Non-Normal Distributions in the Real World
9 hours ago
- #Non-Normal Distributions
- #Statistical Process Control
- #Process Capability Analysis
- The author shares a personal experience where a galvanizing process reported rejects but none were found, challenging the assumption of normal distribution.
- Through research, the author concludes that normal distributions are not common in real-world processes due to management control, measurement systems, physical laws, engineering constraints, and inspection procedures.
- Human behavior often leads to non-normal distributions, as seen in payment patterns, where data spikes around due dates and unbounded delays.
- Management systems and measurement tools can distort data, either creating false normality or non-normality due to low resolution or specific scales.
- Physical laws, like metallurgical processes, often produce bounded distributions, such as galvanizing thickness, which is bounded at the low end.
- Engineering activities, like using stops or NC machine backlash, can create truncated or bimodal distributions.
- Inspection methods, such as true position in ANSI Y14.5, convert data in ways that result in non-normal distributions, even from normal inputs.
- Assuming normality can mislead process capability analysis, causing incorrect predictions of rejects or optimal process settings, and lead to tampering or strained relations.
- Solutions include analyzing histograms thoughtfully, using software for non-normal PCA, and adjusting control limits to better reflect real process behavior.
- Some argue against adjusting for non-normality due to unstable higher moment estimates and potential confusion, but the author counters that these adjustments offer valuable tail information and are practical with modern software.
- The author emphasizes thinking critically over rote statistical application to avoid errors and improve process understanding and management.