Zipping and re-zipping methods to improve the precision and accuracy of manufacturing processes

The concept of minimising waste in manufacturing processes is paramount in promoting sustainability and saving companies' time, money and physical resources in the process. This can be particularly useful in many common manufacturing processes which involve casting, moulding, forming, machining, joining or other additive manufacturing processes such as stereo lithography, which produce products in multiple steps, one layer at a time. Accurate screening inspections may also contribute to a more efficient use of resources in the production process. Scraping and reuse of wasted raw materials as part of a production process can be analysed more precisely through truncated normal distributions, and their associated convolutions. This manuscript explores the mathematical foundations of various truncated normal distributions and the convolutions of these distributions in order to offer insights into noteworthy methods used to meticulously account for material use.