Essays on Capability Indices for Autocorrelated Data

Abstract: The use of process capability indices in the industry is traditionally based on the assumptions that a sample from a process are observations on independently, identically and normally distributed random variables, IIN. However, all three assumptions are open to discussion and in this thesis, the estimation of the indices is studied when the assumption of independence is not fulfilled.In five reports, the indices Cpk and Cpm are studied, and instead of random samples, samples are regarded as observations on a time series.In the first four reports, each index is studied for either an AR(1) or an MA(1) process and the fifth report, both indices are studied for a general ARMA(p,q) process.In all reports, alternatives to Cpk and Cpm are suggested as well as point and interval estimators for the suggested indices. The accuracy of interval estimators are evaluated through large Monte Carlo simulations and the difference between empirical coverage rates and nominal confidence limits are calculated.It was found in all reports that a dependency among observations has a great impact on the coverage rates. The coverage rate difference depends on both the size of the autocorrelation and the type of time series model and for the original Cpk and Cpm the difference can be large. With the suggested alternative indices, however, the differences are always reduced and unless the autocorrelations are close to ±1, the sizes of differences are of little consequence.