Use Statistical Analysis to Create Wear Debris Alarm Limits

Jonathan Sowers, Polaris Laboratories

One of the questions most frequently asked of oil analysis labs is “What are the critical wear metal limits for my equipment?” For years, oil analysis labs have been reluctant to provide this type of information. This is partly because not all labs have well established wear metal limits, and providing this information to unprepared maintenance supervisors can result in premature and unwarranted teardown. With today’s more sophisticated approach to maintenance, and better-prepared supervisors and engineers, it is easier to explain and justify condemning limits for a variety of machine components. This empowers oil analysis users to take control of their oil analysis data interpretation and management. This article discusses one approach to setting wear metal alarms commonly used by commercial oil analysis labs and equipment manufacturers - one that is easily adapted to allow oil analysis users to set their own wear metal limits.

Statistical Wear Metal Alarm Limits
The use of statistics is essential in establishing alarm limits for wear metal concentrations. Oil analysis labs and OEMs use several approaches to determine wear metal limits. The most common, and most readily adaptable to user defined limits, is to use a simple statistical model to analyze the spread of data from similar components. This model assumes that elemental concentrations from similar equipment fall into a normal population distribution (Figure 1). In a normal population distribution, the average (x) of all data points is also the most common value reported, with a certain probability that a reading may fall either above or below this value as indicated.

Figure 1. Frequency Curve

To calculate the average, simply sum all the data point values and divide by the number of data point values.

However, what is required to define what is normal under this type of distribution is to know not only the average value of all data points, but also the range of values which are possible, represented by the width of the curve (Figure 1). To define this width or range, statisticians introduce standard deviation, which in general terms is a measure of the width or range of a normal population distribution. The standard deviation, often given the Greek letter o, may be calculated using the following mathematical formula:

In this equation, xi represents each data point in the data set, x is the average of all data points, and n is the total number of data points. Table 1 shows an example of how o can be calculated based on a data set of 10 sample results.

Assuming a normal population distribution, any reading which falls within x±o lies within 68 percent of all values in the data set; warning limits for wear metal analysis using this approach are typically set at x+o. Expanding this range to x±2o means that any reading that falls within this window lays within 95 percent of all values in the data set. x+2o is typically used as a critical or condemning limit for wear metal concentrations. Based on this and the data given in Table 1, the warning limit for this data set would be set at 28.0 (x+o) and the critical limit at 33.3 (x+2o).

The value of this approach to setting wear metal limits is that it fairly accurately represents the expected wear metals concentrations in used oil samples - provided the data set is selected appropriately and is large enough (typically >25 discrete data points is considered sufficient). Most commercial oil analysis software programs, as well as commonly used spreadsheet software, are able to calculate the average and standard deviation for a selected sample population directly, simplifying the task of calculating user defined limits.

Data Set Selection
The accuracy of the normal population distribution approach to setting wear metal alarms depends not only on the size of the data set, but also on the commonality between the components and sample results from which the data is selected. For example, simply taking wear metal data from all components labeled gearbox will not provide a sufficiently detailed description to provide accurate data. This is because the wear rates for each gearbox depend on the type of gears (hypoid, spur, etc.), the metallurgy (carbon steel, sintered bronze, etc.), the application and load to which the gearbox is subjected and several other factors. The selection criteria that should be used to define the components to be included in any data set are shown in the Information Pyramid (Figure 2).

It is important to note that with each change in selected criteria, the sample results that make up the data set change significantly, resulting in differing alarms and limits. For example, consider a transmission. Using the descriptor auto/power shift transmission may lead to the critical condemning limits shown in Figure 3a based on a data set of sample results listed under the general term transmission. Adding an additional descriptor, in this case the manufacturer Allison, to refine the data set results in a significant change to the calculated alarm limits (Figure 3b). Further defining the data set by adding the model number results in yet another significant change in alarm limits (Figure 3c). In general, the more detailed the descriptor used to define a data set, the more statistically accurate the analysis and the alarm limits will be. In fact, by refining the data set according to the criteria shown in Figure 2, the data set can be refined to such that the statistical analysis is truly representative of what should be considered normal for a specific component and provide accurate, meaningful alarm limits.

The key to success is accurately defining the data set. That means not just tracking samples by an equipment identifier and generic component type; but tracking by manufacturer, oil type, application and other factors so alarm limits can be established that truly reflect an acceptable range for each specific component. Because of the amount of data that can be amassed in a short period of time, this approach is most adaptable to mobile fleet applications, particularly engines. However, with sufficient data from similar components operating under similar conditions, there is no reason why this approach cannot be adapted for use in stationary plant equipment applications as well.

Several years ago, the task of analyzing large amounts of data from multiple components, categorizing them into discrete data sets and performing statistical calculations would have been prohibitively time consuming. The emergence of sophisticated oil analysis tracking and data management software programs has made this type of approach routine for those companies in the upper echelon of oil analysis excellence.

This article is an adaptation of a paper submitted for Practicing Oil Analysis 2002.

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