This paper considers a way of measuring a process capability index in order to obtain the geometric tolerance of a pattern of position elements according to the ASME Y14.5 standard. The number of elements present in the pattern, as well as its material condition (least LMC or maximum MMC), are taken into consideration during the analysis. An explicit mathematical model will be developed to identify the distribution functions (PDF and CDF) of defects on the location and diameter. Using these distributions and the Hasofer–Lind index, we will arrive at a new definition of process capability—meaning the value of tolerances that can meet the threshold of x% compliance. Finally, our method is validated using a variety of typical case studies.

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