A Monte Carlo Approach to Predicting Failure Across Multiple Temperature and Humidity Field Environments

Abstract

Compressed schedules for new technologies often require development of novel strategies for reliability qualification. Highly accelerated test conditions are frequently implemented to meet condensed product schedules. Failures in such aggressive test conditions must be analyzed to classify them either as test-artifacts or potential field issues. In addition, product design complexities often constrain the ability to execute detailed failure analysis and implement risk-mitigating design and/or manufacturing changes. Typically, failure analysis leading to a full understanding of the fundamental physics of failure is the ideal approach to enable an accurate field failure rate prediction. In absence of such failure analysis, application of more empirical risk assessment methodologies is necessary. This is particularly so when field use conditions are difficult to replicate with certainty or if field failure mechanisms cannot be accelerated with confidence. We build on existing Monte Carlo approaches to develop such a risk assessment methodology in this paper. An accelerated temperature-humidity test during product qualification revealed a potentially significant related failure mechanism for a product. Two critical questions were identified. One, will the failure mechanism active in the field or is it just a manifestation of over-stress test conditions? Two, given multiple distributions of temperature and humidity conditions ranging from product assembly to shipping to usage, is there an accurate method to calculate failure rate across the entire spectrum of temperature and humidity field usage? To answer the first question, test data from multiple combinations of temperature and humidity conditions were gathered. The data were analyzed using statistical software to empirically fit an Arrhenius temperature and humidity life stress model. To answer the second question, a novel probabilistic model was developed to characterize the life of a product under varied temperature and humidity conditions. Live shipment data was collected to refine estimates of the distributions of temperature and humidity during transit and storage to feed into the probabilistic model. The double Arrhenius relationship from an Arrhenius temperature and humidity life stress fit was utilized to estimate failure rates for multiple temperature and humidity conditions spanning the expected range of shipping, storage, and field environments. Each selected temperature and humidity condition was converted into an equivalent dew point, and an empirical failure rate vs dew point relationship was fitted. Using either directly measured or historical product data, temperature and humidity distributions were fit for the following relevant field scenarios: product assembly and pack-out, shipping/storage, powered-on usage, and powered-down usage. For each of these scenarios, temperature and humidity conditions were randomly selected from the corresponding distributions. Fifty thousand instances were averaged to yield a Monte Carlo prediction which accounts for the complete set of usage distributions. While this Monte Carlo method was developed specifically for one failure mechanism, the approach is applicable to all temperature and humidity driven failure mechanisms. It is of particular importance in understanding and refining the sensitivity of the many variables included in a typical field failure rate prediction.