# Slide 1 The basic problem Working Age t PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density.

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Slide 1 The basic problem Working Age t PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density Function

Slide 2 The basic problem Working Age t Item has highest tendency to fail around here (highest probability density) Expected (average) failure time (MTTF) PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density Function Here are two of the attributes of a failure time distribution. The mode and mean. The mean is often used to characterize an items reliability.

Slide 3 The basic problem Working Age t PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density Function Is it possible to know what this failure probability distribution is, exactly?

Slide 4 The basic problem Working Age t PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density Function Yes, if we have a sample of an items (or fleet of items) past life cycles. Draw rectangles, as shown, such that their width is a convenient age interval, say a month. And their height is the percentage of the units that failed in that age interval.

Slide 5 The basic problem Working Age t PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density Function But how does knowing the shape of the distribution help us make a decision on when to do maintenance? If we perform maintenance at any age t, we will incur failures represented by the area under the curve between 0 and t. So how can we make the right maintenance decision?

Slide 6 The basic problem Working Age t PDF f(t) Failures do not happen at fixed times. They occur randomly based on a distribution. Probabilty Density Function Imagine that instead of a wide distribution, our failures occur according to this narrow distribution on the right. Now our maintenance decision is clear. We will perform maintenance a the age t 1, just prior to the steep rise in failure probability. t1t1

Slide 7 Working Age t PDF f(t) Unfortunately, however, in maintenance most failure distributions are of the wide, spread-out variety. How, then, can the Reliability Engineer (RE), develop policies for the timing of maintenance? Let us pose the question in another way: How can the RE change the maintenance process in order to arrive at narrow probability distributions for decision making?

Slide 8 Working Age t PDF f(t) The RE begins by introducing another dimension that he believes is relevant to the probability of failure.

Slide 9 Working Age t PDF f(t) FE ppm The relevant dimension could be, for example, the parts per million of Iron dissolved in a sample of oil taken from the crankcase of an engine.

Slide 10 Working Age t PDF f(t) FE ppm 100 We then re-plot the failure distribution curve. But this time we include only those life cycles that ended having a value of dissolved Iron greater than 100 ppm.

Slide 11 Working Age t PDF f(t) FE ppm 100 Assuming that Iron is a significant risk factor, the data will result in the desirable narrow distribution upon which to make a confident maintenance decision. Perform maintenance

Slide 12 Working Age t PDF f(t) FE ppm 100 It is incumbent on the RE, therefore, to discover influential dimensions for maintenance decision making. Adding significant dimensions (called condition indicators) to the maintenance decision making process is the process known as CBM.

Slide 13 Formal definition of CBM Also called: 1.Predictive Maintenance (PdM), Condition 2.Monitoring (CM), Prognostic Health 3.Management (PHM), 4.On-condition maintenance The gathering, processing, and analyzing of relevant data and observations, in order to make good and timely decisions on whether to: 1.Intervene immediately and conduct maintenance on an equipment at this time, or to 2.Plan to conduct maintenance within a specified time, or 3.Continue operating the equipment until the next CBM inspection interval. `

Slide 14 The CBM decision process must consider: 1.The probability of the failure in the upcoming time interval, and the 2.Severity (consequences) of the failure.

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