Date of Award
Doctor of Philosophy (PhD)
Information Systems and Decision Sciences (Business Administration)
The current popularity of the process capability index, a measure of a supplier's ability to meet the product specifications demanded by a customer, has become a matter of some controversy. While admitting the validity of much existing criticism, this research demonstrates that sample estimation of the triple index (Cpl, Cp, Cpu), a variant of the widely used index pair (Cp, Cpk), is equivalent to estimation of the natural parameters (mu, sigma) whenever the measured process characteristic X has an unconditional (marginal) normal probability density function. This includes processes which obey the strictly stationary, normal ARMA( p, q) model. By this extension to stationary normal models beyond ARMA(0, 0), the author shows the continued viability of the process capability index as a decision making tool of wider applicability. Estimators of the indices (Cpl, Cp, Cpu) are studied under conditions of both sample independence and sample autocorrelation. A new method for determining a joint confidence region for the triple index (Cpl, Cp, Cpu) is given. The region presented is, both conceptually and computationally, more direct than previously known approaches.
Magee, Lawrence Lee, "The Effects of Autocorrelation in the Estimation of Process Capability Indices." (1998). LSU Historical Dissertations and Theses. 6847.