Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects

Abstract

Article citation info: IntroductionIn recent years, important developments have been presented in the area of reliability inference of products and systems based on degradation models. Such models are important tools to obtain reliability information when few failure data is available [11], and consists in analyzing the gradual deterioration in performance of a performance characteristic (PC), also known as degradation process, in terms of the accumulated damage over time [27]. For some products, a failure would be defined at a specified critical level of degradation, which means that the product may not stop working completely as in the case of hard failures, but be defined when the cumulative degradation path crosses the critical level of degradation; such failures are known as soft failures. In general, if a failure can be defined in terms of a specified critical level of degradation it is possible to obtain a reliability assessment based on degradation process models [12]. Based on this, a modeling approach for degradation processes may consist in relating the degradation over time with a continuous stochastic process such that it is possible to describe the failure generating mechanisms.For certain PC, the desirable properties that a model must have to describe its degradation process are that the degradation process should always be positive and strictly increasing. In this paper, the gamma process is considered as a model to govern the degradation process of certain PC, given the characteristics that its increments are independent and non-negative having a gamma distribution that results in an always positive, strictly increasing stochastic process. As performance can only decrease over time, this is why it is considered to be suitable to model wear, crack growth, corrosion, consumption, fatigue, erosion, or any PC [16]. Some important applications of the gamma process in the reliability assessment of products can be found in Bagdonavicius and Nikulin [2], Park and Padgett [22], and Bagdonavicius and Nikulin [3].RodRíguez-Picón LA. Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects. eksploatacja i niezawodnosc -Maintenance and Reliability 2017; 19 (1)

Results of aircraft positioning tests in postprocessing using the GNSS

“…The mathematical model for the SPP method is described by the following observational equation (1) [6]:…”

“…Usually the GNSS receiver helps to determine an aircraft's position using C/A code observations at the L1 frequency. This solution, which is called the SPP method, uses pseudorange measuring [6], with the coordinates of an aircraft determined by the ECEF geocentric system, as well as the clock correction of the receiver. The SPP mathematical model may be solved with Kalman filtering or the least squares method [4].…”