Xiaobing Ma

A preventive maintenance policy based on dependent two-stage deterioration and external shocks

This paper proposes a preventive maintenance policy for a single-unit system whose failure has two competing and dependent causes, i.e., internal deterioration and sudden shocks. The internal failure process is divided into two stages, i.e. normal and defective. Shocks arrive according to a non-homogeneous Poisson process (NHPP), leading to the failure of the system immediately. The occurrence rate of a shock is affected by the state of the system. Both an age-based replacement and finite number of periodic inspections are schemed simultaneously to deal with the competing failures. The objective of this study is to determine the optimal preventive replacement interval, inspection interval and number of inspections such that the expected cost per unit time is minimized. A case study on oil pipeline maintenance is presented to illustrate the maintenance policy.

A condition-based maintenance model for a three-state system subject to degradation and environmental shocks

A new maintenance model is established based on a three-state degradation and external environmental shocks.The influence of system state on the internal-based degradation as well as fatal shocks is considered.Two different preventive thresholds are arranged to cut down the maintenance cost.A cost comparison between the proposed policy and the constant threshold policy is conducted for validation. Condition-based maintenance (CBM) is a key measure in preventing unexpected failures caused by internal-based deterioration and external environmental shocks. This study proposes a condition-based maintenance policy for a single-unit system with two competing failure modes, i.e., degradation-based failure and shock-based failure. The failure process of the system is divided into three states, namely, normal, defective and failed, and a defective state incurs a greater degradation rate than a normal state. Random shocks arrive according to a non-homogenous Poisson process (NHPP), leading to the failure of the system immediately. The occurrence of external shocks will be affected to the degradation level of the system. Periodic inspections are performed to measure the state and the degradation level of the system, and two preventive degradation thresholds are scheduled depending on the system state. The expected cost per unit time is derived through the joint optimization of the two preventive thresholds as well as the periodic inspection interval. A numerical example is proposed to illustrate the maintenance model.

Hybrid preventive maintenance of competing failures under random environment

Abstract Competing failures are extensively observed in complex industrial systems, which may result in tremendous economic losses and safety hazards. In this article, we study a system subject to two typical failure modes, degradation-based failure and sudden failure. The system is operating under a random environment where external shocks arrive according to a Poisson process. The impact of shock damage on system failure is two-fold: (a) increase the hazard rate of sudden failure; (b) cause abrupt degradation increment. The system is preventively replaced when its age attains a pre-determined threshold (age-based replacement), and undergoes a finite number of condition monitoring (CM) before this replacement. At a CM, the control limit of preventive replacement varies with the number of CM and is determined by a reliability criterion. The objective of this paper is to jointly optimize the replacement interval, monitoring interval and reliability criterion such that the expected cost per unit time is minimized. A case study on oil pipeline is provided to illustrate the applicability of the maintenance strategy.

A delay time model for a mission-based system subject to periodic and random inspection and postponed replacement

We propose an inspection and replacement policy for a single component system that successively executes missions with random durations. The failure process of the system can be divided into two states, namely, normal and defective, following the delay time concept. Inspections are carried out periodically and immediately after the completion of each mission (random inspections). The failed state is always identified immediately, whereas the defective state can only be revealed by an inspection. If the system fails or is defective at a periodic inspection, then replacement is immediate. If, however, the system is defective at a random inspection, then replacement will be postponed if the time to the subsequent periodic inspection is shorter than a pre-determined threshold, and immediate otherwise. We derive the long run expected cost per unit time and then investigate the optimal periodic inspection interval and postponement threshold. A numerical example is presented to demonstrate the applicability of the proposed maintenance policy.

Optimal design of constant-stress accelerated degradation tests using the M-optimality criterion

In this paper, we propose the M-optimality criterion for designing constant-stress accelerated degradation tests (ADTs). The newly proposed criterion concentrates on the degradation mechanism equivalence rather than evaluation precision or prediction accuracy which is usually considered in traditional optimization criteria. Subject to the constraints of total sample number, test termination time as well as the stress region, an optimum constant-stress ADT plan is derived by determining the combination of stress levels and the number of samples allocated to each stress level, when the degradation path comes from inverse Gaussian (IG) process model with covariates and random effects. A numerical example is presented to verify the robustness of our proposed optimum plan and compare its efficiency with other test plans. Results show that, with a slightly relaxed requirement of evaluation precision and prediction accuracy, our proposed optimum plan reduces the dispersion of the estimated acceleration factor between the usage stress level and a higher accelerated stress level, which makes an important contribution to reliability demonstration and assessment tests.

