Struggling with quality control for products with uneven requirements? This paper introduces a new statistical index for measuring process capability when tolerances aren't symmetrical around a target value. It builds upon existing indices like Cpm, which are used to assess how well a production process meets specified limits, but extends them to handle situations where the upper and lower bounds for acceptable variation are different distances from the ideal value. The proposed index, denoted as a new generalization of Cpm, not only considers how close the process is to the target but also accounts for the asymmetry of the specification limits. The study also investigates the statistical properties of the natural estimator of the new generalization, assuming the process follows a normal distribution. This research offers a practical tool for industries seeking to improve quality control. By providing a more accurate assessment of process capability in asymmetric tolerance scenarios, the new generalization helps manufacturers make informed decisions about process adjustments and optimization. This can lead to better product quality, reduced waste, and increased efficiency in various manufacturing settings.
Appearing in the International Journal of Reliability, Quality and Safety Engineering, this paper directly aligns with the journal's focus on methods for enhancing reliability and quality in engineering processes. The introduction of a new capability index to handle asymmetric tolerances fits well within the journal’s scope. By focusing on improving process control through statistical methodologies, the research is relevant to the engineering community.