Evaluation of a novel loss-based process capacity index \({\mathcal {S}}^{\prime }_{pk}\) and its applications

Process capability indices (PCIs) are often used to assess process performance. Higher PCIs do not mean lower rejection rates. Thus, loss-based PCIs are better for process capability measurement. This study introduces a new capability index, \(\mathcal S^{\prime }_{pk}\) ${\mathcal{S}}_{\mathit{pk}}^{\prime }$ , based on a symmetric loss function for normal process, to include loss into capability analysis. We then estimate PCI \({\mathcal {S}}^{\prime }_{pk}\) ${\mathcal{S}}_{\mathit{pk}}^{\prime }$ employing six standard techniques of estimation and compare their mean squared errors (MSEs) through simulation analysis. For the index \({\mathcal {S}}^{\prime }_{pk}\) ${\mathcal{S}}_{\mathit{pk}}^{\prime }$ , asymptotic confidence intervals (ACI), generalized confidence intervals (GCI), and parametric bootstrap confidence intervals (BCIs) are used to construct confidence intervals . Monte Carlo simulation evaluates ACI, GCI, and BCIs average widths and coverage probabilities. Our experiments showed that MPSE produced the smallest width. \({\mathcal {B}}{\mathcal {C}}_p\) $\mathcal{B}{\mathcal{C}}_p$ -boot outperformed its competitors. For most sample sizes and estimation methodologies, \(\mathcal {P}\) $\mathcal{P}$ -boot has a greater CP. Two electronic industry data sets are evaluated to demonstrate the accuracy of the suggested estimating methodologies, ACI, GCI, and BCIs.