<p>This study utilizes the parametric interval estimation of the difference between two new process capability indices, denoted by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\delta }^{{\prime}{\prime}}=\left({S}_{pk1}^{^{\prime\prime} }-{S}_{pk2}^{^{\prime\prime} }\right),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>δ</mi> </mrow> <mrow> <mo>′</mo> <mo>′</mo> </mrow> </msup> <mo>=</mo> <mfenced close=")" open="("> <mmultiscripts> <mi>S</mi> <mrow> <mi>p</mi> <mi>k</mi> <mn>1</mn> </mrow> <mmultiscripts> <mrow /> <mrow /> <mo>″</mo> </mmultiscripts> </mmultiscripts> <mo>-</mo> <mmultiscripts> <mi>S</mi> <mrow> <mi>p</mi> <mi>k</mi> <mn>2</mn> </mrow> <mmultiscripts> <mrow /> <mrow /> <mo>″</mo> </mmultiscripts> </mmultiscripts> </mfenced> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> to select the better of the two processes or manufacturers (or suppliers) through a simulation study when the underlying process follows a normal distribution. It is quite tedious to obtain the sampling probability theory of δ″; therefore, it cannot be inferred statistically. Thus, we use a generalized confidence interval and a parametric bootstrap confidence interval to determine which of the two processes or manufacturers (or suppliers) has a better process capability. In this paper, we use moment estimators to estimate the parameters of the process distribution. Monte Carlo simulation has been conducted to investigate the estimated relative coverages, coverage probabilities, and average widths of the generalized confidence interval and bootstrap confidence interval of δ″. Finally, four real data sets related to electronic industries are re-analyzed to illustrate the generalized confidence interval and bootstrap confidence interval of the difference between two process capability indices for selecting the better process or manufacturer (or supplier).</p>