A note on stochastically acceptable quality

A random variable of quality, characterized by the quality distribution function, is considered both for continuous and discrete cases. The acceptable quality distribution function is introduced and different types of stochastic comparison are discussed: comparison in the mean, ordering in distribution, variability ordering and hazard-rate ordering. Acceptable, unacceptable and intermediate regions for levels of quality are determined by the discretization procedure. It is assumed that the quality of a product is revealed through usage. A simple reliability setting is considered where the quality of a product is directly dependent on its reliability characteristics in usage. Possible generalizations are discussed.