Set theoretic formulation of performance reliability of multiple response time‐variant systems due to degradations in system components

Abstract

This paper presents a design stage method for assessing performance reliability of systems with multiple time-variant responses due to component degradation. Herein the system component degradation profiles over time are assumed to be known and the degradation of the system is related to component degradation using mechanistic models. Selected performance measures (e.g. responses) are related to their critical levels by time-dependent limit-state functions. System failure is defined as the non-conformance of any response and unions of the multiple failure regions are required. For discrete time, set theory establishes the minimum union size needed to identify a true incremental failure region. A cumulative failure distribution function is built by summing incremental failure probabilities. A practical implementation of the theory can be manifest by approximating the probability of the unions by second-order bounds. Further, for numerical efficiency probabilities are evaluated by first-order reliability methods (FORM). The presented method is quite different from Monte Carlo sampling methods. The proposed method can be used to assess mean and tolerance design through simultaneous evaluation of quality and performance reliability. The work herein sets the foundation for an optimization method to control both quality and performance reliability and thus, for example, estimate warranty costs and product recall. An example from power engineering shows the details of the proposed method and the potential of the approach.

Non-sample based parameters design for system performance reliability improvement

“…From reference [16], system incremental failure probability from time t l during time interval h is written as…”

“…In this paper, Eq. (14) is evaluated by using FORM (first-order reliability method) and second-order bounds on union probability whose detailed explanations are shown in the reference [16].…”

Knowledge‐based reliability assessments for time‐varying climates

“…Still others have discussed conducting time-varying, multi-stress accelerated life tests, but have focused on theoretic solutions and lack an easy-to-use approach [19][20][21][22][23] . As a result, many employ a simplifying assumption under which the use condition is set to be a worse-case steady-state ambient 24 .…”

Lifetime Distribution and Associated Inference of Systems with Multiple Degradation Measurements Based on Gamma Processes

“…Barker and Newby [1] used a multivariate Wiener process to describe the degradation of a complex multicomponent system, and then provide an optimal non-periodic inspection policy for it. Son and Savage [13] proposed a design stage method for assessing performance reliability of systems with multiple time-variant responses due to component degradation. They assume that the system component degradation profiles over time is known and the degradation of the system is related to component degradation using mechanistic models.…”