Non-normal probability distributions

Normal Probability Curve

Other Discrete Distributions

Weibull Distribution

Statistical Analysis Tools

Non-Normal Continuous Distributions

Other Types of Continuous Distributions

Importance in Six Sigma

Binomial Distribution

Other Continuous Distributions

Lognormal Distribution

Exponential Distribution

Poisson Distribution

Normal Probability Distributions Revie

Using Probability Distributions

Described by mean and standard deviation

Symmetrical curve centered around the mean

Continuous data related to an infinite number of points along an interval

Exponential Distribution

Statistical test: Chi-Squared Goodness-of-Fit

Used for arrival times, time between failures, etc

Data concentrated at one end of the x-axis

Histogram/trend line decreases exponentially

Lognormal Distribution

Always positively skewed

Used for time durations, wealth distribution, etc

Asymmetrical, constrained by zero

Weibull Distribution

Used for reliability applications, failure probabilities

Continuous data related to time

Can resemble other distributions

Uniform Distribution: Rare in randomly-sampled data; may indicate measurement issues

Triangular Distribution: Formed using mode and upper/lower limits

Beta Distribution: Flexible, can resemble other distributions

Gamma Distribution: Skewed to the right; encompasses various shapes

Laplace Distribution: Bilateral exponential or double-exponential distribution

Logistic Distribution: Used to approximate other symmetrical distributions

Cauchy Distribution: Elongated normal curve with a tighter peak

Central Limit Theorem allows for analysis of large, randomly-sampled continuous data sets

Use of software like Minitab for analysis

Most commonly used in statistics

Described by mean and standard deviation

Symmetrical in nature

Used for arrival times, time between failures, etc

Decreases exponentially

Describes large range data

Always positively skewed

Asymmetrical

Describes reliability applications

Can resemble other distributions

Gamma Distribution

Beta Distribution

Triangular Distribution

Uniform Distribution

Laplace Distribution

Logistic Distribution

Cauchy Distribution

Describes attribute data

Assumes independence of trials

Used for discrete data with two outcomes

Describes events occurring at random intervals

Related to the exponential distribution

Used for random occurrences within time or distance

Negative Binomial Distribution

Geometric Distribution

Understanding event probabilities

Evaluating process improvements

Helps in making data-driven decisions

Tying financial data to events

Identifying areas for improvement

Helps in assessing process performance