In a stochastic PERT network, the uncertainty importance measure of an activity (UIMA) is used to identify those that deserve high attention in reducing the magnitude of the uncertainty in the project completion time. Similarly, in a fault tree analysis, the uncertainty importance measure of a basic event (UIMB) is used to identify basic events that contribute appreciably to the uncertainty of the top-event probability.
This thesis is concerned with development of the UIMA and UIMB for analyzing stochastic PERT networks and fault trees, respectively.
We define the UIMA as the ratio of the net variability due to the uncertainty of an activity duration to the total variability of the project completion time, and develop a method for evaluating the measure under the assumption that the duration of an activity is independently and symmetrically distributed. Similarly, we define the UIMB as the ratio of the net variability due to the uncertainty of log-scaled basic-event probability to the total variability of the top-event probability, and develop a method for evaluating the measure in a robust manner under the assumption that all basic events are statistically independent and each basic-event probability follows a lognormal distribution.
Each of the proposed methods for evaluating the defined UIMA and UIMB utilizes the Taguchi tolerance design technique with modifications considering the characteristics of stochastic PERT networks (e.g., the effect of an activity duration on the project completion time, and interactions between activity durations) and fault trees (e.g., unstable estimates of UIMB due to the unrobustness of variance estimates of basic-event probabilities). Then, the contribution ratio calculated by each method evaluates the effect of the variability of a factor (i.e., an activity duration or a basic-event probability) on the variability of a system characteristic (i.e., project completion time or top-event probability), and is used as the estimate of the UIMA or UIMB.
The proposed methods are easy to use and, in particular, computationally efficient for large-sized stochastic PERT networks and fault trees as compared to other existing methods which require Monte Carlo Simulation.
