A precision-to-tolerance ratio model for the assessment of measurements uncertainty

• A Novel relationship between actual and observed process capabilities is presented.
• Process capability chances measured by an erroneous or perfect gauge is found.
• A novel γ–δ significance characteristic curve is introduced.
• Type I and Type II errors are computed in the χ2 and Cp domains.

Estimates of process capability indices are distorted by the presence of gauge measurement errors, a matter which results in two quality measures i.e., the actual and observed process capability indices (ACp and OCp). Gauge errors (Gauge uncertainty) add distrust to the measure data, as a result, one has to assure the accuracy of the gauge by conducting a gauge repeatability and reproducibility (GR&R) study. In this paper, we present novel relationships between the ACp and OCp using the precision-to-tolerance ratio (PTR) to assess the gauge as well as the process capability, simultaneously. Particularly, we will find the chances that an estimated process capability is measured by an erroneous or a perfect gauge. In addition, instead of using the strict threshold values of the PTR to judge the measurement gauge, a novel γ–δ significance characteristic curve will be introduced. The values of γ and δ will describe the accuracy of the measurement system while the critical process capability values/ratios will be computed in the so called χ2 and Cp domains. The introduced γ–δ curve symbolizes the PTR paradigm, here, the complications associated with the strict PTR thresholds used in the literature to judge the gauge capability will be avoided. The chances of having a measurement under the assumption of ACp distribution while it is the observed and vice versa will be established as type I and type II errors.To assess the descriptive merits of the proposed model and guidelines, two case studies from the literature of normally distributed data were addressed. The analysis showed that trustable gauge measurements cannot be proclaimed by just setting strict PTR values.