If there are no BC failure modes, the demonstrated
failure intensity is 
. Thus:
In this section, the methods used in RGA to estimate the confidence bounds for the Crow Extended model when applied to developmental testing data will be presented. RGA provides two methods to estimate the confidence bounds on demonstrated MTBF and failure intensity, projected MTBF and failure intensity and growth potential MTBF and failure intensity. The two methods are the Fisher Matrix (FM) method and Crow bounds. The Fisher Matrix is based on the Fisher Information Matrix and is commonly employed in the reliability field. The Crow bounds were developed by Dr. Larry Crow.
This section of the on-line reference includes the following subsections:
If there are no BC failure modes, the demonstrated
failure intensity is . Thus:
and:
(12)
where 
.
If there are BC failure modes, the demonstrated failure intensity,
, is actually the instantaneous failure
intensity based on all of the data. 
must
be positive, thus 
is approximately treated
as being normally distributed.
The approximate confidence bounds on the instantaneous failure intensity are then estimated from:
(13)
where 
.
The variance calculation is the same as described in the Crow-AMSAA (N.H.P.P.) chapter.
If there are no BC failure modes then:
(14)
(15)
where 
.
If there are BC modes then the confidence bounds on the demonstrated failure intensity are calculated as presented in the Confidence Bounds on MTBF for the Crow-AMSAA Model section of this on-line reference.
(16)
where 
and 
can be obtained from Eqn. 12.
(17)
where 
and 
can be obtained from Eqn. 13.
The projected failure intensity 
must
be positive, thus 
is approximately treated
as being normally distributed as well:
(18)
where:
when there are
no BC modes
when there are
BC modes
Ni is the total failure number of the ith distinct BD mode
You can then get:
where:
The 
can be obtained from Fisher Matrix
based on M
distinct BD modes.
(19)
where .
(20)
and 
can
be obtained from Eqn. 18.
(21)
and 
can
be obtained from Eqn. 19.
If there are no BC failure modes, the growth potential
failure intensity is 
. Then
If there are BC failure modes, the growth potential failure intensity
is 
. Therefore,
The confidence bounds on the growth potential failure intensity are as follows:
(22)
where .
The Crow bounds for the growth potential failure intensity are the same as the Fisher Matrix bounds.
where rv and rL can be obtained from Eqn. 22.
The Crow bounds for the growth potential MTBF are the same as the Fisher Matrix bounds.
See
Also:
Crow Extended
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