Engineering Statistics

Engineering StatisticsKANCHALA SUDTACHAT

Statistics Deals with CollectionPresentationAnalysis and use of data to make decision Solve problems and design products and processes

Can be powerful tool forDesigning new products and systems Improving existing designDesigning, developing and improving production

processes

Variability

Collecting Engineering DataRetrospective Study Would be either all or a sample of the historical process

data.

Observational StudyWould be either observations of process or population.Are usually conducted for short time period.

Designed ExperimentsCollect the observations of the resulting system output

data.

Random Samples Statistical methods work correctly and produce valid

results. Random samples must be used. Each possible sample of size n has an equally likely

chance of being selected.

Chapter 2Data Summary and PresentationKANCHALA SUDTACHAT

Content1. Random Sampling

2. Stem-And-Leaf Diagrams

3. Histograms

4. Box Plots

5. Time Series plots

6. Multivariate Data

8

Population and SampleProbability(sampling)

Inference(predict)

Population

Parameters:, , r, etc.

Sample

Statistics:x, s, p, r, etc.

Data Summary and Display

Sample mean

Population mean

Example 2.1

Sample Variance and Sample Standard Deviation

Population variance

Stem-And-Leaf DiagramsStem-And-Leaf Diagrams is a good way to obtain an informative visual display of a data.Each number consists of at least two digits.Steps for constructing

1. Divide each number into two parts: a stem, and a leaf.2. List the stem value in a vertical column.3. Record the leaf for each observation4. Write the units for stems and leaves on the display

Example 2-4

Example 2-4

HistogramsUse the horizontal axis to represent the measurement scale for the data.

Use The Vertical scale to represent the counts, or frequencies.

Example 2-6

Pareto ChartThis chart is widely used in quality and process improvement studies.

Data usually represent different types of defects, failure modes, or other categories.

Chart usually exhibit “Pareto’s law”

Example 2-8

Example 2-8

Box PlotDescribes several features of a data set, such as center, spread, departure from symmetry, and identification of observations.

The observations are called “outliers.”

The box encloses the interquartile range (IQR) with left at the first quartile, q1, and the right at the third quartile, q3. A line, or whisker, extends from each end of the box.

The lower whisker extends to smallest data point within 1.5 interquartile ranges from first quartile.

The upper whisker extends to largest data point within 1.5 interquartile ranges from third quartile.

Box Plot

Example63, 88, 89, 89, 95, 98, 99, 99, 100, 100

A lower quartile of Q1 = 89

An upper quartile of Q3 = 99

Hence the box extends from 89 to 99 and the interquartile range IQR is 99 - 89 = 10.An outlier is any data point that is more than 1.5 times the IQR from either end of the box.1.5 times the IQR is 1.5*10 = 15 so, at the upper end an outlier is any data point more than 99+15=114.There are no data points larger than 114, so there are no outliers at the upper end.At the lower end an outlier is any data point less than 89 - 15 = 74. There is one data point, 63, which is less than 74 so 63 is an outlier.

Time Series Plots

Multivariate Data The corrected sum of cross-products

Scatter DiagramsDiagram is a simple descriptive tool for multivariate data.

The diagram is useful for examining the pairwise (or two variables at a time) relationships between the variables.

Example

Example: Scatter diagrams and box plots

Scatter diagrams Scatter diagrams for different values of the sample correlation coefficient r

Questions?