Lognormal Distribution - Probability Plotting

Techniques

Cumulative Distribution Function

Cumulative Hazard Function

Weibull Distribution

Normal Distribution

Lognormal Distribution

Exponential Distribution

Exam

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The following section describes probability plotting for the lognormal distribution using the Reliability & Maintenance Analyst.  The manual method is located here.

Probability plotting is an excellent method for determining goodness-of-fit. To determine the goodness-of-fit click the "Plot" button. If the plotted points form a straight line, the distribution provides a good time to fail model for the data. The "R-Squared" value is a measure of how well the data forms a straight line. An R-Squared value of 1.0 indicates a perfectly straight line. R-Squared is also known as the coefficient of determination.  To estimate the parameters of the lognormal distribution using prabability plotting, follow these steps:

1. Enter the data using one of the data entry grids, or connect to a database.
2. Select the "Parameter Estimation"
3. Select "Lognormal"
4. Select "Probability Plot"

The figure below shows the lognormal probability plotting screen using the data in the file "Demo2.dat".

Clicking the "Plot" button gives a hazard plot. If the plotted points do not follow a straight line, the lognormal distribution with the estimated parameters does not provide an adequate time to fail model. The untransformed option plots the cumulative distribution function against time. This is useful for determining the probability of failure at a given time. The title of the graphs can be changed by editing the text in the Graph Title frame. To check the spelling of the title, click the "Spell Check" button.

To predict reliability or time-to-fail using the estimated parameters use the Predicting Module.

Manual Probability Plotting

Probability Plotting for the lognormal distribution is accomplished by transforming the lognormal data to normal by taking the logarithm. After the transformation, the probability plotting procedure is the same as the procedure used for the normal distribution shown here.