Power law behavior in Navy and Marine Corps avionics systems

Abstract

A power law distribution is a mathematically lopsided probability distribution in which one quantity varies as a power of another. Probability distributions, in general, describe the percentage of items that have a particular value in a data set. Empirical examples of power law distributions typically involve a small group of "bad actors" within a population that cause the tail of the distribution to skew away from that of a straight line. Avionics failures within the Naval Air Enterprise (NAE) also typically involve a small population of bad actors which account for a large portion of failure conditions. Therefore, the authors were eager to investigate whether Navy and Marine Corps avionics systems failures fit a power law distribution. If so, it would suggest that radical change is needed to current maintenance practices, including a change in investments in automatic test equipment. To address this question, the top five hundred avionics degraders from across the NAE were analyzed using a method laid out by Clauset, et al [1]. First, data was gathered and candidate systems were identified using visual inspection of the data. Data from candidates was then analyzed such that the tail of the distribution could be compared to the power law distribution. Finally, a goodness of fit calculation was performed to find whether or not the power law distribution appropriately described the behavior of the candidate system. All power law candidates were then compared to other types of distributions. This information was used to determine if the power law distribution truly is the favored distribution for a given data set. Analysis was done on two data sets: one from 2000 to 2010 and with data from 2010 to mid-2015 . It was found that the results from this comparison favored other types of distributions over the power law in almost every case. Furthermore, it was found that no-fault-found maintenance actions can create the illusion of power law failure behavior in some systems, where none actually exists.