 # Statistical Techniques to Simplify Oil Analysis Data

In oil analysis, we often must interpret a change in one parameter relative to a change in another to reach a meaningful conclusion. For example, an increase in wear levels combined with a corresponding decrease in zinc might tell us that wear is increasing due to the loss of antiwear additive protection.

Further “reading between the lines” using viscosity, acid number (AN) and infrared analysis data might tell us whether the reduced antiwear protection is the result of the addition of the wrong oil or additive depletion, and so forth.

Unfortunately, while these parameters are all important to our analysis, they use widely varying units and each has its own degree of random variation (data fragility).

That makes charting the values over time on a common graph difficult. Also, different alarming logic is applied to the different parameters. One way around this problem is to trend statistically derived percentile ratings instead of actual parameter values. Figure 1

## Benefits

This simple technique yields the following benefits to the oil analyst:

• All parameters can be reviewed on a common trend graph using common units (the percentile). This makes it easy to see what is rising and what is falling simultaneously, facilitating the process of reading between the lines. In Figure 1, it is apparent that viscosity is decreasing while particle count and iron have increased dramatically, suggesting that the wrong oil might have been added to the machine, and that has induced high wear rates.

• Common alarms can be set for all parameters and displayed on a common graph. For example, one standard deviation might represent a caution, while two might suggest a critical situation (Table 1).

• The noise effects of normal variation are factored out because each parameter’s percentile calculations are based upon its own standard deviation.

• Percentiles can be understood by anyone, including management. Particle count, mg KOH/g of oil, etc. are not so obvious to the untrained observer.

• Non-oil analysis parameters ranging from vibration overalls to skirt length can easily be incorporated into the graphics and, thus, into the analysis and decision processes.

• The technique is fast and easy. Table 1

Transfer Data into Percentiles

1. Using historical data, determine the average value (mean) for each parameter (Equation 1).

2. Calculate the standard deviation for each parameter using the same data set used to calculate the mean (Equation 2).

3. Generate a Z-Score by subtracting the mean value from the current reading, then divide by the standard deviation (Equation 3). This number tells how many standard deviations you are over or under the mean value.

4. Use cumulative normal distribution tables. Most commercially available spreadsheet programs generate a cumulative distribution value for a given Z-Score.

5. Present the normal distribution value as a percentile value. For example, suppose a machine has a mean iron level of 15 ppm and a standard deviation of 3 ppm. An observed value of 18 ppm would yield a Z-Score of 1, or one standard deviation greater than the mean. The 18 ppm value would occur at the 84th percentile. If our observation occurred at the mean (15 ppm), our value would be the 50th percentile. Table 1 illustrates where various Z-Scores occur on the cumulative normal distribution curve.

This and other techniques can be effectively applied to simplify oil analysis data and ease the diagnostic process. Try variations on the percentile theme like using a 10-sample moving average and standard deviation in place of the fixed values where it is appropriate. Such simplification is important for oil analysis to gain acceptance into the mainstream of the decision-making process.

## Making Statistics Work for You

When attempting to schedule maintenance actions based upon oil analysis data, simple statistics can be a powerful tool to simplify data, identify relationships between oil analysis parameters and increase confidence in conclusions.

Statistical techniques like correlation analysis can help ensure that we are making the right decision. They can also help focus our efforts to uncover the root cause of the abnormal condition.

Review of the oil analysis data from nine identical hydraulic machines performing the same function in the same environment reveals substantial variation in zinc levels as a function of the time the oil is in service. Further investigation leads us to conclude that acid numbers (AN) also decline as a function of time. Upon calculating the correlation, we see that zinc and AN values are highly correlated (Figure 2). Figure 2

## The Role of ZDDP

We know that the zinc dialkyldithiophosphate (ZDDP) used in most antiwear oils reacts with the potassium hydroxide (KOH) reagent used to measure AN, elevating the numbers when the oil is new.

The AN decreases as the additive is depleted. Once the ZDDP antiwear/antioxidant additive is depleted, it leaves the base stock with reduced protection from oxidation, and acid numbers will begin to increase from their minimum point as the base stock degrades.

Also, once the ZDDP is depleted, the machine is subject to increased wear due to lost antiwear protection from the fluid. Zinc and AN tend to correlate well in most oils equipped with a ZDDP antiwear additive. It is important to quantify this correlation with test data specific to an application.

The analysis indicates that one of the machines is running with low zinc levels and low AN. Because both zinc and the acid numbers have depleted, and knowing that the correlation between these two parameters is strong in this application, we have high confidence that our ZDDP additive is depleted, perhaps to the point of exhaustion. This is a situation that warrants maintenance action. It is likely that the oil has simply reached the end of its life. 