On successful completion of this assignment, you will:
1. Know how to perform correlation and regression analyses on a set of given data and interpret the results.
2. Perform straightforward statistical inferences.
3. Practice the principle of risk-based approach to data analysis through a mathematically case study with analytical and numerical approaches.
4. Use the probabilistic-based method so derived to support decision making underuncertainty.
5. Be able to carry out your own literature research prior to solving engineering decision making problems (in the form of an independent learning project) and present the result with an in depth discussion.
The assignment forms the main part of the portfolio for the assessment of the module KB7044 which consists of elements of research linked to the teaching and learning of this module. You are also expected to carry out research related to data analysis and decision making. You willneed to demonstrate competency in two approaches of data analysis/modelling techniques to deal with variability and uncertainty through two given computation cases. In addition you will carry out an independent learning project involving modelling of a problem with uncertainty to support decision making.
Analytical Approach: Case 1
Company ABC designs and builds supporting structures for machinery. There have been a number of complaints about yielding (i.e. the actual stress of the section exceeds the yield stress of the material) of an important section of a given type of structure designed and built by the company. There is also a cause for concern for failure of the structure which will have a range of consequences from malfunctioning (reliability issues) to serious consequence leading to loss of lives and damage to both public and private properties (safety and risk issues). (Differences and similarities of reliability, quality and risk/safety are important and interesting areas for researchers and practitioners).
Your first task is to investigate if there is a reasonable degree of correlation between uncertainty and actual stress in the section. If there are reasons to believe that correlation exists between certain factors then a regression analysis needs to be performed. A sample consisting of 22 data items, which is shown in Table 1, is then collected.
Table 1: Data for Correlation & Regression Analysis
Organise/sort the data to see if patterns can be observed. Perform correlation and regression analysis on this set of data. Explain and interpret the results as clearly as possible.
Your second task is to look into variability in the yield stress of the material used. According to the supplier of the material, the yield stress of the material is 130 MPa. A sample consisting of 10 specimens have been prepared and tested. The results are shown in Table 2. Analyse the data by plotting histogram and/or x-y plot.
Question: Is there sufficient evidence to accept the manufacturer’s claim that the mean yield stress of the material is 130 MPa? What would you recommend? Do you have reason to suspect “noise” from the data set?
Table 2: Yield Test Result from the Sample
You then feel that the vague classification of uncertainty into three arbitrary categories,
although this serves the first task adequately well, does not fit very well with a rigorous riskbased modelling framework. The feasibility of this framework is to be illustrated with a “design case”. This proposed design case involves a given load, and the structure is to be designed using a given material.
The next logical task is to set up an analytical framework to model the process using a riskbased approach which aims to estimate the load and the capability of the structure in an attempt to obtain a rational and defensible solution. The concept of balancing load versus capability of structure is illustrated in Figure 1.
Figure 1: The Concept behind Risk-Based Approach to Structural Design