Statistical Analysis: Key Concepts and Applications

Fundamentals of Statistical Analysis

Frequency Distribution

Ungrouped Data

Ungrouped data are lists of observed values when the pooled data represent a mass of observed data.

Pooled Data

When data are grouped in a frequency distribution.

• Collect data and make a tally sheet

Determination of Range

The range is the difference between the highest observed value and the lowest value observed.

Determining the Range of Classes

The range of classes is the enactment between the midpoint of classes.

Determine the Midpoints of the Class

The midpoint of the class must include the minimum data value in that class.

Determine the Class Boundaries

The class limits are the extreme values or limits of a class and are called the upper limit and lower limit.

Identify the Frequency of Class

The number of values in each class is determined by the frequency column.

How the Histogram Describes the Variation in the Process

• Solve problems
• Determine process capability
• Compare with specifications
• Suggest how the populations
• Data indicate discrepancies

Histogram Analysis

The histogram can give information about the specific form of the frequency distribution for the population.

Median Central Tendency

Average

It is the sum of observations divided by the quantity of observations.

Ungrouped Data

It is the technique used when the data are not organized.

Pooled Data

When data are grouped in a frequency distribution.

Weighted Average

When several different frequency averages are combined, they accumulate in a weighted average.

Median

It is defined as the value that divides a set of observations arranged so that the number of elements above them is the same number of elements below them.

Mode

In a set of numbers, it is the value that occurs with the highest frequency.

Rank

In a series of numbers, it is the difference between the highest and lowest observations.

Standard Deviation

It is a numeric value whose units are those of the observed trend in the measured scattering data.

Relationship Between Measures of Dispersion

The range is a very common measure of dispersion and is used in one of the main control charts.

Asymmetry

It is a number whose magnitude indicates the degree of deviation from the symmetrical.

Kurtosis

Kurtosis is an adimensional value that is used as a measure of the peak height in a distribution.

Coefficient of Variation

It is a measure of how much variation exists in relation to the average.

Concept of Population and Sample

Sample: To present all the steel shafts similarly, collect data about the speed of cars.

The population may have a finite number of elements, such as the production of steel shafts in one day.

Relationship Between the Mean and Standard Deviation

Probability Plots

• Sort the data
• Rank the observations
• Calculate the position in the graph

Scatterplot

It is the easiest way to determine if a cause-and-effect relationship exists between two variables: to plot a scatter diagram.

Graphic Control Variables

Variation

The variation can be very large and significant, or it can also be very small.

There are 3 Categories of Change in Output

• Changes in the piece
• Changes between the workpieces
• Change from time to time

The Graphical Control Method

To indicate the observed variations in quality are more.

Objectives of the Variance Control Chart

• To improve the quality
• To determine process capability
• To take regarding specific sessions
• For the moment decisions about the process
• For decisions of the moment to articles

Techniques to Develop Control Charts

Procedural Steps

• Select the quality characteristic
• Choose the rational subset
• Collect the data
• Determine tentatively
• Establish centerline
• The goal