Meaning
Continuous probability distributions whose logarithm is normally distributed model data that are skewed and strictly positive. Using the log normal probability density allows quality control engineers to analyze process variables that cannot fall below zero, such as the wear life of moulding tools or the size of filler particles in polymer composites. This statistical model accounts for the long tail of high values often seen in real-world manufacturing data.
Process Analysis
The mathematical function describes the likelihood of occurrence for various measurement values across a production run. In injection moulding, the injection pressure or the cycle time often follows this skewed distribution rather than a symmetric bell curve. Analyzing the log normal probability density of these parameters helps the moulder set realistic alarm limits on their monitoring equipment.
This analysis prevents false alarms caused by natural, non-symmetric process variations.
Quality Assessment
Understanding this distribution is useful for predicting the failure rate of plastic gears under constant mechanical stress. It allows engineers to estimate the percentage of parts that will fail prematurely during operation.
Parameter Calculation
The distribution is defined by two parameters that must be calculated from the sample data using maximum likelihood estimation. Software tools use these parameters to plot the probability curve against the actual measurement data to verify the fit. If the fit is poor, alternative distributions such as the Weibull model should be evaluated.
