Statistical Process Control Fundamentals in Packaging Substrate Converting
Statistical process control in substrate converting relies on sub-grouping across machine direction variance and isolating non-normal barrier defects.
Weibull Distribution
Probability Model
A continuous probability distribution models the life expectancy and failure rates of industrial materials under stress. In the structural analysis of paperboard, the weibull distribution is applied to evaluate the variability in the cracking and breaking points of fiber-based products. This statistical tool accommodates the asymmetric failure patterns typical of natural materials, where a few weak points can trigger the failure of the entire structure.
Mathematical Application
The distribution is characterized by a scale parameter, which indicates the characteristic strength of the material, and a shape parameter, which measures the scatter of the strength values. A higher shape parameter indicates that the paperboard’s breaking point is highly predictable, meaning there is little variation between samples. When analyzing tensile test results, using the weibull distribution helps engineers predict the likelihood of material failure under the complex stress of creasing and folding.
This model is superior to simple averages because it focuses on the lower tail of the distribution, where the weakest sheets will cause machine jams or cracked cartons.
Quality Control
By focusing on the probability of early failure, paper converters can adjust their fiber blends to eliminate weak points. This adjustment improves the runnability of the board during long, high-speed production runs.