Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Industrial and Manufacturing Systems Engineering


In the field of engineering valuation, life distributions are typically constructed on the basis of item values, rather than item counts. The fact that value and life are not independent leads to the observation that the univariate distributions used in previous research can not fully describe their relationship;In the first part of this study, F(t), the proportion of dollar surviving up to age t is formulated when the underlying joint distribution of value and life is bivariate lognormal of gamma;The second part of the study is concerned with the derivations of retirement ratios and the corresponding large sample covariance-variance structures of mortality data from a single vintage. When the value groups within the vintage are assumed to have the same multinomial life distribution, (i.e., the case of independence of value and age) it is shown that the retirement ratios for each age interval are nearly independent. Therefore, a weighted least square method involving only diagonal terms would be used in fitting linear models to retirement ratios;The third part of this study is devoted to modifying and/or applying results obtained in part two to the mortality data available to industrial firms;Special attention is given to geometric life distributions in the fourth part of the study. Mortality characteristic for long-lived property can be represented by the geometric distribution having small parameter p. Under this distributional assumption, covariances and variances of retirement ratios obtained in part two and three are much simplified;For long-lived property retirements, the ordinary and weighted least-squares estimators are compared for their efficiencies and biases. Examples of the calculations of efficiencies and biases for those estimators are given.



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179 pages