A statistical method for evaluating the absence of defects factor in United States standards for processed fruits and vegetables

The following three conversations might be overheard in different parts of the country: A plant manager to his boss, "This report from the foreman in Cannery No. 1 says that approximately three per cent of the peaches packed today were bruised and blemished. I wonder if they will meet the defect requirement for Grade A that our prospective customers require?" A purchasing agent to his assistant, "I need to purchase a large quantity of canned lima beans for the coming month. If I rely on United States Standards and the inspection service furnished by the Agricultural Marketing Service (AMS), what are the chances that I will buy beans that are more than two per cent defective?" A standardization specialist of the Agricultural Marketing Service to himself, "This standard that I am writing is slightly vague and complicated in the defect section. I wonder what would happen if I just eliminated the sample unit tolerance and decreased the sample tolerance to four per cent?" The objective of this paper is to help answer these questions and others like them. More specifically the objective is to develop a statistical method for evaluating portions of the absence of defects factor in United States Standards when the allowable number of defectives for each grade is specified as a per cent of the weight or number of units in each sample unit. In addition, the method is to be simplified so that it would be of practical value to people of limited mathematical and statistical thinking.