Validation of tolerance interval

The tolerance interval receives very much attention in literature and is widely applied in industry. However, it is generally constructed through the criterion of minimum width by Eisenhart et al. (1947). Although effort for clarification of several prediction related intervals has been made recently by Huang et al. (2010), the appropriateness of the tolerance interval for its role in industry applications is insufficiently discussed. According to manufacturersʹ requests, a concept of admissibility of tolerance intervals is defined in this paper and we show that these types of tolerance intervals are not admissible due to short of confidence. We further prove that a 100 ( 1 − α ) % confidence interval of a γ - coverage interval is admissible and is appropriate for use.