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Optimal burn‐in policy based on a set of cutoff points using mixture inverse Gaussian degradation process and copulas
Author(s) -
Morita Lia H. M.,
Tomazella Vera L.,
Ferreira Paulo H.,
Ramos Pedro L.,
Balakrishnan Narayanaswamy,
Louzada Francisco
Publication year - 2021
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2601
Subject(s) - cutoff , gamma process , burn in , gaussian , inverse , wiener process , copula (linguistics) , mathematical optimization , reliability (semiconductor) , mathematics , monotone polygon , computer science , process (computing) , gaussian process , set (abstract data type) , econometrics , statistics , reliability engineering , engineering , physics , power (physics) , geometry , quantum mechanics , programming language , operating system
Burn‐in tests have been discussed extensively in the reliability literature, wherein we operate items until high degradation values are observed, which could separate the weak units from the normal ones before they get to the market. This concept is often referred to as a screening procedure, and it involves misclassification errors. Commonly, the underlying degradation process is assumed to be a Wiener or a gamma process, based on which several optimal burn‐in policies have been developed in the literature. In this article, we consider the mixture inverse Gaussian process, which possesses monotone degradation paths and some interesting properties. Under this process, we present a decision rule for classifying a unit under test as normal or weak based on burn‐in time and a set of cutoff points. Then, an economic cost model is used to find the optimal burn‐in time and the optimal cutoff points, when the estimation of model parameters is based on an analytical method or an approximate method involving copula theory. Finally, an example of a real dataset on light amplification by stimulated emission of radiations, well known in the reliability literature, is used to illustrate the model and the inferential approach proposed here.