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This topic describes how to use the parametric RDA folio control panel to perform recurrent event data analysis. It includes the following sections:
The parametric RDA folio control panel is arranged into groups of related tasks. Each group has its own page on the control panel. The Main page contains the settings for selecting the number of parameters to calculate and the virtual age model.
Tip: There is a horizontal splitter bar directly above the Main button. If you drag it as far up as it will go, all of the pages of the panel will be accessed by large buttons. If you drag it all the way down, all of the pages will be accessed by small icons. Positions in between allow you to use some large buttons and some small icons. See Control Panels.
The Analysis Summary area of the control panel displays the calculated values of the parameters and the likelihood (LK) value of the GRP model. Click anywhere within the area to open the Results window, which displays the calculated results in a worksheet. From the Results window, you can edit, copy or print the results.
The folio tools are arranged on the left side of the panel.
Calculate estimates the parameters of the GRP model, based on the current data set. This tool is also available by choosing Recurrent Event Data > Analysis > Calculate.
Plot creates a new sheet in the folio that provides a choice of applicable plot types. In parametric RDA folios, this includes cumulative failures vs. time, failure intensity vs. time, etc. This tool is also available by choosing Recurrent Event Data > Analysis > Plot.
QCP opens the RDA Quick Calculation Pad, which allows you to calculate results based on the analyzed data sheet, such as the number of failures and mean time between failures (MTBF). This tool is also available by choosing Recurrent Event Data > Analysis > Quick Calculation Pad.
Change Units opens the Change Units window, which allows you to change the time units of an existing data sheet.
The GRP model uses the concept of virtual age to mathematically capture the effect of the repairs on the subsequent rate of occurrence of failure (i.e., failure intensity). The rate of occurrence of failure over time is modeled by the power law function. This means that the GRP analysis method has three parameters, two of which are used to describe the power law function and a third for estimating the virtual age of a system.
The following settings are available on the Analysis page of the control panel:
The Virtual Age Model area allows you to select one of two ways that the GRP model can calculate the virtual age after each repair:
Only since last repair (Type I) assumes that the repairs will remove some portion of the damage that has accumulated since the last repair.
From the beginning (Type II) assumes that the repairs will remove a portion of all the damage that has accumulated since the system was new.
The ReliaWiki resource portal explains the mathematical concept behind these two models at: http://www.ReliaWiki.org/index.php/Imperfect Repairs. (Note that the article is written for ReliaSoft's BlockSim software, but the theory remains the same.)
Since it may not be feasible to classify real-world repair situations into one of these two abstract categories, the virtual age type is usually selected based on what provides a better statistical fit for the data. The model fit can be assessed by using the likelihood (LK) value that is displayed in the Analysis Summary area on the control panel, where the higher value indicates the better fit.
The Simulation Settings are for the Monte Carlo simulation. In general, the application uses the failure times supplied by the data set in order to calculate virtual age. However, when extrapolating for results that are outside of the range of observations, the failure times are unknown. Therefore, unless the virtual age parameter q = 1, there are no analytical solutions available for metrics such as total failure number and failure intensity. In this case, the solution can be obtained only through Monte Carlo simulation.
In the Number of Simulations field, specify the number of data points to generate in the simulation.
The Use a Fixed Seed checkbox is an optional setting that allows you to specify a starting point from which random numbers are generated in the simulation. The same random numbers and, therefore, the same simulation results will be generated when the same seed value and number of data points are used.
The Parameterization option allows you to select how you want the parameters to be calculated. By default, the software calculates for the beta, lambda and q parameters. However, if you want to publish the model and use it in BlockSim, then you need to express the power law parameter, lambda, in terms of the Weibull parameter, eta, and express the virtual age parameter, q, in terms of the RF parameter (which users of BlockSim will recognize as the restoration factor of a maintenance action). To do this, select the check box in the Parameterization area shown next.
The relationship between the power law parameter, lambda (λ), and the Weibull parameter, eta (η), is described as:
The relationship between the q and RF parameters is described as:
The RF parameter indicates the degree to which the condition of a system will be restored after each repair. Parameter q indicates the opposite. A value between 0 and 1 indicates the extent of the repair, where:
An RF = 1 indicates that the system will be “as good as new” after the repair. This is also called perfect repair.
An RF value between 0 and 1 indicates that the system will be “better than old but worse than new” after the repair. This is also called imperfect repair.
An RF = 0 indicates that the system will be “as bad as old” (i.e., no improvement) after the repair. This is also called minimal repair.
If you select the 2-parameter GRP on the Main page of the control panel, you will be prompted to specify a value for the RF parameter (or the q parameter, if you use the default setting) based on your own knowledge about the effectiveness of the repairs. If you select the 3-parameter GRP, the software will calculate the RF parameter based on the data, giving you an indication of the effectiveness of the repairs as reflected by the data set.
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