; Design of X̄ control chart; Industrial experimentation; Additive exponential distribution; Sensitivity analysis; Non-normal variates
• ISSN: 2590-1230; 2590-1230
• DOI: 10.1016/j.rineng.2025.103986

•X¯Control Chart for Non-normal Data: The study introduces a new and novel X¯ control chart designed for processes characterized by non-normal quality variables for which the skewness and kurtosis include different patterns characterized by Jhonson Distribution.•Additive Exponential Distribution in Shock Model: In-control times are modeled by the Additive Exponential distribution, which is the sum of two exponential random variables with different parameters one for natural assignable causes and the other for man-made assignable causes.•Cost Optimization with Economic and Statistical Integration: The model integrates the economic and statistical design to optimize the control chart's design parameters by minimizing the average cost per unit of time subject to the conditions on Type I and Type II error probabilities.•Optimization via Lingo Software: The Grid Search Method of LINGO Computer Package 20.0 for Non-Linear Programming Problem is used to derive the optimal design parameters for the X¯ control chart.•Sensitivity Analysis for Robustness: The paper examines the impact of the Additive Exponential shocks under non-normal variables for in-control and out of control times on chart performance through sensitivity analysis, demonstrating the chart's flexibility and efficacy across various industrial contexts. The Additive Exponential Distribution plays a vital role in analyzing datasets arising from industrial experimentation, where control charts are the primary tool utilized. Control limits (k), sampling interval (h), and sample size (n) are crucial for obtaining the optimal design parameters in control charts. An Economic Statistical Design of control charts with a suitable probability distribution for quality characteristics and process in-control times is necessary. Hence, in this paper, we presume that the quality feature X¯ adheres to a Johnson distribution, which models the quality characteristic with different values of skewness and kurtosis for non-normal variates, and that the process in-control times follows an Additive Exponential Distribution. The beauty of the Additive Exponential Distribution lies in its ability to characterize the in-control times of the process. The in-control time is the sum of two random times that are exponential with different parameters: one for natural shocks and the other for man-made shocks. The average cost per unit time is determined by using cost perspectives. By fixing the α and β, the optimal design parameters for the X¯ control chart are derived and analyzed. A sensitivity analysis is carried out. This chart is suitable for manufacturing processes such as chemical, glassware, paints, and seafood industries, where the variable under study is non-normal and the in-control times are subject to the sum of two exponential variates. Mathematics Subject Classification System (MSC2020): 90C30, 62P30