Time-dependent limits monitor factors that are not absolute – in other words, parameters that cannot be judged as normal or abnormal without taking time into account. Consider the example of 100 ppm iron (Fe) at 10 hours or 100 ppm at 1,000 hours. Without the time qualification, a simple “100 ppm” is meaningless.

Time-dependent limits can be broken into two subsets. The first one, rate-of-change (RoC) limits may be applied to any parameter that demonstrates time dependence. The second type, short oil fill interval (SOFI) limits, is an alternative means of monitoring wear parameters in certain types of components

Rate-of-change Limits
Consider a wear profile of a typical industrial lubricated component.

Figure 1. Typical Wear Profile of an Industrial Component

Wear levels start at approximately zero. As the component wears, the concentrations of wear metals can be expected to build up over time. Figure 1 shows a typical wear profile. An oil change was conducted after the sample at 400 hours, hence the drop in the wear metal levels. Looking at Figure 1, it appears that the wear generation rates are fairly constant, but taking a look at an RoC plot shows different information.

To convert a parameter to a RoC parameter, use the following:

Equation 1. Calculation of RoC Parameter


is the RoC parameter
x0 is the parameter reading for the current sample
x-1 is the parameter reading for the previous sample
t0 is a time reading taken at the time of the current sample
t-1 is a time reading taken at the previous sample

In Equation 1, two factors must be considered:

  • If the sample is the first one since the component was last drained and filled, then x-1 and t-1 are not defined. For x-1, substitute what could reasonably have been expected from a sample if one was taken immediately after draining, refilling and restarting. If viscosity was being limited, then use the new-oil viscosity for the oil. If a wear reading is being limited, then use a value of zero.

  • The time parameter can have various units. It could be hours/miles on the oil, hours/miles on the machine’s service meter, an estimate of time on the oil if a service meter is not available, and even gallons of fuel consumed in an engine. The unit of time used is not important, however it is necessary that t0 and t-1 are measured in the same units.

Taking the values from Figure 1, a new plot of RoC versus time can be generated. The gradient, or first derivative, of the parameter-time curve in Figure 1 is now being plotted, so what was a steadily increasing line now approaches a horizontal trend (Figure 2).

Figure 2. RoC Plot for Iron

Figure 2 illustrates a definite jump in iron generation at 300 and 350 hours (samples 7 and 8). This is not clearly evident in Figure 1.

In many cases, it is not sufficient to use as defined in Equation 1. During a component’s oil-fill life, makeup oil is often added to the system. This must also be taken into account because every time oil is added, certain properties of the oil in use are diluted, such as wear, contaminants and additives.

To account for makeup oil and ensure that the dilution does not affect the results, the lab numbers for this makeup oil must be normalized. To do this, a normalization factor for makeup oil should be introduced. The mathematics of normalization for volume have been simplified in order to aid understanding:

Equation 2. Normalization Factor for Makeup Oil

Nm is the normalization factor for makeup oil
V is the sump volume of the component
v is the volume of makeup oil added since the last oil drain

The units of V and v are insignificant, as long as they are the same.

Equation 1 should then be modified to:

Equation 3. RoC Limits Modified for Oil Consumption

is the RoC parameter normalized for makeup oil

How important is normalization for makeup oil? It depends on accuracy. If one assumes that the addition of the makeup oil is constant, and in some cases this is a fair assumption, then the normalization factor is a constant from sample to sample and may therefore be ignored. However, problems do occur and oil consumption rates can change. Consider the example in which an engine ingesting dirt is going to wear the rings, and worn rings lead to increased oil consumption. In this case, ignoring normalization will not help.

Take a look at an example of how RoC limits can be applied to an engine.

Table 1. Typical Set of Data for
Fe Generation in an Engine

Table 1 represents a typical set of data for iron generation in an engine. Oil changes were performed immediately after samples 2, 4, 5 and 7, and the makeup oil quoted is the amount since the previous oil fill.

Figure 3. Plot of Raw Iron Data

A plot of the raw data, as in Figure 3, is n ot very informative. The data is erratic and difficult to interpret.

Plotting an RoC graph, Figure 4 provides a different picture. The saw-tooth curve of Figure 3, has been replaced by a curve to which it is easier to apply a limiting level. Note in Figure 4, the data has not been normalized for makeup oil. The limits represented in Figure 4 have been arbitrarily chosen, but help illustrate the principle. It would appear that this engine is running smoothly, with just a slight jump in the iron at sample 3.

