Sarwar Muhammad Atif, Hanif Muhammad, Albogamy Fahad R, Nabi Muhammad
COMSATS University Islamabad-Lahore Campus, Lahore, Pakistan.
National College of Business Administration and Economics, Lahore, Pakistan.
Sci Rep. 2024 Dec 27;14(1):30640. doi: 10.1038/s41598-024-83780-y.
Control charts are commonly used for process monitoring under the assumption that the variable of interest follows a normal distribution. However, this assumption is frequently violated in real-world applications. In this study, we develop an adaptive control chart based on the exponentially weighted moving average (EWMA) statistic to monitor irregular variations in the mean of the Truncated Transmuted Burr-II (TTB-II) distribution, employing Hastings approximation for normalization. We propose a continuous function for the adaptation of the smoothing constant. The performance of the proposed TTB-II distribution is compared with multiple existing distributions, including TB-II, TB-III, TB-XII, B-II, B-III, and B-XII, to demonstrate its competitive advantages. The run-length profiles, including the average run-length (ARL) and the standard deviation of run-length (SDRL), are computed under various parameter settings. The effectiveness of the proposed chart is evaluated using Monte Carlo (MC) simulations in terms of run-length profiles. The practical implementation of the proposed chart is demonstrated with a real dataset, illustrating the design and application procedures.
控制图通常在感兴趣的变量服从正态分布的假设下用于过程监控。然而，在实际应用中，这一假设经常被违反。在本研究中，我们基于指数加权移动平均（EWMA）统计量开发了一种自适应控制图，以监测截断变换布 Burr-II（TTB-II）分布均值的不规则变化，并采用 Hastings 近似进行归一化。我们提出了一个用于调整平滑常数的连续函数。将所提出的 TTB-II 分布的性能与多个现有分布进行比较，包括 TB-II、TB-III、TB-XII、B-II、B-III 和 B-XII，以展示其竞争优势。在各种参数设置下计算运行长度分布，包括平均运行长度（ARL）和运行长度的标准差（SDRL）。使用蒙特卡罗（MC）模拟根据运行长度分布评估所提出控制图的有效性。用一个真实数据集展示了所提出控制图的实际应用，说明了设计和应用程序。
