On a Sampling Design for Estimation of Negligible Accident Rates Involving Electronic Toys

Abstract

Motivated by an actual problem, we discuss a sampling situation involving estimation of the incidence rate of a rare phenomenon in connection with the functioning of an electronic toy. Because of a manufacturing fault, such toys may have a built-in loose metallic piece which moves freely while the children play with the toy. As soon as the freely moving metal lands into a designated potential danger zone inside the toy, it gives an electric shock! The problem is to provide point and interval estimators of the chance of this event happening which is a priori known to be rather negligible.