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The Elusive P-F Interval

 By Murray Wiseman

 Extracted from Reliability-Centered Knowledge

 

J. Moubray coined the phrase "P-F interval". He used it

to highlight two pre-requisites of CBM, namely:1. A clear indicator of decreased failure resistance - the potential

failure, and2. 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 (Figure1). 

Figure 1

The P-F interval is a

deceptively simpleidea. 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 theformer, however, that poses the greater

challenge. Therefore, before addressin

g the P-F interval, we need to determinewhen and how to declare a potential

failure. 

Figure 1 implies that if we could

monitor a condition indicator that tracksthe resistance to failure, then declaring

the potential failure level would be aneasy matter. Two stumbling blocks,

unfortunately, arise and obstruct ourplan. The obstacles to theimplementation of Figure 1 are:

 1. A single condition indicator that

faithfully tracks the resistance-to-

failure curve is rare, and

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2. The resistance-to-failure curveitself is rarely available.

 

Condition monitoring data, on the other hand, isabundant. How may we overcome obstacles 1 and 2? That is,

how may we apply CBM to the numerous physical assets wherecondition monitoring data abounds, yet, where few alert limitshave been defined? This (setting of the declaration level of the potential failure) isthe problem encountered by many asset managers deluged withcondition monitoring data. The unavoidable question facing anyimplementer of a CBM program is where to set the potentialfailure. 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 isoften the case), a “policy” for declaring a potential failure is farfrom 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 eachsignificant risk factor. The curve of  Figure 1, therefore, looses

its simple geometrical visuality. This is where software comes tothe rescue. EXAKT summarizes the risk factors associated with working ageand monitored variables and creates a new kind of graph bytransforming the significant risk information onto a 2-dimensional optimal decision graph. Professor DraganBanjevic, 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 transformedthe age-related risk factor into the shape of the limit boundary.Presto, one 2-dimensional graph, Figure 2, shows it all. 

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Figure 2

 

EXAKT handles the probabilistic nature of P and the P-F interval rigorously. EXAKT does not assume a

deterministic[1] P or P-F interval.

.

Figure 3

Instead it draws (from historicalrecords) a probabilistic

relationship among all significantfactors (including working age).

 It uses that relationship toestimate the remaining useful life

at any given moment. One of thebenefits of this approach is the

ability to deal with noisy data,

illustrated in Figure 3. On the leftside of Figure 3 are 3 examples of 

ideal data. Note how themonitored values increase

monotonically, with the red alarmset conveniently to the potentialfailure declaration level.

Unfortunately conditionmonitoring data seldom looks like

this.

 On the right side of Figure 3 is

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data from the nasty real world. Itcontains random fluctuations and

trends that contradict one

another. In other words, theusual situation! EXAKT alleviates

randomness (see Tutorial 4) andconflicting trend data

(see Tutorial 3). The OMDEC

team can show you how. 

Summarizing, EXAKT overcomes both obstacles to the

application of Figure 1:

 1. It uncovers the weighted combination of monitored variables that

most truly reflect degraded failure resistance, and2. It provides a virtual failure resistance curve that accounts for

multiple risk factors.3. It sets the “P” (potential failure alert limit) dynamically so as to

optimize risk.[2]

4. It provides a residual life estimate and optimal recommendaton,based on probabilty and cost.

 

 Do you have any comments on this article? If so send themto murray@omdec.com.