Wearout and sample size for MTBF test plans

Applications Area Topics:

AQL Primer
Audit for Bed Bugs
Inventory Sampling
Xbar Charts
Color Measurement
Reliability Growth Test Plan
Wearout and MTBF
TP414 -vs- Mil-Std-414
Switching Rules

Wearout and sample size for MTBF

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What is the basis for using the exponential distribution to calculate the sample size for a reliability test plan when wearout and/or infant mortality might occur?

Software program TP781 uses the exponential distribution, but that does not pose a serious problem.

Wearout - always leads to a safely inflated sample size.i.e.

	Wearout causes the weibull slope (b) to increase
	Decreases the variance
	Reduces the actual sample size(test time/cycles) required for acceptance.

The following relationship between weibull slope and variance is from page 293 of Kapur and Lambertson, "Reliability in Engineering Design":
SLOPE	VARIANCE/(SCALE)
0.5	20.000
1.0	1.000
2.0	0.215
3.0	0.105
4.0	0.081

Infant mortality - these failures cause the weibull slope (b) to decrease, which increases the variance, increases the sample size required.

In the infant mortality case, the exponential distribution will understate the sample size needed for the chosen oc-curve. In most situations, this is not dangerous because the infant mortality failures will prevent erroneous acceptance.

In conclusion, we recommend using the exponential distribution to develop an initial test plan using TP781. Once the test data is collected, if there are signs of wearout or infant mortality, weibull methods can be used to make the acceptance decision.