Process capability indices are a very helpful tool, used mostly in the manufacturing industry to assess the performance of a monitored process. Quantifying the proportion of conforming items within a specified tolerance interval is often essential. In this paper, we estimate the confidence interval (CI) of the generalized process capability index (GPCI) \(C_{py}\) , proposed by Maiti et al. (2010), using a fiducial approach when the quality characteristics of interest follow a location-scale distribution or transformable to a location-scale distribution such as log location-scale distribution. We discuss the cases of four important distributions: normal, lognormal, Weibull and gamma distribution. We also estimate the CI of the difference between two GPCI, \(\delta _{py}=C_{py1}-C_{py2}\) using the fiducial approach. Fiducial pivotal quantities (FPQ) are proposed based on the maximum likelihood estimator (MLE). The performance of the proposed fiducial generalized confidence interval (FGCI) is compared with three non-parametric bootstrap confidence intervals namely standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB) in terms of coverage probability (CP) via Monte Carlo simulation. Comparison results indicate that the proposed fiducial generalized confidence interval outperforms the comparison. Two examples are provided to illustrate the application of the proposed confidence interval.
