**Module code:** DIP50

**ECTS Credit Points:** 30

**Module Type:**Compulsory

**Year:** 1st

**Language:**

**Greek**

**Module general description:**

Probability

Probability models and probability, the scope of statistics, the role of probability in statistics. Basic probability theory, interpretations and definitions of probability, probability space and events, axiomatic foundation and basic laws, symmetric experiments and combinatorial analysis, conditional probability. Random variables and characteristics of their distributions, random variables and univariate distributions, joint discrete and continuous distributions, idepedence, descriptive measures of distributions, the mean of a random variable and of a function of a random variable, other descriptive measures of univariate and bivariate distributions, useful inequalities. Useful probability models, the binomial, hypergeometric geometric, negative binomial and Poisson distributions, the Poisson process, the normal distribution, the exponential distribution and applications of reliability, the uniform, lognormal, gamma, Weibull, and bivariate normal distributions, use of the Minitab statistical package.

Statistics

Methods of descriptive statistics, data types and data collection, description of the distribution of a data-set, arithmetic measures, histograms, the stem and leaf diagram, the quantile plot, box plots, graphics for attribute data, comparison of distributions of two data sets, graphics for the appropriateness of theoretical distributions. Sampling distributions, statistical functions and their distributions, the sample mean and its distributional properties, sampling from the Bernoulli and the Poisson population, sampling from a normal population, the chi-squared the t and the F distribution. Parameter estimation and testing hypotheses, point estimation, criteria and desirable properties of estimators, basic characteristics of confidence intervals and tests, tests of hypotheses and tests of significance, operating characteristic curve and power of the test, confidence intervals and tests for the mean of a population and for the difference of two population means with the use of independent samples, estimation and testing of the mean-difference with paired samples, confidence intervals and tests for a single proportion and for the difference of two proportions with independent and large samples, confidence intervals and tests for the variance and the standard deviation of a normal distribution, estimation and testing for the ratio of variances of two normal distributions with independent samples. Regression analysis, regression models and their utility, simple linear regression, correlation analysis, multiple linear regression, fitting, hypothesis testing, estimation of a mean and prediction of a future observation, stepwise regression. Introduction to the theory of errors and the statistical analysis of measurement systems, measurement errors and properties of measurement systems, evaluation of repeatability and reproducibility, formulae of random-error propagation. Use of the Minitab statistical package

Quality Control Techniques, Statistical Quality Control and Sampling

Introduction to metrology and calibration, measurement systems, instruments, standards and errors of measurement, metrology, the calibration of instruments and quality assurance, measurement instruments for length, measurement instruments of mass, uncertainty of measurement.

Introduction to statistical quality control, histograms, cause and effect diagrams, Pareto analysis, check sheets, flow charts, a brief presentation of the main control charts for attributes and variables, other tools for statistical quality control, use of the Minitab statistical package.

Acceptance sampling for attributes, simple sampling and characteristic curve, rectifying sampling, the MIL_STD-105E (ANSI-ASQC Z1.4), acceptance sampling for variables, the MIL-STD-414 (ANSI/ASQC Z1.9), use of the Minitab statistical package.

**Learning Outcomes:**After completing this module, students are expected to be able to,

1. identify the basic elements of a probability model and use laws of the axiomatic theory of probability to find unconditional and conditional probabilities.

2. describe univariate and bivariate probability distributions and calculate probabilities, moments and descriptive measures for specified distributions.

3. select appropriate probability models in order to describe the variability of measurable quality characteristics and calculate probabilities and percentiles of well-known distributions by means of formulae, tables or the Minitab statistical package.

4. use descriptive measures and graphical procedures to perform exploratory data analysis.

5. identify proper statistics and their corresponding sampling distributions for estimation and tests relating to means, proportions and variances of performance characteristics.

6. find confidence intervals and perform tests of hypotheses in one and two-sample problems.

7. apply simple and multiple linear regression analyses, correlation analysis and methods of selecting an appropriate model.

8. distinguish the categories of measurement errors, apply the laws of propagation of random and systematic errors and estimate the variability due to repeatability, reproducibility, and the uncertainty of measurement.

9. understand the function of measurement systems and measuring instruments, select an instrument based on its metrological characteristics and explain the process of calibration and the associated documents.

10. apply the 7 main tools of statistical quality control, understand the application of 15 additional tools and select the appropriate tool for confronting specific problems.

11. select, construct and interpret the proper control chart to monitor a process.

12. design plans of acceptance sampling for attributes, interpret characteristic curves and apply appropriate standards (MIL-STD-105E, ANSI/ASQC Z1.4, etc).

13. determine sampling plans for variables and apply the system MIL-STD-414 (ANSI/ASQC Z1.9).

**Subjects covered:**

1. Probability and Statistics

2. Quality Control Techniques

3. Statistical Quality Control

4. Sampling

**Learning Material:**The HOU publications can be viewed here.

**Teaching Method:**Distance education with five Contact Sessions held at weekends during the academic year

**Evaluation:**Completion of five written assignments during the academic year, the average grade of which constitute a 30 percent of each student's grade, if a pass is obtained in the final or repetitive examination. Final exam grades constitute a 70 percent of the students' final course grade. More information is available here.