Chapter 33 - Random Variables and Uncertainty Analysis

Abstract

This chapter discusses random variables and uncertainty analysis. The chapter presents the basics of statistical description of the random variables that are the foundation for reliability analysis. Measures of uncertainty are discussed. Loads and capacities of ship structures are used to illustrate uncertainty analysis. All variables in engineering structures are stochastic to a certain degree. Structural reliability analysis deals with the rational treatment of random variables and uncertainties in structural engineering design, inspection, maintenance, and decision-making. The corresponding probability distributions can be defined, based on statistical analyses of available observations of the individual variables, providing information on their mean values, standard deviations, correlation with other variables, and in some cases distribution types. In some cases, correlation between variables exists—for example, the two parameters used to describe the Weibull long-term stress distribution. This chapter discusses random variables that may be used to describe uncertainties in basic variables, such as spatial and time variation of external loads, material properties and dimensions, under the subdivisions of statistical descriptions and probabilistic distributions. Uncertainty in ship structural design is explained with the objective to discuss the uncertainties in loads and strength. For the purpose of reliability analysis, the uncertainties may be classified as inherent, measurement, statistical, and other uncertainties. Uncertainties in ship structural design, loads acting on ships, and ship structural capacity that may contribute to the operation of a ship are also discussed in this chapter.