Chapter 24 - Random Variables and Uncertainty Analysis

Abstract

This chapter discusses random variables and uncertainty analysis. The chapter presents the basics of statistical description of random variables that are the foundation for reliability analysis. Measures of uncertainties are discussed. Loads and capacity of ship structures are used to illustrate the uncertainty analysis. All the variables in the engineering structures are stochastic to a certain degree. Structural reliability analysis deals with the rational treatment of random variables and uncertainties in the 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 also their distribution types. In some cases, the correlation between variables exists, e.g., the two parameters used to describe Weibull long-term stress distribution. This chapter discusses random variables, which may be used to describe the uncertainties in the basic variables such as spatial and time variation of external loads, material properties, dimensions, etc. 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 uncertainty, measurement uncertainty, statistical uncertainty, etc. Uncertainty in ship structural design, uncertainties in loads acting on ships, and uncertainties in ship structural capacity are also discussed in this chapter, which may contribute to the operation of a ship.