Multi-level maintenance strategy of deteriorating systems subject to two-stage inspection

Abstract Preventive maintenance, including time-based and condition-based maintenance, plays an important role in reducing system economic losses caused by unexpected failures. This paper studies a multi-level preventive maintenance strategy for a three-state industrial system subject to two competing failure processes. The first is a continuous degradation process characterized by the general path model, and the second is a shock process arriving according to a non-homogenous Poisson process. The degradation/hazard rate of the system undergoes an abrupt increase upon the initialization of the defective state, and the magnitude of the damage caused by a shock load is correlated to two factors: (a) operational age; (b) degradation speed. The system is preventively replaced at a pre-determined operational age, before which a finite number of inspections are executed according to a two-stage interval partition. The objective of this paper is to minimize the expected cost per unit time via the optimization of the replacement age, the control limit and two inspection intervals. A case study on a peristaltic pump is provided to illustrate the application of the maintenance model.

Equivalence analysis of accelerated degradation mechanism based on stochastic degradation models

For an effective accelerated degradation test, it is important to ensure that the degradation mechanism under different stress levels remains unchanged. In this article, we are interested in the equivalence analysis of accelerated degradation mechanism based on degradation data rather than physical or chemical techniques. Under the assumption that products underlying degradation follows stochastic degradation models, we first introduce the relationship between mechanism equivalence and parameters of stochastic degradation models based on the acceleration factor invariant principle. Then the necessary conditions for mechanism equivalence, which should be satisfied under different stress levels, are derived and tested by the proposed parameter equivalence test method based on the modified Bartlett statistic and T statistic. Next a novel selection method for stochastic degradation models is derived therefrom by comparing the variation of coefficients of acceleration factors. The accuracy of the necessary conditions and the parameter equivalence test method is demonstrated through a simulation study. In addition, an electrical connector example with real stress relaxation data is analyzed to illustrate the proposed method further.

A CBM policy for systems subject to finite maintenance times

This paper proposes a condition-based maintenance (CBM) policy for a gradually deteriorating system that could only be repaired for finite times. Periodical inspections are performed to measure the degradation level, and the system is preventively or correctively repaired when the level reaches the preventive and failure threshold, respectively. Both preventive and corrective maintenance actions in this paper are considered imperfect. After each maintenance action, the system is restored to a “better than old” state but the effectiveness of maintenance is stochastically reduced as its number increases. In this way, the system can only keep its desired function for a very small period after sufficient number of maintenances. Therefore, the system cannot be in service for infinite duration and its usage life which is defined as number of maintenance actions needs to be determined systematically. In this respect, system service life is jointly optimized with periodical inspection interval and preventive threshold by minimizing life-cycle cost rate. A nonhomogeneous Markov model is developed to describe the evolution of maintained system and corresponding cost function. Numerical examples are presented to illustrate the application of this maintenance policy.

Rubber lifetime prediction for ADT data considering non-arrhenius behavior

In reliability engineering, accelerated degradation test (ADT) has been widely used to obtain adequate data within a reasonable period of time. All test units are exposed on higher-than-usual stress levels so that extrapolation is needed to predict actual performance in normal condition. When the accelerated stress is temperature, the commonly used extrapolation methods are based on linear Arrhenius model which has been proved inadequacy over a wide range of temperatures in recent literatures. Therefore this paper focuses on the non-Arrhenius model due to two competing processes which is consistent with our experience that there were two competitive reactions, cross-link or degradation during the aging of rubber. Motivated by a rubber degradation data, we introduce a lifetime prediction method for ADT data taking non-Arrhenius behavior into consideration, and the lifetime distribution of the rubber under normal condition is obtained. Then the validity of non-Arrhenius ADT model is illustrated based on the rubber data and the result indicates a good fit for the degradation data. Finally, we investigate the effects of model misspecification. The results reveal that in normal condition the p-quantile under an incorrect model is overestimated. Meanwhile, the effect resulted by incorrect acceleration model on degradation model parameter is quite severe under temperatures higher than 120º C or lower than 50º C. Moreover, there are still some points should be emphasize: (1) The non-Arrhenius behavior is discovered in a part of polymers, but it doesnt mean the phenomenon is inevitable. In addition, this behavior manifests in a relatively wide range of temperatures, so the non-Arrhenius model is not suitable for tests conducted over a small temperature region. (2) The degradation path model used in this paper can be extended to similar degradation path models as well as stochastic process models according to the practical requirement. (3) In this paper, we concluded that the non-Arrhenius ADT model considering two competing processes fits better for the degradation paths through statistical method. This conclusion should be further demonstrated by degradation mechanism analysis. (4) There are various non-Arrhenius models, such as the quadratic Arrhenius model [15]. Consequently, a procedure discriminating among different non-Arrhenius models will be very useful for further research

Random and periodic inspection of mission-based systems with a defective stage

We propose an inspection and replacement policy for a mission-based system based on the delay time concept, which assume the system state to be either normal or defective before failure. Such a system executes missions successively with random durations, and inspections are schemed at every completion of missions (random inspection) as well as periodic times to identify the defective state. Random inspections are perfect in that they can fully reveal the defective state. However, two cases are considered for the periodic inspection, i. e, a perfect inspection case and an imperfect case where the inspection has a fixed probability to miss the defective state. Renewal probabilities for both cases are formulated respectively so as to derive the long run average cost. The optimal periodic inspection interval is studied. A numerical example is proposed to validate the models.