Application of a three-parameter Lindley distribution in quality control

Statistical quality control in industries enables businesses to improve product quality, reduce defects, optimize processes, increase customer satisfaction, and gain a competitive edge in the market. It provides a systematic and data-driven approach to quality management, enabling industries to consistently deliver high-quality products and services while driving continuous improvement across all operations. This paper examines the applications of the Harris extended modified Lindley distribution, a generalization of the well-known Lindley distribution. We demonstrate the practical utility of this distribution in the field of quality control. Using the lifetime distribution, an acceptance sampling plan is devised that can determine whether a large batch of products submitted for inspection should be accepted or rejected. The operational characteristic functions that were generated allow for a greater understanding of the performance of the sampling plan. Computed tables show sample sizes and parameters in the article. To demonstrate the efficacy of the proposed methodology, two distinct datasets pertaining to the ordered product failure times of a software development project and ball bearing failure times are utilized.