Quantitative Methods in Environment and Safety

« Return


Learning goals (LG)
1. Understand concepts relative to exploratory data analysis
2. Understand the basis of sampling theory
3. Understand hypothesis testing procedures
4. Widen the concepts of correlation and regression to generalized linear models (GLM)
5. Recognize classification and ordination methods
6. Understand the use of questionnaires
7. Develop a framework for concepts related to reliability
8. Distinguish constant and variable failure modes
9. Identify typical survival curves
General (GS)
1. Team work
2. Search literature and write synthesis
3. Write a technical report
Specific (CSS)
1. Develop statistical reasoning
2. Suggest procedures for data treatment
3. Calculate sample size
4. Apply hypothesis testing
5. Calculate correlations, regressions and GLM
6. Apply classification and ordination methods
7. Analyze reliability of questionnaire scales
8. Simulate random variables used in reliability
9. Calculate and discuss reliability and maintenance


1. Exploratory data analysis
Distributions and tables
Statistics and charts
2. Sampling
Confidence intervals
Number of samples and error margin
3. Hypothesis testing
Comparison of two or k samples
Parametric and non-parametric tests
4. Correlation, regression and GLM
Correlation and simple linear regression
Multiple regression
Maximum likelihood
Hierarquical models
5. Classification and ordination methods
Cluster analysis
Discriminant analysis
Principal component analysis
6. Questionnaires
Structure of a questionnaire
Scale validation
7. The concept of reliability
Different aspects of reliability
Reliability and statistics
8. Random variables

Negative exponential and Weibull distributions
9. Equipment association
Block diagramme
Configurations and redundancy
10. Human reliability
Human errors, consequences and categories
Error versus verification/inspection costs
11. Availability of repairable systems
Availability and maintenance
Failure and repair rates

Teaching Methodologies

This subject is organized in two parts, Statistics (20 h) and Reliability (25 h). Lectures are used to introduce learning themes. Concepts and definitions are presented succinctly. Teaching of statistics recipes is avoided, but concrete application of tools and simulations is favored. Examples are explored and problems are solved in order to consolidate knowledge and to develop skills. Classes occur in a computer room and tutorial files with instructions are used as well as data files and files with expected results. Assessment includes answering an individual questionnaire about reliability and the writing of a report (groups of 1-3 students) about statistics, aiming to develop and assess several skills (GS1-GS3). The questionnaire includes all reliability topics and some of the taught examples. In the report, three of the taught themes are developed.


Afonso, A. & C. Nunes (2011). Estatística e probabilidades: aplicações e soluções em SPSS. Escolar Editora,
Lisboa, 554 pp.
Gotelli, N. J. & A. M. Ellison (2004). A primer of Ecological Statistics. Sinauer Associates, Inc., Sunderland, 510 pp.
Heeringa, S. G., B. T. West, P. A. Berglund (2010). Applied survey data analysis. Chapman & Hall/CRC, Boca Raton,
FL, 467 pp.
Hill, M. M., A. Hill (2009) Investigação por questionário, 2ª ed. Edições Sílabo, Lisboa, 377 pp.
Oliveira AG (2008) Bioestatística, Epidemiologia e Investigação. Teoria e Aplicações. LIDEL, Lisboa, 255 pp.
Qian S.S. (2010) Environmental and ecological statistics with R. Chapman & Hall/CRC, Boca Raton, 421 pp.
Reis E (2001) Estatística multivariada aplicada. 2ª Edição. Edições Sílabo, Lisboa.
Smith, David J. (2011) Reliability, maintainability and risk: practical methods for engineers, 8th ed. Elsevier, Amsterdam, 440 p.

Zuur A.F., E.N. Ieno & G.M. Smith (2007) Analysing ecological data. Springer, New York, 672 pp.



ECTS Credits



  • Teóricas - 35 hours