Figure 4. RoC Plot for Fe, Not
Normalized for Makeup Oil

In Figure 5, the RoC data has now been normalized for makeup oil.

Figure 5. RoC Plot for Fe with Data
Normalized for Makeup Oil

It is immediately apparent that an abnormal operating condition on this engine has been encountered. A look back at Table 1 shows that the wear levels have remained more or less constant (in relation to the period oil in use), but the oil consumption rate has increased dramatically.

This situation occurs regularly in engines: increased dirt ingress leads to increased wear and oil consumption. The additional makeup oil further dilutes the increased wear (and the contamination readings), so the wear is not apparent without taking into account the makeup oil. This can also occur with overheating. Overheating can cause volatiles, or light fractions in the oil, to evaporate. This volumetric loss must be made up with top-up oil. Some type of wear is usually associated with overheating, and the wear readings will be diluted by the makeup oil. So if accuracy of interpretation is important, then obtaining and recording oil makeup volumes are imperative.

Recording makeup volumes has not always been easy. But with a little innovation and readily-available technology, it is not an insurmountable challenge. Access Noria’s buyers guide at http://www.machinerylubrication.com/BuyersGuide/ for a selection of dispensing meters and other equipment to help obtain the information needed.

Short Oil Fill Interval Limits
Another type of limit that can be employed to monitor wear parameters in certain cases is the short oil fill interval limit (SOFI). It may be viewed as an alternative to RoC limits.

The SOFI limit can be used where:

  • The oil-fill period is relatively short

  • There are typically few samples, possibly only one, during the oil-fill time

  • Samples are more often than not taken at more than half a predefined “standard time” and less than twice the standard time

The “standard time” would typically be the OEM’s recommended oil drain interval.

SOFI intervals are suited to engines and other automotive components where the conditions discussed above are fulfilled.

The technique relies not only on normalizing for makeup oil, but also on time on the oil. Once again, the time does not have to be hours – it could be miles or fuel consumed.

Normalization for makeup oil has already been discussed. Normalization for time is accomplished using:

Equation 4. Normalization Factor

Nt is the normalization for time factor
ts is the defined standard time
tp is the period the oil has been in use

To normalize a parameter for time, use the following:

Equation 5. Normalization for Time

xt is the normalized parameter
x is the parameter to be normalized, the raw data

To normalize for time and makeup oil,

Equation 6. Normalizing a Parameter for Time and Makeup Oil

xtm is the parameter normalized for both time and makeup oil

Using the same data in Table 1 and normalizing for both time and makeup oil produces the curve in Figure 6.

Figure 6. SOFI Limits Applied to Data in Table 1

Figures 5 and 6 are slightly different, but they still convey the same important information. In practice, SOFI interval limits would probably be used where only one sample is taken during an oil-fill interval, in which case the result would be the same as a RoC plot normalized for makeup oil.

A few notes on SOFI limits:

  • Ignore samples where the period oil in use is less than half the defined standard time, or more than double the defined standard time. This is because the SOFI limit assumes a linear parameter-vs.-time relationship, and also an assumed starting value of zero. While this is approximately true for wear generation in the area around the standard time, it is not true everywhere else on the curve. Wear levels do not start at zero, because there is usually some residue left over from the previous fill. When oil has been in use for a long time, deposition rates can approach generation rates and the wear curve will start to flatten.

  • Do not attempt to use SOFI limits for parameters that do not start at or close to zero at the beginning of an oil’s life. Take viscosity for example. If one has a time in use of 125 hours, a defined standard time of 250 hours, and assuming no makeup oil added, then using Equation 4 to normalize for time would result in a factor of 0.5. Substituting into Equation 5 will give a normalized viscosity half its starting value, which is obviously false.

  • SOFI limits should not be used on contamination parameters. Use proactive time-independent (PTI) or reactive time-independent (RTI) limits for these. Contamination is a time-independent parameter.

Setting the Limits
Now that the correct limit or limits have been selected, one can choose the numbers which define those limits.

There are various ways of setting the limit. It is beyond the scope of this article to go into full detail; however, a couple of starting points are suggested below:

  • For time-independent limits, look at both the lubricant OEM and the machine OEM specifications. Use these recommendations as a ceiling level. There are various techniques for refining these specifications based on the oil and machine life expectancies needed.

