Applications
Area Topics: AQL Primer Audit for Bed Bugs Inventory Sampling Xbar Charts Color Measurement Reliability Growth Test Plan Wearout and MTBF TP414 vs MilStd414 Switching Rules 
Wearout and sample size for
MTBF 
visitors= 
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 occurve. 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.
