Tolerance Limits Under Normal Mixtures: Application to the Evaluation of Nuclear Power Plant Safety and to the Assessment of Circular Error Probable

• Activity Number: 30
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Zachary Zimmer* and Thomas Mathew and DoHwan Park
• Companies: and University of Maryland, Baltimore County and University of Maryland, Baltimore County
• Keywords: Tolerance Limits ; Mixture Models ; Circular Error Probable

Abstract

The presentation develops tolerance limits under two scenarios: (i) a univariate random variable following a normal mixture distribution, and an upper tolerance limit is required, and (ii) a bivariate random variable following a bivariate normal mixture distribution, and an upper tolerance limit is to be computed for its Euclidean norm. The computation uses asymptotic normality of the MLE, along with bootstrap calibration. The set up (i) is appropriate for modeling the peak cladding temperature (PCT) of nuclear power plants; an upper tolerance limit is used to check if the PCT distribution is mostly below the regulatory requirement of 2200 F, a safety requirement for preventing loss of coolant accidents. Traditionally, non-parametric upper tolerance limits are computed for this purpose. The upper tolerance limit computed under a mixture distribution is smaller compared to the non-parametric counterpart. The scenario in (ii) can arise for data representing impact locations of projectiles launched from different locations or systems. The problem of interest is inference concerning the circular error probable (CEP), used to assess the impact accuracy of ballistic projectiles.