A New Loss Function Based on BURR XII for Using Risk Estimation
DOI:
https://doi.org/10.23055/ijietap.2025.32.1.10167Keywords:
Burr XII distribution, quality loss functions, risk function, inverted probability loss functionsAbstract
Achieving a competitive advantage in today's fast-paced and globally competitive business environment is one of the main goals for organizations across all industries. To attain this, businesses must adopt effective strategies and tools to enhance their operational efficiency, product quality, and overall customer satisfaction. One of the most significant tools that can help businesses achieve this goal is the implementation of quality control methods. Quality control not only ensures that products and services meet predefined standards but also helps reduce costs, increase customer loyalty, and maintain a sustainable competitive edge. In recent years, the importance of loss functions in quality assurance has grown considerably. Loss functions are used to quantify the deviation of a product's performance or quality from its desired target, translating this deviation into a monetary loss. This concept enables businesses to assess the broader impact of poor quality, not only on the organization but also on society as a whole. The monetary value of the loss represents the cost associated with a product's failure to meet expectations, including customer dissatisfaction, warranty claims, and potential reputational damage. Advancements in statistical methodologies, particularly those involving inverted probability density functions (PDFs), have opened new avenues for the application of loss functions. Inverted PDFs allow for a more detailed understanding of quality-related losses. This paper introduces the Inverted Burr XII Loss Function (IBXIILF) as a novel member of the inverted probability loss function family. The IBXIILF provides a robust framework for evaluating and minimizing quality-related losses in various industrial settings. The performance and applicability of the IBXIILF are demonstrated through a comparative study and an industrial example, highlighting its practical relevance and effectiveness in monitoring losses.
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