LÍNEAS ELECTRIFICADAS. CATENARIA Y LÍNEA DISTRIBUCIÓN

This section describes what data is needed, how it is obtained and what ma- nipulation is required if any. It is appropriate to first name what data is needed and then suggest a way to ensure the necessary data is obtained.

3.3.1

Required Data

Section 2.3.2.5 mentions the three parameters which are necessary for survival analysis. Since prognostics makes use of both the historical failure data and the CM data, both are to be obtained from the selected experts. The first parameter is the historical event times (Xi) of the equipment considered. An

event can be a functional or physical failure, a preventative maintenance action that was conducted or a predictive maintenance action. This leads to the second parameter required, the event indicator (Ci).

The event indicator is meant to show if the observation was recorded at a failure or not. This is usually a binary indicator with one representing a failure and zero a censored observation. The different types of censoring are discussed in Section 2.3.2.5.

The final parameter needed is a matrix of covariate values; these covariates are explained to be characteristic values of the equipment considered. These values are obtained from CM equipment. Values are needed from the initial time of operation since some models require the covariate behaviour over the entire period of operation for time-varying covariates. The final parameter can thus be a matrix that has a column for each covariate and shows the covariate behaviour over the period of the study. The progression of each covariate over time is necessary for each period of operation and for all the assets involved in the study. The final data set only contains the final covariate values (the covariate value at the time of the event) but it is also necessary to have the progression of the covariate value over time.

To summarize, the data needed to conduct reliability analysis consists of three different parameters, namely the time to the event, the event indicator and the value(s) of the selected covariate(s). This is data that should be generally available at organizations with a mature AM system but, unfortunately, it is not that simple in industry. The necessary data is rarely available, which is why this study aims to extract this data from experts and to use this subjective data in the survival models. After knowing what data needs to be obtained, the next step is to obtain the data.

3.3.2

Obtaining the Data

It is now known what data is to be obtained and from whom. The exact steps of extracting the data are now presented in a way that eases the process of collecting the data as much as possible. There are three different techniques of obtaining the required data.

First Technique

The first technique is to provide the selected experts with event times. Once the experts are given the event times, they will be required to provide the be- haviour of the relevant covariates during the operating periods. This is meant to be representative of the population for the system considered. The covariate values over the operating time for each observation should also be obtained from the experts; this is important in order to compare the knowledge of the experts against the data available from research done and used in industry. Figure 3.2 presents a table of all the data that is provided and what must be obtained from the experts. The figure also displays the behaviour of the covariates for the duration of one observation. The experts will be expected to provide this for each time period in the data set. This means that there will

t Z1 t Z2 t Z3

Figure 3.2: Data extracted with first technique.

be a set of covariate behaviour curves for each of the observations describing the progression of each covariate from the start until the time of observation or failure.

Second Technique

The second technique of extracting the necessary data from the experts would be to provide them with the covariate values and ask them to deliver the failure times. Here they will be provided with the starting and ending values of the characteristic covariates for certain time intervals. They are then to provide the event times as well as the progression of the covariates over the time periods which they provide.

Table 3.3: Example of data provided for second technique.

# Xi Ci

Z1 Z2 Z3

Start End Start End Start End

1 ? 1 1.0 2.8 0.8 1.9 25 40

2 ? 1 1.4 2.4 0.9 1.6 25 38

· · · ·

· · · ·

12 ? 1 1.7 4.4 1.5 3.3 25 55

Table 3.3 presents the data provided before the experts deliver their opinions. Together with this, there will also be the regression of the covariates over the time period of each observation.

Third Technique

The last option is to combine the first two techniques and obtain the data through a combination the techniques. The data set will then be created by

obtaining the first half of the data points with the first technique and the second half by applying the second technique. There are certain aspects which are needed for all three of the techniques as discussed next.

Collecting Data for All Techniques

With all of the different techniques it is necessary to ensure that the experts agree about the data. Consensus concerning the opinions delivered is thus important. Here, a suggestion is made to provide each expert with the same information set and have each one deliver their own opinion on that informa- tion. An attempt must then be made to ensure that the different experts agree upon their opinions before continuing. Figure 3.3 presents a flow diagram of the data acquisition process.

Stepk3

Techniquek1kkor Techniquek2kkor Techniquek3

Supplykinformativekdatak kkktokindividualkexperts Collectkindividualk kkkkkkkopinions Presentkindividualkopinionk kkkkktokallkotherkexperts Consesuskreachedkonk kkkkkkkkkkopinions Usekactualkdataktokprovekor kkdisprovekthekproblematick kkkkopinionkifknokconsensusk kkkkkkkkkafterkthirdkround Askkexpertsk tokreconsider Useknewkdatakset Savekdatakpoint Stepk4 No Afterkfirstkand ksecondkround Afterkthird round Yes

Figure 3.3: Flow diagram of data extraction process.

A single data point is thus yielded from a successful round of one of the tech- niques from this step. If there is no consensus after the third round, the actual

data, which the data set provided to the experts is based upon, must be pre- sented to them. The data set that is obtained at the end of this process is then to be used to populate the survival models, thus, using the Step 4 of the proposed solution to select the most appropriate survival model for the specific data set. To ensure that the data can be used in the survival models, slight manipulations might be required; this is now considered.

3.3.3

Manipulation Required

Step 3 is meant to eliminate the need for large manipulating processes of the data before feeding into the survival models. The different models might re- quire small changes to be made depending how the models are implemented in the relevant software. Thus, small modifications might be required for some models; should this be necessary. Each model will be discussed separately in Section 3.4. The next section explains the process of selecting the appropriate survival model for the specific data set.