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Stress/Strength Interference

As previously stated, a generic part's strength varies within a lot, from lot to lot, and from manufacturer to manufacturer. Strength is a random variable that can be represented by a statistical distribution. Likewise, the stress applied to a part in a given application may also be considered random, changing with temperature, vibration, mechanical shock, electrical transients, radiation and other environmental factors. These stresses can also be represented by a statistical distribution.

Figure 1 illustrates the relationship between the strength of a part and the applied stress.

Figure 1. Part Stress vs. Part Strength Relationship (Click to Zoom)

Failure is likely to occur whenever the applied stress exceeds the strength of the part. This is represented by the interference (the overlap) between the two distributions, the shaded area on the two subfigures. A more detailed explanation of interference theory may be found in the RIAC publication "Mechanical Applications in Reliability Engineering" (Reference 3).

This interference can be reduced using one of two obvious ways: 1) move the distributions farther apart, i.e., increase the strength of the part and 2) narrow the distributions, i.e., reduce the part strength variability. Considering these two approaches, we can see that, other things being equal, a part whose strength parameter variability is tightly controlled (e.g., a part produced in large quantities in continuous production for a long time with good statistical process controls (SPC)) will require less derating than a part that exhibits significant strength parameter variability (e.g., a part intermittently produced in small batches with minimum or no SPC).

The principle sources of variation for a specific generic part are a function of the part type as shown in Table 1.

Table 1. Part Type vs. Principal Sources of Variation
Source of Variation Part Type
Transistor Diode Integrated Circuit Resistor Capacitor Inductor Relay
Temperature X X X X X X X
Aging X     X X