Weibull Reliability and Optimal Maintenance with Spotfire® and TIBCO® Enterprise Runtime for R (TERR)

You can find the Community Exchange component here. 

Data Used

Data used directly by this template take the form of a data table with these columns describing the usage and status of "units", e.g., tires on a car, motors or valves or pumps in a machine, or batteries in devices.

• Metric that measures "usage". This might be hours, days, or years of service, or a number of cycles (for example the number of charging cycles of a battery), or the amount ("mileage") of use on tires.   Each row might correspond to a single unit, or if several units all have the same wear, one group.
• Metric that contains a string that describes the last recorded state of the unit, e.g. "Failed" or "Functioning"
• Optionally, a metric with a count of how many units are described by this row (amount of wear).  For example, a complex machine may be shut down for servicing and many parts replaced whether they failed or not.   If this servicing is done periodically then all the parts replaced might have the same usage.

Example: In the figure below each row of the table corresponds to a single unit.  The "Interval days" column contains the number of days that the unit was in service and the "status" contains the string describing the unit's status.

Analysis Plots

Failure Plot

An initial look at the data is provided by a failure plot, as below.  Here each horizontal bar represents a unit or group of units with a unique amount of usage.   The left edge of each line segment is aligned at x=0 and represents that unit going into service.  The length of each segment depicts the usage of that unit (or group).  Longer bars represent units with longer usage.   Red x symbols represent units that failed.  Blue triangles (right-arrows) represent units that were still functioning at the time they were replaced or observed.

Weibull Plot

The main analysis page of the file has a number of controls around the Weibull fit. There are user controls to map the columns of the input data, and specify a probability level, discussed next:

The main Weibull fitting plot is where the fit to the data can be evaluated:

The Weibull plot represents the fitted failure Weibull model to the failure data.   Only the failed units appear on this plot. The x-axis (labeled "Time" as this is the most common situation) represents usage.  The scaling is nonlinear and is arranged to make the Weibull curve linear.  The y-axis, on a logarithmic scale, is the fraction of the units that have failed by this usage, or the probability of failure for the fitted model.  The gray straight line is the fitted Weibull model that best fits the data, and the outer curved lines are the uncertainty bounds for this fit.

Reference Lines

• The dashed blue horizontal line (here prob=0.15) is a probability level that can be set by the user.  Here prob=0.15 represents 15% of the units of a theoretical population failing.
• The dashed blue vertical line is drawn at the intersection of the dashed blue horizontal line with the gray line corresponding to the model.  The x-location of the dashed blue vertical line is the estimated usage ("Time") where that fraction will have failed.   In this example, the x-axis is hours of service, and the blue vertical dashed line is at 4724.77 hours as is reported in the table below.  The lower and upper confidence intervals (CI) are also reported in this table, these are shown by the two vertical solid blue lines.  These solid vertical lines are drawn at the locations where the horizontal dashed probability level intersects the two curved gray lines for the model, and the CI is also reported in the table below.

Optimal Maintenance

The optimal maintenance page uses this fitted model with an economic ratio to determine the best maintenance interval.

Here the user enters the relative cost of an "Unplanned" failure versus a planned maintenance event.   Generally the "unplanned" event will be more costly, and the key parameter here is the multiplicative factor of how much more costly the unplanned event is compared with the planned event.

With this information, the Optimal Maintenance plot can be constructed (below).   On this plot the horizontal axis is the time interval (or equivalent) for the preventative maintenance.  The red curve indicates costs of unplanned maintenance - it rises with increasing time between the maintance interval.  The blue curve is the cost of the planned maintenance - these costs are highest at small intervals.   The net cost (green) has a minimum which indicates the optimal maintenance interval.

Data Preparation

Some preparation is commonly required to convert data from stored tables into the format needed.

Data Snapshot for units in service

A data table that probably comes to mind would be a table of all the units that are currently functioning and in service.   Here the individual units would have differing dates for going into service.  The end date of the observational interval would be the same for all units: the date of the data snapshot.  However the lengths of the time in service would vary greatly:

This data might be visualized as segments on a time axis, here the right side of all the segments line up at the snapshot date:

Maintenance Log for Replaced Units

A table in a database might contain a maintenance record, recording the start and end times of units, and whether they were functioning or failed at the time of replacement.   The interval in days (or other appropriate units) is calculated:

One might imagine plotting these lifetimes as segments on a time scale, for the failed units (short segments represent units that failed quickly):

and for the units that were replaced through routine maintenance, the bars here might be relatively uniform, representing that the functioning units were replaced at a certain maintenance interval.  All of these units would still be functioning at the end of their service:

In this example, one would need to combine the results of these tables to arrive at the data ready for the analysis.