Search results for "Pivotal quantity"
showing 4 items of 4 documents
A Novel Intelligent Technique for Product Acceptance Process Optimization on the Basis of Misclassification Probability in the Case of Log-Location-S…
2019
In this paper, to determine the optimal parameters of the product acceptance process under parametric uncertainty of underlying models, a new intelligent technique for optimization of product acceptance process on the basis of misclassification probability is proposed. It allows one to take into account all possible situations that may occur when it is necessary to optimize the product acceptance process. The technique is based on the pivotal quantity averaging approach (PQAA) which allows one to eliminate the unknown parameters from the problem and to use available statistical information as completely as possible. It is conceptually simple and easy to use. One of the most important featur…
A New Simple Computational Method of Simultaneous Constructing and Comparing Confidence Intervals of Shortest Length and Equal Tails for Making Effic…
2021
A confidence interval is a range of values that provides the user with useful information about how accurately a statistic estimates a parameter. In the present paper, a new simple computational method is proposed for simultaneous constructing and comparing confidence intervals of shortest length and equal tails in order to make efficient decisions under parametric uncertainty. This unified computational method provides intervals in several situations that previously required separate analysis using more advanced methods and tables for numerical solutions. In contrast to the Bayesian approach, the proposed approach does not depend on the choice of priors and is a novelty in the theory of st…
Improvement of Inventory Control under Parametric Uncertainty and Constraints
2011
The aim of the present paper is to show how the statistical inference equivalence principle (SIEP), the idea of which belongs to the authors, may be employed in the particular case of finding the effective statistical decisions for the multi-product inventory problems with constraints. To our knowledge, no analytical or efficient numerical method for finding the optimal policies under parametric uncertainty for the multi-product inventory problems with constraints has been reported in the literature. Using the (equivalent) predictive distributions, this paper represents an extension of analytical results obtained for unconstrained optimization under parametric uncertainty to the case of con…
Weibull Prediction Limits for a Future Number of Failures Under Parametric Uncertainty
2012
In this paper, we present an accurate procedure, called “within-sample prediction of order statistics,” to obtain prediction limits for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the same sample. The failure-time of such units is modeled with a two-parameter Weibull distribution indexed by scale and shape parameters β and δ, respectively. It will be noted that in the literature only the case is considered when the scale parameter β is unknown, but the shape parameter δ is known. As a rule, in practice the Weibull shape parameter δ is not known. Instead it is estimated subjectively …