Assessment of Two Process Capabilities by Using Generalized Confidence Intervals and its Applications

In this article, we use Monte Carlo simulation study to calculate the generalized confidence interval of the difference between two recently proposed process capacity indices ( $$\mathcal S^{\prime }_{pk1}-{\mathcal {S}}^{\prime }_{pk2}$$ S p k 1 ′ - S p k 2 ′ ) when the underlying process follows a normal process distribution. Method of moment estimate is used to estimate the parameters of the process distribution. The proposed generalized confidence interval can be effectively employed to determine which one of the two processes or manufacturer’s (or supplier’s) has a better process capability. Also Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the generalized confidence intervals of ( $${\mathcal {S}}^{\prime }_{pk1}-\mathcal S^{\prime }_{pk2}$$ S p k 1 ′ - S p k 2 ′ ). The findings of the simulation demonstrated that as sample size rises, the mean squared errors decrease. To illustrate the generalized confidence intervals of the difference between two process capacity indices for improved supplier selection, three real data sets linked to the electronic industries are investigated.