6. Distributions

This chapter is on distributions, a quantitative way to represent uncertainty.

6.1. Two Contexts

To ground this chapter, we will compare and contrast two case studies:

6.1.1. Context One: Materials Selection

  • Objective: Choose one material among several for a structural application (design question)

  • Consequences:

    • A poor early choice will lead to an underperforming design

    • Early decisions will lead to future investments, sinking cost into the given choice

    • Hard-to-quantify factors (such as manufacturability) may cause future economic headaches

Materials

Al 2024-T3

Al 7075-T6

Al 6061-T6

Fe 1040

Ti 6Al 4V

6.1.2. Context Two: Structural Sizing

  • Objective: Choose a size for a structural component (design question)

  • Consequences:

    • An oversized component will be too heavy, leading to a non-competitive design

    • An undersized component will be unsafe, leading to dangerous failures

A lower realized strength value is more unsafe; the part in question can handle less of a load.

A lower assumed strength value is more safe; we will offset a lower strength by building a larger structure, leading to a generally safer design.

To illustrate doing analysis and making decisions in this context, we will use the cast steel dataset.