168 consuming particularly when the underlying state is continuous, hence we explore
approximation approaches namely grid based method and particle filtering. In short, here we demonstrate several important conclusions from the study.
1. Defining the underlying state of the system and their relationship with the
condition monitoring towards a failure is important to quantify the condition of the system. If different variables are used to define the underlying state of the system,
they should produce similar outcome in predicting the failure.
2. This research proves that monitoring information plays an important role in
prediction the condition of the itemsystem concerned.
3. It is a crucial to explore the observed condition monitoring data before
fitting it into the model. Any presence of trends or other patterns in data can provide valuable information in the study.
4. A simulation approach is useful to help us in establishing and testing a
model before it can be applied with a real data.
5. Approximation by numerical techniques is used to overcome problems exist
in the analytical form. It provides us with a balance between result and computational effort to gain the result.
6. This research also proves that subjective information is helpful while facing
non-identifiable parameters estimation.
In the next section, the contributions of this study are presented.
9.2 Contributions of the Research
The aim of this thesis is to address the need of modelling to support maintenance decision- making given the condition monitoring data. For this purpose, we reveal that modelling
169 maintenance decisions based upon condition monitoring data is under explored. As the
problem is addressed, our aim is to investigate how previous techniques are used to approach similar problems. One of the techniques that pay us a lot of interest is CRT
modelling. In Chapter 3, a new idea for CRT model is presented. Here, we assumed that the CRT is no longer a continuous measure but it could take a set of discrete values, which
could explain the state of the system. We consider this matter because in practice, after the monitoring took place, one would like to know the state of the system such as normal,
defect or failed as it is easy to understand and then performs actions as necessary. Since each state can move to another state randomly, we formulated the transition probability that
best describes the Markov process of our model. It is shown that the transition from one state to another is a time dependent. Using this model, we developed a model to identify the
initiation of a random defect based upon the simulated data that was motivated from vibration monitoring.
In Chapter 4, the model developed in Chapter 3 is tested and validated with actual data obtained from a study of six rolling elements bearing Wang, 2002. Also, an attempt to
compare the result that we produce based upon the model developed in Chapter 3 with another study Zhang, 2004 using the same data is carried out. In Chapter 5, we noticed
that calculating the ‗hidden‘ state of the system, as shown in our model in Chapter 3 is complex and time-consuming. Therefore, as a contribution to this thesis, Chapter 5
proposed the numerical approximation solutions for the model developed in Chapter 3, namely a grid based and particle-filtering approach. Both approaches are widely used to
solve a problem related to Bayesian filtering approach, which has a similar representation with our Hidden Markov Model. In addition to this contribution, there is no evidence that
both approaches have been used in any study in maintenance or reliability tasks.
In Chapter 6, a huge amount of oil analysis data from diesel engines is obtained, which required a lot of effort to clean, analyse and organize the data for our models. The
contribution in this chapter is mainly on cleaning, analysing and organizing the data that need to be used in the CRT model. Issues such as approximate the complete data from
incomplete data and how we regularize the monitoring interval from irregulars monitoring
170 interval is discussed. It is noted that, a technique called principal component analysis is
used to reduce the dimension of the data input.
In Chapter 7, we extend the model developed in Chapter 6 with a few new extensions as we embed lubricant and contaminant data as responsive factors that could increase or decrease
the residual time. The contribution of this chapter is the extension of the model and organizing data for model input. We applied independent component analysis to the dataset
due to the fact that each element from the responsive dataset does influence the residual time, but correlated to each other.
As we mentioned in the thesis, residual time is only a measure used to describe the deterioration process of an item. In Chapter 8, another measure that we believe to be
appropriate in describing the deterioration process is introduced. A general wear deterioration process is presented and the transition probability of this continuous state is
modelled by a beta distribution. An attempt to investigate the relationship between the wear model and residual time model is carried out. The analysis concludes that both models
produced similar results. One critical advantage of this model is that the threshold level normally needed is no longer used.
9.3 Future Research and Other Issues
