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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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