Reliability HotWire

Issue 80, October 2007

Tool Tips

* When should rank regression or maximum likelihood estimation (MLE) be used when conducting life data analysis in Weibull++?

When analyzing life data in Weibull++, you need to select a method for estimating the parameters for your chosen distribution: rank regression on X (RRX) or Y (RRY) or maximum likelihood estimation (MLE). How do you know which method is most appropriate?

Regression generally works best for data sets with smaller sample sizes (as sample sizes get larger, 30 or more, these differences become less important) that contain only complete data (i.e. data in which all of the units under consideration have been run or tested to failure). There are two forms of regression: regression on X and regression on Y. Failure-only data is best analyzed with rank regression on X, as it is preferable to regress in the direction of uncertainty. If a reliability test is repeated with the same number of units operated to failure in each experiment, the failure times would change from test to test, but the rank values would remain the same, since they are based solely on sample size and order number. Hence, the uncertainty is on the failure time values, which is on the x-axis, thus regression in the X direction is the most appropriate. It has also been shown that for smaller sample sizes, rank regression on X tends to produce more accurate results than rank regression on Y. Analyzing the results of Monte Carlo simulation has shown that the rank regression on X results are closer to the actual distribution used to generate the data than the results of regression on Y.

Rank regression on Y is best used with data other than time-to-failure data, such as free-form data. An example of this would be warranty data that have unreliability estimates for each month of a warranty period. These would be plotted on a probability plot in much the same way as regular failure time data. Since we know the time values in question, and the unreliability values are estimates, the uncertainty is in the Y direction, and regression on Y would be more appropriate.

When heavy or uneven censoring is present and/or when a high proportion of interval data is present, maximum likelihood estimation methods usually provide better results. MLE better incorporates the time-to-suspension points into the parameter estimates and can therefore handle suspensions and interval data better than rank regression, particularly when dealing with a heavily censored data set with few exact failure times or when the censoring times are unevenly distributed. It can also provide estimates with one or no observed failures, which rank regression cannot do.

* How can I model a specific maintenance routine in a phase diagram in BlockSim?

The powerful new phase diagramming features in BlockSim 7, which model systems that change over time, also let you define a specific maintenance routine for components in those systems. When a maintenance phase is added to a Reliability Phase Diagram (RBD), it must be associated with a Maintenance Template. In the example shown below, the production of an oil refinery is modeled with a maintenance phase following the shut down phase. This maintenance phase is associated with Maintenance Template1, as specified in the Phase Properties window.

During this maintenance phase, maintenance actions will be performed on all the blocks listed in Maintenance Template1. The Maintenance Template serves as an inventory, or checklist, of components that need maintenance. By default, the maintenance priority will be set according to the order in which the blocks were added to the Maintenance Template. When a new block is added, BlockSim automatically assigns the block a number, which appears below the block name, as shown below.

You can move the blocks into a different configuration within the sheet, if desired, but the numbers assigned automatically by BlockSim or via the Set Maintenance Priority window will determine the maintenance order of the blocks. Unlike RBDs and RPDs, the configuration of blocks within the Maintenance Template does not impact a simulation.

If you want to change the maintenance order, click the Set Maintenance Priority button. In the Set Maintenance Priority window, you can select the block you would like to move and then click the Move Up or Move Down button to move it up or down the priority list, or drag the block to its new priority in the list.

When the maintenance phase begins, the maintenance actions will start on the first block and progress down the list. Note that maintenance actions can be performed on multiple blocks simultaneously if they do not share any resources. For example, if the first block in the list is associated with one crew policy, and the second block in the list is associated with a different crew, maintenance may begin on both blocks at the start of the maintenance phase, rather than in sequence. If you change the maintenance order and click OK, you will see that the block numbers are automatically updated in the Maintenance Template to reflect the new maintenance priority, regardless of where the blocks are located within the Maintenance Template.

(To examine this example further, select Open Examples Folder from the Help menu in BlockSim 7. The file "Oil Refinery.rbp" is located in the Phases folder.)

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