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## The Elusive P-F Curve

- A clear indicator of decreased failure resistance - the potential failure, and
- A reasonably consistent warning period prior to functional failure - the P-F interval

Both these requirements are captured in the well known empirical graph of failure resistance versus working age (Figure 1).

The P-F interval is a deceptively simple idea. Deceptive, because it takes for granted that we have previously defined "P" (the potential failure). Of the two concepts, "P" and "P-F", it is the former, however, that poses the greater challenge. Therefore, before addressing the P-F interval, we need to determine when and how to declare a potential failure.

Figure 1 implies that if we could monitor a condition indicator that tracks the resistance to failure, then declaring the potential failure level would be an easy matter. Two stumbling blocks, unfortunately, arise and obstruct our plan. The obstacles to the implementation of Figure 1 are:

- A single condition indicator that faithfully tracks the resistance-to-failure curve is rare, and
- The resistance-to-failure curve itself is rarely available.

Condition monitoring data, on the other hand, is abundant. How may we overcome obstacles 1 and 2? That is, how may we apply CBM to the numerous physical assets where condition monitoring data abounds, yet, where few alert limits have been defined?

This (setting of the declaration level of the potential failure) is the problem encountered by many asset managers deluged with condition monitoring data. The unavoidable question facing any implementer of a CBM program is where to set the potential failure. Which indicator, from among many monitored variables, should he select for this purpose? At what level? When the physics of the situation are not well known (as is often the case), a "policy" for declaring a potential failure is far from obvious.

Why does Figure 1 stubbornly elude our grasp? The reason is that this graph is often not 2-dimensional, but multi-dimensional. There is one dimension for each significant risk factor. The curve of Figure 1, therefore, looses its simple geometrical visuality. This is where software comes to the rescue.

EXAKT summarizes the risk factors associated with working age and monitored variables and creates a new kind of graph by transforming the significant risk information onto a 2-dimensional optimal decision graph. Professor Dragan Banjevic, CBM Lab director, brilliantly captured the multi-dimensionality of Figure 1 in two ways. First, he combined the significant monitored variables (other than age) into a risk-weighted sum. That became the y-axis. Then he transformed the age-related risk factor into the shape of the limit boundary. Presto, one 2-dimensional graph, Figure 2, shows it all.

EXAKT handles the probabilistic nature of P and the P-F interval properly. EXAKT does not assume a deterministic^{[1]} P or P-F interval. Instead it draws (from historical records) a probabilistic relationship among all significant factors (including working age). It uses that relationship to estimate the remaining useful life at any given moment. One of the benefits of this approach is the ability to deal with noisy data, illustrated in Figure 3. On the left side of Figure 3 are 3 examples of ideal data. Note how the monitored values increase monotonically, with the red alarm set conveniently to the potential failure declaration level. Unfortunately condition monitoring data seldom looks like this.

On the right side of Figure 3 is data from the nasty real world. It contains random fluctuations and trends that contradict one another. In other words, the usual situation! EXAKT alleviates randomness (see Tutorial 4) and conflicting trend data (see Tutorial 3). The OMDEC team can show you how.

Summarizing, EXAKT overcomes both obstacles to the application of Figure 1:

- It uncovers the weighted combination of monitored variables that most truly reflect degraded failure resistance, and
- It provides a virtual failure resistance curve that accounts for multiple risk factors.
- It sets the "P" (potential failure alert limit) dynamically so as to optimize risk.
^{[2] } - It provides a residual life estimate and optimal recommendation, based on risk and cost.

Article submitted By Murray Wiseman (Extracted from Reliability-Centered Knowledge) OMDEC

^{[1] }That is, it recognizes that a potential failure and the ensuing functional failure tend to occur randomly according to some probability distribution.

^{[2]} for a required objective (such as low overall cost or high availability).

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