Reliability of two dissimilar devices degrading in a periodic alternating sequence—Application to opto-isolators

Abstract

A novel failure model, representing a small system of two devices degrading in a periodically alternating sequence, is formulated for an opto-isolator because its LED degrades only in the low voltage on-state while the optically-coupled Si phototransistor (PT) deteriorates in the high voltage off-state. The model is introduced by combining two exponential distributions, the major assumption being that the PDFs of each of the two devices can be constructed piecewise by periodic breaks and translations along the time axis of the PDFs of continuously operating discrete elements. From these PDFs, we derive the staggered individual reliability functions which permit the evaluation of the system's reliability function, failure rate and MTTF. The mathematical treatment of the joint lognormal distribution follows the pattern outlined for the combination of two exponential distributions. In the limit of high frequency operation, elegant closed-form approximations for the major reliability-related functions including the MTTF have been obtained. In particular, the system's failure rate is given by λ joint = δ 1 λ 1( δ 1 t) + δ 2 λ 2( δ 2 t) where δ i is the duty factor of the LED ( i = 1) and PT ( i = 2). The failure rate λ i is that for a discrete lognormal distribution wherein the time is replaced by its effective value in a cycle, δ i t. The results for the combined lognormal failure distribution are displayed in convenient graphical forms and these diagrams are applied to the evaluation of the properties of an opto-isolator operating over a wide range of duty factors in a practical system.