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The purpose of this paper is to propose a novel condition-based maintenance (CBM) policy with two sampling intervals for a system subject to stochastic deterioration described by the Cox’s proportional hazards model (PHM).

In this paper, the new or renewed system is monitored using a longer sampling interval. When the estimated hazard function of the system exceeds a warning limit, the observations are taken more frequently, i.e., the sampling interval changes to a shorter one. Preventive maintenance is performed when either the hazard function exceeds a maintenance threshold or the system age exceeds a pre-determined age. A more expensive corrective maintenance is performed upon system failure. The proposed model is formulated in the semi-Markov decision process (SMDP) framework.

The optimal maintenance policy is found and a computational algorithm based on policy iteration for SMDP is developed to obtain the control thresholds as well as the sampling intervals minimizing the long-run expected average cost per unit time.

A numerical example is presented to illustrate the whole procedure. The newly proposed maintenance policy with two sampling intervals outperforms previously developed maintenance policies using PHM. The paper compares the proposed model with a single sampling interval CBM model and well-known age-based model. Formulas for the conditional reliability function and the mean residual life are also derived for the proposed model. Sensitivity analysis has been performed to study the effect of the changes in the Weibull parameters on the average cost.

The results show that considerable cost savings can be obtained by implementing the maintenance policy developed in this paper.

Unlike the previous CBM policies widely discussed in the literature which use sequential or periodic monitoring, the authors propose a new sampling strategy based on two sampling intervals. From the economic point of view, when the sampling is costly, it is advantageous to monitor the system less frequently when it is in a healthy state and more frequently when it deteriorates and enters the unhealthy state.

Considers an economic manufacturing quantity (EMQ) model with an unreliable production facility and a production process subject to random deterioration. Notes that the shift of the process to the “out‐of‐control” state, which may result in producing defective items, is recognized only through inspections; and that the production unit can be replaced preventively or overhauled after finishing a certain number of production runs. Proposes that the objective is to determine the lot size, inspection interval and a preventive replacement time minimizing the expected average cost per unit of time. Obtains the formula for the expected average cost for a generally distributed time to failure. Presents computational results and studies the joint effect of process deterioration and machine breakdowns on the optimal policy.

To investigate wavelet modulus maxima distribution (MMD) in machinery condition monitoring and extract a parameter that can give a quantitative description of machinery‐operating status.

Signal decomposition technique is applied to extract gear motion signal and then wavelet transform modulus maxima are utilized to define fault growth parameter (FGP).

MMD were proposed and the distribution used to derive an EWMA statistic representing machinery fault growth. A comparison with other research works indicates better performance of this parameter.

This paper presents an innovative scheme for the machinery condition monitoring, on the basis of wavelet modulus maxima representation. The definition of MMD can be utilized to derive a parameter that describes the operating status of machinery. This parameter is load‐independent so that it demonstrates better performance when compared with other research works. Further, the MMD may be treated as input of condition classification system in the future work.

The idea for this paper stems from wavelet modulus maxima representation, whilst the application in vibration signal analysis is new. It was found that, by applying this approach, the occurrence of failure is correctly identified and the proposed EWMA FGP is independent of the load applied, which is a very important property in machinery condition monitoring and fault detection.