Parameter estimation for partially observable systems subject to random failure

Abstract

In this paper, we present a parameter estimation procedure for a condition-based maintenance model under partial observations. Systems can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is driven by a continuous time homogeneous Markov chain and the system state is unobservable, except the failure state. Vector information that is stochastically related to the system state is obtained through condition monitoring at equidistant sampling times. Two types of data histories are available -data histories that end with observable failure, and censored data histories that end when the system has been suspended from operation but has not failed. The state and observation processes are modeled in the hidden Markov framework and the model parameters are estimated using the expectation-maximization algorithm. We show that both the pseudolikelihood function and the parameter updates in each iteration of the expectation-maximization algorithm have explicit formulas. A numerical example is developed using real multivariate spectrometric oil data coming from the failing transmission units of 240-ton heavy hauler trucks used in the Athabasca oil sands of Alberta, Canada. Bus. Ind. 2013, 29 279-294 Appl. Stochastic Models Model assumptionsWe assume that a technical system's condition can be categorized into one of three states: a healthy or 'good as new' state (state 0), an unhealthy or deteriorated state (state 1), and a failure state (state 2). In many real world applications the state of an operational system is unobservable, and only the failure state is observable. For example, the state of an operational transmission unit in a heavy hauler truck cannot be observed without full system inspection, which is typically quite costly.Appl. Stochastic Models Bus. Ind. 2013, 29 279-294 As detailed in Section 2, to satisfy the assumption of independence and normality, we first need to fit a model that accounts for autocorrelation in the data histories, and choose as the observation process, in the hidden Markov model, the residuals of the fitted model. Before fitting a model to the data histories, we have to approximate the healthy portions of the

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

“…In Figure , the relative errors (RE) ( RE = | ARL − MRL |/ ARL × 100%) between the actual remaining useful lives and the prediction results using different models are presented. As can be seen in Figure , with the increase of the amount of the collected data, both the RE in the prediction results for TR#5 and TR#13 using the competing risk model are smaller than those when using the HMM in Kim et al, and they are closer to the actual values. Thus, the life prediction method proposed in this paper gives considerably better prediction results than the model which does not consider the dependence of the two failure modes.…”

“…While in TR#13, the prediction results of the catastrophic failure show that although the prediction errors are relatively large in the first 30 files, they decrease rapidly later, which indicates that the proposed HMM in this paper can better predict catastrophic failure of the gear system. When using HMM by Kim et al, the prediction errors are larger for these two tests. This is mainly because the model proposed by Kim does not take into account the likelihood of system failure when the machine is working under healthy condition.…”

Reliability estimation of a system subject to condition monitoring with two dependent failure modes

“…We also compare the capability of the fault prediction of the proposed model with a three state HMM assuming that the catastrophic failure can only occur after completing the sojourn time in the healthy state with probability p 12 or it can fail due to degradation after completing the sojourn time in the unhealthy state [17] which we have already called Model 3. Using all 42 suspension and failure histories, we estimate the parameters of the Model 3 (see Table 3).…”

Reliability estimation of a production system subject to condition monitoring with two modes of failures

“…Recently,Kim et al (2012) developed a parameter estimation for a HMM in the same framework assuming that the sudden failure can only occur after completing the sojourn time in the healthy state with some probability (Model 2). For the performance evaluation,…”

“…The effect of considering different number of degradation failure histories on performance of estimation procedure and computational time we estimate the parameters of the Model 2 using the results inKim et al (2012) as well as the CMRL and CRF for model 2.…”