Reliability and condition-based maintenance modeling for systems operating under performance-based contracting

Highlights

• Two-stage degradation-based and shock-based failure processes are established.

• System state transition and unit-specific heterogeneity are incorporated.

• Reliability and CBM models are formulated.

• Optimal maintenance policy is obtained under performance-based contracting.

• Applicability of the models is demonstrated through a numerical study.

Abstract

Performance-based contracting motivates service providers to implement effective maintenance policies so as to boost profits and improve system performance at a lower cost. This paper deals with reliability and condition-based maintenance modeling for single-unit systems operating under performance-based contracting. For a system subject to degradation and sudden shocks, there involves three states: normal, degraded and failed. Once entered into the degraded state, the system deteriorates faster and becomes more susceptible to shocks. The degradation conforms to a two-stage inverse Gaussian process with random effects characterizing unit-specific heterogeneity in the population. Furthermore, the arrival of sudden shocks follows a doubly stochastic Poisson process. A reliability model is developed based on degradation-based and shock-based failures modeling. Afterwards, the long-run maintenance cost rate and the average system availability are evaluated. Optimal inspection-based preventive replacement policy is obtained by maximizing the expected profit rate to the service provider. Finally, a numerical example along with sensitivity analysis of model parameters is presented to demonstrate the applicability and solution procedure of the proposed models.

Introduction

After-sales support and maintenance services have become a major source of revenue, profit and competitive advantage in manufacturing industries (Cohen, Agawal, & Agrawal, 2006). This is especially true for those firms selling capital-intensive products, such as aircraft engines, wind turbines, and oil pipelines, among others (Dennis & Kambil, 2003). Customers of these systems are more concerned with the performance outcome (e.g. reliability, availability), and less sensitive to the costs (Xiang, Zhu, Coit, & Feng, 2017). In recent years, a new service paradigm named as performance-based contracting (PBC) has emerged. This new form of support contract is often referred to as performance-based logistics (PBL) (Randall, Nowicki, & Hawkins, 2011) in the defense sector and Power by the Hour (PBH) (Neely, 2008) in the commercial sector. Different from the traditional fixed-price and cost-plus contracts, under PBC, service providers are paid for the realized system performance (Guajardo et al., 2012, Kim et al., 2007). A detailed review of various issues related to PBC can be referred to Selviaridis and Wynstra (2015).

Since PBC rewards the service provider based on the same performance outcome that the customer cares about, it motivates the problem of how to plan a viable maintenance policy to both improve the system reliability/availability at a lower cost and gain profitability under PBC. Different maintenance policies for complex industrial systems under support contracting approach have been received growing attention (Qiu et al., 2018, Sultana et al., 2013). Using modern sensor technology, condition-based maintenance (CBM) suggests “necessary” preventive maintenance actions based on the inspection of working conditions. See Alaswad and Xiang (2017) for an excellent review of mathematical models and optimization approaches of CBM. In practice, many dynamic systems are not only subject to degradation with operational age but also to sudden shocks which can lead to a complete system failure (Singpurwalla, 1995). The stochastic degradation-threshold-shock (DTS) models (Lehmann, 2009, Lemoine and Wenocur, 1985, Singpurwalla, 1995) are commonly applied to describe these two competing failure causes. Reliability analysis and CBM policies planning based on DTS models have been extensively investigated (Caballé et al., 2015, Che et al., 2018, Gao et al., 2019, Huynh et al., 2012, Liu et al., 2016, Peng et al., 2010, Rafiee et al., 2014, Rafiee et al., 2016, Shafiee et al., 2015, Shen et al., 2018, Tang et al., 2015, Zhao et al., 2018, Zhou et al., 2016, Zhu et al., 2015). In particular, increasing attention has been paid to the determination of optimal maintenance policies within the framework of PBC (Qiu et al., 2017, Wang et al., 2019, Xiang et al., 2017, Yang et al., 2019).

The DTS models applied in the above-mentioned literature assumed stationary degradation process for binary-state systems. Whereas a system may experience multiple states during its lifecycle; e.g., “normal”, “degraded”, “failed”, etc (Bian & Gebraeel, 2014). For such systems, their degradation processes are non-stationary and the degradation rates are not static but dependent on the system states. There has been research focusing on maintenance optimization for multi-state systems (Ma et al., 2020, Wei et al., 2019, Yang et al., 2017, Yang et al., 2017, Zhang et al., 2016), assuming constant degradation rate in each state for all units. However, due to heterogeneous working conditions or variations in the raw materials, degradation for systems within the same population may exhibit different degradation rates. Ignoring the effect of heterogeneity on the system deterioration may result in inaccurate reliability and cost estimation, and an inferior maintenance decision.

The present paper considers single-unit and non-repairable systems whose failures are due to the competing causes of degradation and shocks. The main objective is to develop system reliability and CBM models within the framework of PBC from the service provider’s perspective. There exists three possible states for a system, which are normal, degraded and failed. Transition from the normal state to the degraded state accelerates both the degradation and shock processes, resulting in increased degradation rate and higher shock failure intensity. Degradation is modeled as a two-stage inverse Gaussian (IG) process with random effects, allowing for unit-specific heterogeneity within the same population. Sudden shocks arrive according to a doubly stochastic Poisson process (DSPP). Based on the reliability model developed by incorporating the degradation-based and shock-based failure processes, we formulate a CBM model derived from the inspection-based preventive replacement policy. Along with the assessment of the long-run maintenance cost rate, the average availability of the system as the performance metric is evaluated. Adopting the profit-centric approach under PBC, the optimal maintenance policy is determined so as to maximize the expected profit rate to the service provider.

The main contributions of the present study are:

• Extending DTS models through investigating the impact of system state transition on the evolution of degradation and shock processes;

• Establishing a two-stage IG degradation model accounting for unit-specific heterogeneity, and analyzing system reliability based on competing failure processes modeling;

• Developing a CBM model and evaluating system performance outcome (average availability) based on inspection-based preventive replacement policy;

• Providing service providers for choosing the optimal maintenance strategy adopting the profit-centric approach under PBC.

The remainder of this article is organized as follows. Section 2 lists the assumptions and notations used in the reliability and maintenance modeling studies. In Section 3, we develop the system reliability model based on two competing failure processes due to degradation and sudden shocks. Section 4 proposes the CBM optimization model based on the periodic inspection-replacement policy under PBC. Section 5 presents a numerical example along with sensitivity analysis illustrating the reliability model and maintenance policy. Finally, Section 6 summarizes the main conclusions and provides suggestions for future research.