Nonparametric Confidence Limits of Quantile-Based Process Capability Indices

<table>Simulated kernel density curves of various PCIs using different sample sizes based on  Weibull process with shape parameter <svg height="16.6625" id="M250" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 49.612499 16.6625" width="49.612499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5
t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z" id="x1D6FD"></path></g><g transform="matrix(.017,-0,0,-.017,14.647,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,29.351,12.162)"><use xlink:href="#x33"></use></g><g transform="matrix(.017,-0,0,-.017,37.511,12.162)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,41.386,12.162)"><use xlink:href="#x32"></use></g>
</svg> and scale parameter <svg height="12.4375" id="M251" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 36.174999 12.4375" width="36.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123
t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" id="x1D703"></path></g><g transform="matrix(.017,-0,0,-.017,13.237,12.162)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,27.94,12.162)"><use xlink:href="#x37"></use></g>
</svg>.</table>

Journal of Quality and Reliability Engineering

fig2

Figure 2

Figure 2: Nonparametric Confidence Limits of Quantile-Based Process Capability Indices 