Optimal constant-stress ADDT plan with one main effect and one interaction effect

Abstract

PurposeDegradation measurement of some products requires destructive inspection; that is, the degradation of each unit can be observed only once. For example, observation on the mechanical strength of interconnection bonds or on the dielectric strength of insulators requires destruction of the unit. Testing high-reliability items under normal operating conditions yields a small amount of degradation in a reasonable length of time. To overcome this problem, the items are tested at higher than normal stress level – an approach called an accelerated destructive degradation test (ADDT). The present paper deals with formulation of constant-stress ADDT (CSADDT) plan with the test specimens subject to stress induced by temperature and voltage.Design/methodology/approachThe stress–life relationship between temperature and voltage is described using Zhurkov–Arrhenius model. The fractional factorial experiment has been used to determine optimal number of stress combinations. The product's degradation path follows Wiener process. The model parameters are estimated using method of maximum likelihood. The optimum plan consists in finding out optimum allocations at each inspection time corresponding to each stress combination by using variance optimality criterion.FindingsThe method developed has been explained using a numerical example wherein point estimates and confidence intervals for the model parameters have been obtained and likelihood ratio test has been used to test for the presence of interaction effect. It has been found that both the temperature and the interaction between temperature and voltage influence the quantile lifetime of the product. Sensitivity analysis is also carried out.Originality/valueMost of the work in the literature on the design of ADDT plans focusses on only a single stress factor. An interaction exists among two or more stress factors if the effect of one factor on a response depends on the levels of other factors. In this paper, an optimal CSADDT plan is studied with one main effect and one interaction effect. The method developed can help engineers study the effect of elevated temperature and its interaction with another stress factor, say, voltage on quantile lifetime of a high-reliability unit likely to last for several years.