Traditional Limit Setting

Traditionally, limits used for MCM have been based on either the statistical analysis of historical data or a significant change from previous values (e.g. a percentage change). For example, a significant change in a lubricant’s viscosity is likely to indicate a problem with the lubricant. A sudden decrease in viscosity could indicate contamination by a foreign fluid (e.g. fuel in an aircraft lubricating system due to a leaking heat exchanger), whereas an increase in viscosity could be an indication of oxidation of the fluid. In this instance a percentage deviation from the fresh fluid viscosity could be applied (e.g. +/- 20% of the fresh fluid viscosity). Alternatively an analysis of recent samples could be analysed using statistics to determine in-service limits.

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Garvey (143) suggests the following methodologies used to determine limits for MCM applications.

1. Judgement-based: this technique relies on the availability of experienced analysts who are familiar with the type of machinery being monitored;

2. Industry Standards: These are typically generic limits based on groupings of machines based on working pressure or type (gearbox, gas turbine, Diesel engine etc.);

3. Statistical Alarms: The two statistical methods described are the cumulative distribution function and Gaussian distribution. Both of these are widely used to set limits.

4. Trend-based or rate of change limits: These methods are essentially looking for an unacceptable departure from a normal level. Garvey quotes Poley (144) as suggesting there are three ways of achieving trend or rate-of-change alarms:

a. Relative Magnitudes: This technique simply looks for a significant change in magnitude.

b. Rolling Average: This technique compares the current value to an average of several historical measurements.

c. Factoring Delta Settings: This technique uses a weighting method that requires very large changes to occur before an alarm is tripped for small values. As the values increase, the required percentage change decreases. Garvey also notes that human interpretation is also used for the detection of abnormal conditions, however the context must be considered. The repeatability and robustness of

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this approach is questionable particularly in industries where workforce turnover is high or where MCM is contracted out.

ASTM International (145) have published a guide for setting oil analysis limits that describes the CDF and Gaussian (SPC) statistical approach. This document suggests that the CDF method can be successfully used where more than 100 samples are available. It is also stated that tentative limits can be set (with caution) where 50 samples are available however this would require review after some further period of operation; ideally 1000 samples are stated to provide the best results. This indicates that there would be some value in a method that allowed initial limits to be set where no pre-existing data is available. The ASTM guide also states that where the Gaussian technique is used, a sample of at least 30 is required to have any statistical validity. Generally, the document recommends the Gaussian method for data that is normally distributed and the CDF method for analysis independent of the data distribution (provided sufficient samples are available).

The ASTM guide for Gaussian alarm setting utilizes a double tail (Figure 46) approach (e.g. defining an upper and lower limit where deviation from an acceptable band must be indicated), however a single tail approach can also be applied to MCM data (figure 47). Table 6 shows the acceptable percentage of a population for various standard deviations. Any alarms set for wear debris analysis would typically be set using an upper limit, since machines that generate little if any wear debris are seldom of interest in MCM.

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Figure 46: Sketch of a Gaussian distribution of data showing upper and lower tail limits.

Figure 47: Sketch of Gaussian distributed data showing an upper tail limit only.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 1 2 3 Measurement4 5 6 7 8 O ccur rence Average 99.73% 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 1 2 3 Measurement4 5 6 7 8 O ccur rence Average 99.87%

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Table 6: Percentage of population contained within statistical interval

Number of standard deviations

(

σ

Percentage of Population Within Interval

Average +

σ

Average +/-

σ

1 84.14% 68.27%

2 97.73% 95.45%

3 99.87% 99.73%

The CDF provides the proportion of a population (or sample) with a value less than x (i.e. a percentile). To produce a CDF the sample is first ranked as a percentage from lowest to highest and then plotted against the sorted measured values. Once the plot has been created, the limits are simply read off at the desired percentile. Figure 48 shows a CDF for the rate of debris generation for a fleet of T56 turbo-shaft gas turbine engines. The units used in this data set are Debris Quantity per hour (DQ/hr), which are non-SI units obtained from a proprietary bulk inductive instrument2. As the CDF technique is

independent of an assumed distribution, a limit at the 95th percentile can simply be read

off the plot (in this case the 95th percentile limit is 1.6 DQ/hour). This however raises the

question as to what percentages should be used for the various limits. Garvey (143) suggests the 80th _{percentile and the 98}th _{percentile as possible alarm limit settings. The}

ASTM guide does not explicitly state a percentile but does show the 95th and 98th

percentiles as possible limits but does not expand on this in the text. Instead, it states that the actual percentiles are selected based on experience; a somewhat arbitrary approach.

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Figure 48: CDF of Debris Quantity rate (DQ/hour) for a fleet of T56 turbo-shaft gas turbine engines showing how a limit at 95% can be read on the abscissa.