Statistics in engineering

Statistics in Engineering and Science

The Role of statistics in Experimentation

Populations and samples

Parameters and Statistics

Mathematical and Statistical Modeling

Study of variation: construction of experimental designs and development of models

Measurement does not exclude qualities responses

Scatterplot: 2 dimensional graph of individual data values for pairs of quantitative variables

1. Statistical considerations should be included in the project design phase of any experiment

2. A statistical design should be selected that controls variation from known sources, allow the estimation of the magnitude of uncontrollable variation

Uncontrollable variation

Experimental error

Measurement error

When test conditions are changed

Arise from the inability to obtain exactly the same measurement on two successive test runs when experimental conditions are unchanged

3. Statistical analysis of the experimental results should allow inferences to be drawn on the relationships between the design factors and measurements

Population

All possible items possessing one or more common characteristics under specified experimental

Process

A repeatable series of actions that results in an observable characteristic

Variable

Characteristic on which information is obtained in an experiment

Observation

Collection of information in an experiment or actual values obtained

Response Variable

Result of an experiment

Factors

Controlled variables that influence the observed values of response variables

Sample

Group of observations taken from a population

Collected by a convenience sample, judgmental sampling, simple random sample, with or without replacement, systematic, stratified random samples, cluster sampling, and more.

Parameter

Numerical characteristic of population

Statistics

Numerical characteristic that is computed from a sample of observations

Distribution

The possible values of a variable along with some measure of how frequent they occur.

Sampling Distribution

Theoretical model that describes the probability of obtaining the possible values of a sample statistic.

Histograms

Construted by dividing the range of the data into several intervals, counting the # of observations in each interval and constructing a bar chart of the counts

Mathematical Model

Occurs when is derived from theoretical considerations that represent exact, error-free assumed relationships among the variables

Are poor descriptors of the physical systems because of the lack of accounting for the various types of errors included in statistical models

Statistical Model

Occurs when is derived from data that are subject to various types of specification, observation, experimental and measurement errors.