  • For time-dependent limits, use statistical analysis. Gather the oil history data, apply the conversions and normalizations where applicable, then calculate the mean and standard deviations of the data set. Create an alarm or cautionary limit at the mean plus and/or minus (whichever is applicable, perhaps both are) one standard deviation, and set the critical limit using the mean plus or minus two standard deviations. 1

  • Limits are not meant to be set and forgotten. Like the rest of a lubrication management program, limits should be subjected to continuous-improvement principles. Use common sense here too: if the limit never gets touched, then maybe it is set too loosely. If the limits are continually exceeded, maybe they’re unrealistic for the application.

Limit Interpretation
The correct type of limits has been selected, and the limiting values have been determined. Now it’s time to put the limits into practice. There are three rules to follow:

  • If a parameter intermittently exceeds the cautionary limit do not take action, merely continue to monitor.

  • If a parameter exceeds a cautionary limit three times in a row, then intervention is required.

  • If a parameter exceeds the critical limit once, then intervention is required.

These results are illustrated in Figure 7.

Figure 7. Use of Limits2

Tying It Together
To summarize the limit selection process:

  • Determine the time-dependent or the time-independent properties of the parameter in question. Investigate the parameter’s “absoluteness”. If its value at a particular moment in time is irrelevant to the actual time in use, it is time-independent. A time-dependent parameter is one which is meaningless unless the period for which the oil has been in use is taken into account.

  • Choose time-independent limits (RTI- and PTI-limits) on parameters that fit the definition of time-independence.

  • Select PTI limits to monitor parameters which can be immediately and directly controlled. Such parameters typically include moisture contamination and particulate contamination. An out-of-limit situation here does not mean the oil or machine is damaged, it simply suggests something needs to be done, otherwise the oil or the machine will soon be damaged.

  • Choose RTI limits to monitor those time-independent parameters that are not directly controllable. Such parameters include acid number, base number, viscosity and additive levels. In most cases, reaching an actionable RTI limit indicates a needed oil change.

  • Choose RoC limits to monitor time-dependent parameters. All parameters can be monitored with RoC limits. Normalize for oil consumption where possible.

  • Some parameters have time- independent and time-dependent properties, so use more than one limit to monitor the same parameter. Viscosity can employ an RTI limit to determine oil-change time and an RoC limit to monitor abnormal rates of change.

  • Select SOFI limits, as an alternative to RoC limits, to monitor wear parameters in components with relatively short oil-fill intervals and few samples, likely only one, during the oil-fill interval. Normalize these parameters for both time in use and oil consumed.

Table 2 indicates where the limits discussed in this article are most likely to be used for common oil analysis tests. This table should be seen as a generalization rather than an instruction. Also note that where two time-dependent limits or two time-independent limits are indicated, it is sufficient to choose only one.

Description Parameters directly
Parameters not
directly controllable
Most parameters Everything with approximately linear
relationship to time and starting
(new oil) values approximately 0
Set Limits: Use OEM or published
Use OEM or published
Statistical analysis Statistical analysis
Particle Count X      
Moisture X      
AN/BN   X X  
Viscosity   X X  
Elemental Analysis (additives)   X X  
Elemental Analysis (contamination) X X X  
Elemental Analysis (wear)     X X
Ferrous Density     X X
Flash Point   X X  
Table 2. Summary of Limit Selection

Selecting the correct limits is not difficult once one understands the concepts behind them. Unfortunately, not having a grasp of these concepts can lead to incorrect selection and use, as well as a reduction in the benefits that oil analysis can provide. The most common example of this is choosing a time-independent limit for wear. This approach might lead to either premature disposal of the oil, or excessive wear needing to be generated in order to reach the limit.

Having a sound grasp of the limit selection process is imperative to harness the full benefits of this powerful technique. There is more to limits than just a reactive aging limit, so get proactive with limit selection in order to nail down reliability goals.


  1. Statistically Derived Rate-of-Change Oil Analysis Limits and Alarms.” Practicing Oil Analysis magazine, January-February 2002.
  2. KOWA as cited in Oil Analysis II Course Notes. 2004.

Related Reading

Mayer, A. “A Hands-on Approach to Limit Selection and Use.” Practicing Oil Analysis magazine, September-October 2004.