Introduction to Six Sigma Statistics in 8 Easy Steps

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1. Learn the Scales of Measure

Nominal

• It is in the name

• Marital status, Phone numbers

•  

Ordinal

• Relative, unequal value ranking

• Race finish, opinion poll response 

• temperature 

Interval

• Equal intervals are equal differences

• Calendar year, Fahrenheit

Ratio

• Proportional amount of difference

• Has a real zero value

• Annual income, Kelvin temperature

2. Learn the Measures of Central Tendency

Median: Midpoint in a string of sorted data, where 50% of the observations, or values, are below and 50% are above

• Does not necessarily include all values in calculation

• Is “robust” to extreme scores

• Organize the data from low values to high when determining the Median

Mean: Arithmetic average of a set of values

• Reflects the influence of all values

• Strongly Influenced by extreme values

Mode: The most frequently occurring value

3. Learn the Measures of Dispersion

Range: the distance between the extreme values of a data set (Highest to Lowest)

• The range is more sensitive to outliers than the variance

Variance: the Average Squared Deviation of each data point from the Mean

Standard Deviation: Square Root of the Variance

• measure of the average deviation about the mean 

4. Understand the Different Types of Data

Continuous or Variable Data (Quantitative)

• Time (seconds)• Pressure (psi)• Conveyor Speed (ft/min)• Rate (inches

Attribute (Qualitative)• Categories• Good/Bad (Pass/Fail)• Machine 1, Machine 2, Machine 3• Shift number• Counted things (# of Errors in a

document, # units shipped, etc.)

 Convert Attribute to Continuous wherever possible

Examples of attribute data converted to continuous data: • Count of defects to ‘% defects’ • Y/N late to ‘average days late’• Leaks/No leaks to ‘rate of leaks on a

continuous scale’• Success or failure of electrical parts to ‘voltage

flow of good parts’

5. Gain Knowledge of Descriptive Statistics

• Consists of basic statistics and graphical techniques used to summarize data

• Measures of central location

• Measures of spread (dispersion)

• Evaluation of symmetry & skewness

• Typical graphical techniques• Histograms• Boxplots• Dotplots• Normal probability plots

6. Be able to Identify Different Data DistributionsNormal Distribution (Bell Curve)• The “Normal” Distribution is a distribution of data which has certain consistent properties (the

mean, median and mode are equal in value)

• These properties are very useful in our understanding of the characteristics of the underlying process from which the data were obtained

• Most natural phenomena and man-made processes are distributed normally, or can be represented as normally distributed

• The Normal Distribution is a continuous distribution which is symmetrical and extreme values are less likely than moderate values (unimodal)

• An example would be measuring heights of people or the length of a table. In either case the measurement is continuous and can be broken down into finer increments

6. Cont’d

t-distribution• The t distribution assumes samples are

drawn from a normal distribution but the population variance, 2, is not known… The shape of the t-distribution varies as the sample size, n, changes

• The distribution becomes more narrow as the sample size becomes larger. As n becomes very large, the critical value corresponding to the area under the curve approaches the Normal distribution’s Z value

Poisson Distribution• Appropriate as a model of number of defects

or nonconformities in a unit of product• X is number of defects found in a per unit

basis• Per unit area, per unit volume, per unit time, etc.• Area X is a discrete, positive integer• Area for opportunity is a finite region of space, time or product• When the average is high, the distribution can

be approximated by the normal distribution• When the average is low, the distribution is

skewed to the right

6. Cont’d

F DistributionA continuous distribution formed from the ratio of variances calculated from two independent samples drawn from Normal Distributions

Chi-square DistributionA continuous distribution used in statistical hypothesis testing and confidence interval estimation for many different applications, including inferences about a population variance

7. Know About Sample and Population Sizes

• Population is every possible observation (census)

•  Samples are subsets of populations

•  Data is obtained using samples because we seldom know the entire population

•  Descriptive statistics apply to any distribution• Sample or population

•  Population statistics are desired, but often not available

•  Samples from a population can be used to ‘infer’ or approximate population parameters

8. Know the Statistics and Reporting Tools

The most used Six Sigma tools is Microsoft Excel. Excel provides most of the day to day uses required to manage most Six Sigma projects. Getting the Data Analysis Pack will allow you to stretch Excel to its limits by providing additional statistical analysis tools

•Anova•Correlations•Covariances•Descriptive Statistics•Exponential Smoothing•F-Tests and Two-Samples for Variances•Fourier Analysis•Histograms•Various t-tests

8. Cont’d

However, the ultimate tool for Six Sigma Black Belts is Minitab. Minitab will get you going where Excel leaves you hanging.

Minitab’s features delve deeply into:

•Measurement System Analysis•Multivariate Analysis•Anova•Regression Analysis•Statistical Process Control•Reliability/Survival Analysis•And other great simulations

8. Cont’d

While you are trying out Minitab, don’t forget to check out the powerful reporting tools that will provide the following graphical reports:

•Dotplots/Histograms/Normal Plots•Run charts / Time Series•Pareto Diagrams•Stratification (2nd Level Pareto)•Boxplots•Scatter Plots•Checksheets/Concentration Diagrams