Efficient Handling of Empirical Probability Distributions in RAMS Models

Abstract

Performing reliability assessments always relies on utilizing data. Most often, this data is provided in the form of historic failure dates. To understand this data, models are used to derive reliability characteristics from it.

These models can be parametric, trying to describe the system by means of mathematical equations. They can also be empirical, letting the raw data describe the system without assuming a certain outcome.

Handling parametric models is convenient, as they are described by often just one value. Empirical probability distributions are built on all available data and hence requires them to be fully defined. Handling this amount of data is cumbersome.

Part of this thesis is proposing different methods to represent the empirical reliability estimator. These representations try to combine convenient usage while keeping accuracy.

Representing the empirical reliability graph by a reduced amount of linear segments is proposed and discussed. This is an efficient way to compress huge datasets to a low number of descriptive points to interpolate in.

Furthermore, the feasibility to use polynomial regression on the empirical probability distribution is evaluated.

The computational efficiency of all methods is compared. For all practical purposes, the time to retrieve a reliability estimate is negligible.

Parametric and empirical approaches are applied to various datasets and the results discussed. The empirical methods outperform the exponential estimator in all cases.

The given experiment hypothesis is validated on each of the four experiments: The empirical probability distributions do match sufficiently well the reference reliability and the computational efficiency is negligible for all practical purposes.