Lean six sigma process improvement tools and techniques by donna summers chapter 17

• Measurement error is considered to be the difference between a value measured and the true value.. • A frequency diagram shows the number of times each of the measured values occur

Chapter 17

• Statistics, the collection, tabulation,

analysis, interpretation, and presentation

of numerical data, provide a viable method

of supporting or clarifying a topic under

discussion.

• Statistical information should illuminate the user’s understanding of the issue or

problem at hand

• A population is a collection of all possible

elements, values, or items associated with

a situation

– A population can contain a finite number of

things or it may be nearly infinite Limitations

may be placed on a collection of items to

define the population.

• A sample is a subset of elements or

measurements taken from a population

• Descriptive or deductive statistics describe

a population or complete group of data

When describing a population using

deductive statistics, the investigator must

study each entity within the population This

provides a great deal of information about the population, product, or process, but gathering the information is time-consuming

• Inductive statistics deal with a limited

amount of data or a representative sample of the population.

• Measurement error is considered to be

the difference between a value measured

and the true value The error that occurs is

one either of accuracy or of precision.

• Accuracy refers to how far from the actual

or real value the measurement is.

• Precision is the ability to repeat a series

of measurements and get the same value

each time

• A frequency diagram shows the number

of times each of the measured values

occurred when the data were collected

This diagram can be created either from

measurements taken from a process or

from data taken from the occurrences of

events

• To create a frequency diagram:

• 1 Collect the data Record the measurements or counts of the

characteristics of interest.

• 2 Count the number of times each measurement or count occurs.

• 3 Construct the diagram by placing the counts or measured values on

the x axis and the frequency or number of occurrences on the y axis The

x axis must contain each possible measurement value from the lowest to the highest, even if a particular value does not have any corresponding

measurements A bar is drawn on the diagram to depict each of the

values and the number of times the value occurred in the data collected.

• 4 Interpret the frequency diagram Study the diagrams you create and

think about the diagram’s shape, size, and location in terms of the

desired target specification

• Histograms

– Similar to frequency diagrams

• The most notable difference between the two is that on a histogram the data are grouped into cells Each cell contains a range of values

Statistics

• To create a histogram:

– Step 1: Collect the data and construct a tally sheet

– Step 2: Calculate the range

– Step 3: Create the cells by determining the cell

intervals, midpoints, and boundaries

– Step 4: Label the axes

– Step 5: Post the values

– Step 6: Interpret the histogram

• Analysis of Histograms

– Shape, spread, and location are the

characteristics used to describe a distribution

Statistics

– Shape: refers to the form that the values of

the measurable characteristics take on

when plotted or graphed

– Shape is based on the distributions symmetry,

skewness, and kurtosis

– Spread: the distance between the highest

and lowest values

– Location: Where is the distribution in relation

to the target?

• Measures of Central Tendency

– Mean

– The mean of a series of measurements is determined

by adding the values together and then dividing this sum by the total number of values.

– Median

– The median is the value that divides an ordered series

of numbers so that there is an equal number of values

on either side of the center, or median, value.

– Mode

– The mode is the most frequently occurring number in a

• Measures of Dispersion

– Range

• The range is the difference between the highest

value in a series of values or sample and the lowest value in that same series.

– Standard Deviation

• The standard deviation shows the dispersion of

the data within the distribution

• The Central Limit Theorem

– The central limit theorem states that a group

of sample averages tends to be normally

distributed; as the sample size n increases,

this tendency toward normality improves

– The central limit theorem enables conclusions

to be drawn from the sample data and applied

to a population

• To Find the Area under the Normal Curve:

X average

s standard deviation