Applied Mathematical Modelling - Q1

Adel Ahmadi Nadi , Bahram Sadeghpour Gildeh , Jaber Kazempoor , Kim Duc Tran, Kim Phuc Tran 

International Research Institute for Artificial Intelligence and Data Science, Dong A University, Danang, Vietnam

Abstract

This article introduces a conditional reliability sampling plan for the Weibull distribution. The plan is applicable when the interested quality characteristic is a lower quantile and the life data are observed according to a progressive type-II censoring scheme. It is called “conditional”, since its operating characteristic function is derived by conditioning on a vector of ancillary statistics. We approximate the conditional operating characteristic function by a fixed vector that does not change by the sample. The plan is optimally designed by concentrating on economic considerations while the producer’s and consumer’s confidences are satisfied. In this regard, three cost models are proposed. The first cost function is constructed based on the inspection cost, while the second model accounts for the inaccurate estimation cost. The third cost function is a weighted-relative combination of the other two costs. Based on some combinations of requirements, the optimal plan parameters are prepared in some tables. We further conduct a series of simulations to show that the approximated conditional operating characteristic function can ensure the inspection’s risks well. Finally, an example based on the well-known data set on the strength of carbon fibers is discussed to demonstrate the applicability of the proposed plan.

Source: https://doi.org/10.1016/j.apm.2022.11.004