Date of Award

Spring 2002

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Dileep Sule

Abstract

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival time is calculated from the curve. This estimator converges to the Product-Limit estimator (Kaplan and Meier, 1958) when a complete data set is available. Several measures of uncertainty are considered. Using a modification of the Bootstrap method (Efron, 1979) an estimate of both the random uncertainty from the data, and the vague uncertainty from the censoring in the data are calculated. In addition, this method allows for the incorporation of expert knowledge into the estimator and the weighting of data groups. In the latter situation, a group of units that has had much time in service is given larger weights and a group of units that have had little time in service is given smaller weights when making the estimates.

The estimator is tested under several circumstances. Data are generated from several distributions, the estimates are made, and the results are compared to the distribution parameter and estimates made using the Product-Limit Estimator.

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