The development of a process capability index for non-normal processes naturally bound at zero

Process capability indices are used widely throughout U.S. industry to give a relatively quick indication of process capability in a format that is easy to compute and understand. The indices in current use all assume normally distributed data. Adaptations for skewed distributions have been derived for these indices, but these adaptations are not applicable to physically-bound processes whose target is the physical boundary. Zero-bound processes present an even greater challenge with regard to process capability quantification, due to difficulties in data modeling.; In this dissertation, a new process capability index {dollar}(Csb{lcub}pb{rcub}){dollar} and a new process performance index {dollar}(Csb{lcub}pu(ln){rcub}){dollar} are developed for non-normal zero-bound process dimensions. The lognormal distribution was selected for data modeling because of the unique relationship that exists between the lognormal and the normal distributions. {dollar}Csb{lcub}pb{rcub}{dollar} and {dollar}Csb{lcub}pu(ln){rcub}{dollar} were developed from this relationship and from lognormal quality control techniques developed by Morrison (1958) and Ferrell (1958). The normal-based index {dollar}Csb{lcub}p{rcub}{dollar} was used as the model for {dollar}Csb{lcub}pb{rcub}{dollar}, whereas the normal-based index {dollar}Csb{lcub}pk{rcub}{dollar} was used as the model for {dollar}Csb{lcub}pu(ln){rcub}{dollar}.; A significant result of this research lies in the fact that {dollar}Csb{lcub}pb{rcub}{dollar} and {dollar}Csb{lcub}pu(ln){rcub}{dollar} are also applicable to positively-skewed data with a natural lower boundary greater than zero, as well as negatively-skewed data with a natural upper boundary.