Degradation Tests Using Geometric Brownian Motion Process for Lumen Degradation Data

Running a traditional life test over an affordable time period with highly reliable products is inefficient to collect the lifetime information of products even if the products are subject to higher stress conditions. This fact makes it difficult to infer the reliability of highly reliable products. The accelerated degradation test (ADT) method has been suggested as an alternative to infer the reliability of highly reliable product based on its degradation measurements. The current study is motivated by the statistical modeling of the lumen degradation date set of transistor outline can packaged light emitting diodes (LEDs). All degradation measurements were collected from an ADT, which was conducted with two stress loadings, the ambient temperature and drive current. To study the reliability of the LEDs under the ADT, the geometric Brownian motion process and generalized Eyring model are applied to estimate the distribution parameters and percentiles of the LEDs. Planning strategies of the sample size and measurement times for the proposed ADT are established to minimize the asymptotic variance of maximum‐likelihood estimator of the lower 100pth percentile of LED lifetimes under the given budget. An algorithm is provided to reach the planning strategy. The guidelines of this study can be extended to infer the reliability of other highly reliable product besides LEDs.