Reliability Prediction of Complex Repairable Systems: an engineering approach Yong Sun Thesis submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy School of Engineering Systems Faculty of Built Environment and Engineering Queensland University of Technology June 2006 Reliability Prediction of Complex Repairable Systems: an engineering approach __________________________________________________________________________________ Keywords Reliability prediction, failure distribution functions, hazard, interactive failure, dependent failure, complex system, repairable system, condition monitoring, preventive maintenance, imperfect repairs, split system approach, Taylor’s expansion approach, proportional covariate model. i Yong Sun, PhD Dissertation at the Queensland University of Technology __________________________________________________________________________________ ABSTRACT This research has developed several models and methodologies with the aim of improving the accuracy and applicability of reliability predictions for complex repairable systems. A repairable system is usually defined as one that will be repaired to recover its functions after each failure. Physical assets such as machines, buildings, vehicles are often repairable. Optimal maintenance strategies require the prediction of the reliability of complex repairable systems accurately. Numerous models and methods have been developed for predicting system reliability. After an extensive literature review, several limitations in the existing research and needs for future research have been identified. These include the follows: the need for an effective method to predict the reliability of an asset with multiple preventive maintenance intervals during its entire life span; the need for considering interactions among failures of components in a system; and the need for an effective method for predicting reliability with sparse or zero failure data. In this research, the Split System Approach (SSA), an Analytical Model for Interactive Failures (AMIF), the Extended SSA (ESSA) and the Proportional Covariate Model (PCM), were developed by the candidate to meet the needs identified previously, in an effective manner. These new methodologies/models are expected to rectify the identified limitations of current models and significantly improve the accuracy of the reliability prediction of existing models for repairable systems. The characteristics of the reliability of a system will alter after regular preventive maintenance. This alternation makes prediction of the reliability of complex repairable systems difficult, especially when the prediction covers a number of imperfect preventive maintenance actions over multiple intervals during the asset’s lifetime. The SSA uses a new concept to address this issue effectively and splits a system into repaired and unrepaired parts virtually. SSA has been used to analyse system reliability at the component level and to address different states of a repairable system after single or multiple preventive maintenance activities over multiple intervals. The results obtained from this investigation demonstrate that ii Reliability Prediction of Complex Repairable Systems: an engineering approach __________________________________________________________________________________ SSA has an excellent ability to support the making of optimal asset preventive maintenance decisions over its whole life. It is noted that SSA, like most existing models, is based on the assumption that failures are independent of each other. This assumption is often unrealistic in industrial circumstances and may lead to unacceptable prediction errors. To ensure the accuracy of reliability prediction, interactive failures were considered. The concept of interactive failure presented in this thesis is a new variant of the definition of failure. The candidate has made several original contributions such as introducing and defining related concepts and terminologies, developing a model to analyse interactive failures quantitatively and revealing that interactive failure can be either stable or unstable. The research results effectively assist in avoiding unstable interactive relationship in machinery during its design phase. This research on interactive failures pioneers a new area of reliability prediction and enables the estimation of failure probabilities more precisely. ESSA was developed through an integration of SSA and AMIF. ESSA is the first effective method to address the reliability prediction of systems with interactive failures and with multiple preventive maintenance actions over multiple intervals. It enhances the capability of SSA and AMIF. PCM was developed to further enhance the capability of the above methodologies/models. It addresses the issue of reliability prediction using both failure data and condition data. The philosophy and procedure of PCM are different from existing models such as the Proportional Hazard Model (PHM). PCM has been used successfully to investigate the hazard of gearboxes and truck engines. The candidate demonstrated that PCM had several unique features: 1) it automatically tracks the changing characteristics of the hazard of a system using symptom indicators; 2) it estimates the hazard of a system using symptom indicators without historical failure data; 3) it reduces the influence of fluctuations in condition monitoring data on hazard estimation. These newly developed methodologies/models have been verified using simulations, industrial case studies and laboratory experiments. The research outcomes of this research are expected to enrich the body of knowledge in reliability prediction through effectively addressing some limitations of existing models and exploring the area of interactive failures. iii Yong Sun, PhD Dissertation at the Queensland University of Technology __________________________________________________________________________________ Table of Contents Keywords....................................................................................................................... i Abstract........................................................................................................................ ii List of Figures........................................................................................................... viii List of Tables............................................................................................................. xiii Notations ................................................................................................................... xiv Glossary.......................................................................................................................xx Abbreviations.......................................................................................................... xxvi Statement of Original Authorship ..........................................................................xxx Acknowledgment .................................................................................................... xxxi Chapter 1 INTRODUCTION ................................................................. 1 1.1 INTRODUCTION OF RESEARCH..............................................................1 1.2 OBJECTIVES AND METHODS OF THE RESEARCH..............................2 1.2.1 Objectives...............................................................................................2 1.2.2 Research Methods..................................................................................5 1.3 OUTCOMES OF THE RESEARCH.............................................................8 1.3.1 Research Results Achieved....................................................................8 1.3.2 Relationship of the Developed Models and Methodologies ................10 1.4 ORIGINALITY AND INNOVATION........................................................11 1.5 THE STRUCTURE OF THE THESIS ........................................................15 Chapter 2 LITERATURE REVIEW.................................................... 18 2.1 INTRODUCTION........................................................................................18 2.2 GENERAL REVIEW...................................................................................21 2.2.1 Frameworks..........................................................................................21 2.2.2 Reliability Assessment and Analysis ...................................................27 2.2.3 Maintenance Optimization Policies .....................................................32 2.2.4 Advanced Tools and Methodologies....................................................37 2.2.5 Comments and Discussion ...................................................................38 2.3 SPECIFIC REVIEW – ANALYTICAL MODELS.....................................40 2.3.1 Basic Principles of Probability.............................................................40 iv Reliability Prediction of Complex Repairable Systems: an engineering approach __________________________________________________________________________________ 2.3.2 Markovian Theory................................................................................42 2.3.3 Poisson Process....................................................................................44 2.3.4 Condition Monitoring Data Based Models..........................................45 2.3.5 Bayesian Theory...................................................................................51