###### Abstract  
An accelerated degradation test (ADT) has become a popular method to accelerate degradation mechanisms by stressing products beyond their normal use conditions. The components of an automobile are degraded over time or cycle due to their constant exposure to friction or wear. Sometimes, the performance degradation can be measured only by destructive inspection such as operating torques of return-springs in a bi-functional DC motor system. Plastic deformation of the return-spring causes the degradation of actuating forces for shield movement, resulting in deterioration of the shield moving speed in a headlight system. We suggest a step-by-step procedure for a reliability analysis for a bi-functional DC motor in a headlight system, based mainly on accelerated destructive degradation test (ADDT) data. We also propose nonlinear degradation models to describe the ADDT data of the return-springs. Exposure effects of high temperatures on the return-springs are quantitatively modeled through the ADDT models. We compare the estimation results from both the closed-form expression and Monte Carlo simulation to predict the failure-time distribution at normal use conditions, showing that the lifetime estimation results from the closed-form formulation are more conservative. accelerated destructive degradation test; degradation model; fault tree analysis; Monte Carlo simulation; reliability +
Footnote †: journal: Applied Sciences  
15 February 2021  
5 March 2021  
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**C.O. ADDT has been commonly employed in industrial practice to evaluate the long-term material properties. [PERSON] [1] conducted ADDT to evaluate dielectric breakdown strength of insulation specimens using accelerated temperatures. [PERSON] et al. [2] proposed a parametric approach to ADDT for the adhesive bond B data. [PERSON] and [PERSON] [3] analyzed ADDT testing data of the seal strength at accelerated temperature conditions. Recently, [PERSON] et al. [4] proposed a semiparametric model to describe ADDT data of the adhesive formulation K. In the literature, the analysis of the ADDT data involves a model fitting to the degradation paths over time. Meanwhile, accelerated stress effects should be explicitly incorporated into the ADDT model in a parametric manner. See [PERSON] et al. [2] for more details on the models and data analyses of ADDT. In the literature on reliability analyses in the field of automobiles, [PERSON] [5] proposed a model-based fault detection method based on the parity-space and parameter estimation approach for the reliability improvement of automotive actuators. [PERSON] et al. [6] employed the reliability sensitivity analysis of design parameters to multiple case studies including coil springs and composite springs in automobiles. [PERSON] and [PERSON] [7] proposed the reliability analysis of small DC motors for automobiles with Accelerated Life Testing. The application of the inverse-power law model indicates its main failure mechanism--performance degradation by brush wear out. [PERSON] et al. [8] also studied the reliability analysis of automobile welding structures to analyze its strength degradation of key components, to name a few. In this work, we provide a step-by-step procedure of the reliability analysis for bifunctional DC motor systems, based mainly on ADDT data. We also propose nonlinear degradation models to describe the ADDT data of the return-springs in a bi-functional DC motor system. To derive the failure-time distribution from the ADDT data, both the closed-form formulation approach and Monte Carlo simulation were conducted. The DC motors are replacing solenoid motors which have been widely used in various industry areas. In particular, DC motors have garnered more attention for its effective usage, due to its limited dimension and weight, for electronic devices in automobiles.