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The Crow-AMSAA model can be adapted for the analysis of success/failure data (also called "discrete" or "attribute" data).
Suppose system development is represented by i configurations. This corresponds to i - 1 configuration changes, unless fixes are applied at the end of the test phase, in which case there would be i configuration changes. Let Ni be the number of trials during configuration i and let Mi be the number of failures during configuration i. Then the cumulative number of trials through configuration i, namely Ti, is the sum of the Ni for all i, or:
And the cumulative number of failures through configuration i, namely Ki, is the sum of the Mi for all i, or:
The expected value of Ki can be expressed as E[Ki] and defined as the expected number of failures by the end of configuration i. Applying the learning curve property to E[Ki] implies:
(59)
Denote f1 as the probability of failure for configuration 1 and use it to develop a generalized equation for fi in terms of the Ti and Ni. From Eqn. (59), the expected number of failures by the end of configuration 1 is:
Applying Eqn. (59) again and noting that the expected number of failures by the end of configuration 2 is the sum of the expected number of failures in configuration 1 and the expected number of failures in configuration 2:
By this method of inductive reasoning, a generalized equation for the
failure probability on a configuration basis, fi,
is obtained, such that: 
(60)
For the special case where Ni = 1
for all i, Eqn.
(60) becomes a smooth curve, gi,
that represents the probability of failure for trial by trial data, or:
(61)
In Eqn. (61), i
represents the trial number. Thus using Eqn. (60), an equation for the
reliability (probability of success) for the ith
configuration is obtained: 
And using Eqn. (61), the equation for the reliability for the ith
trial is: 
This section describes procedures for estimating the parameters of the
Crow-AMSAA model for success/failure data. An example is presented illustrating
these concepts. The estimation procedures described below provide maximum
likelihood estimates (MLEs) for the model's two parameters, λ and β.
The MLEs for λ and
β allow for point
estimates for the probability of failure, given by: 
(62)
And the probability of success (reliability) for each configuration i is equal to:
(63)
The likelihood function is: 
Taking the natural log on both sides yields: 
Taking the derivative with respect to λ and β respectively, exact MLEs for λ and β are values satisfying the following two equations:
(64)
(65)
where: 
A one-shot system underwent reliability growth development testing for a total of 68 trials. Delayed corrective actions were incorporated after the 14th, 33rd and 48th trials. From trial 49 to trial 68, the configuration was not changed.
Figures 5.16 and 5.17 show plots of the estimated unreliability and reliability by configuration.
Table 5.6 - Estimated failure probability and reliability by configuration
Configuration (i) |
Estimated Failure Probability |
Estimated Reliability |
1 |
0.333 |
0.667 |
2 |
0.234 |
0.766 |
3 |
0.206 |
0.794 |
4 |
0.190 |
0.810 |
Figure 5.16: Estimated unreliability by configuration |
Figure 5.17: Estimated reliability by configuration |
In the RGA software, the Discrete Data > Mixed Data option gives a data sheet that can have input data that is either configuration in groups or individual trial by trial, or a mixed combination of individual trials and configurations of more than one trial. The calculations use the same mathematical methods described in Grouped Data for the Crow-AMSAA Model for the Crow-AMSAA grouped data.
Table 5.7 shows the number of failures of each interval of trials and the cumulative number of trials in each interval for a reliability growth test. For example, the first row of Table 5.7 indicates that for an interval of 14 trials, 5 failures occurred.
Table 5.7 - Mixed data for Example 9
Failures in Interval |
Cumulative Trials |
5 |
14 |
3 |
33 |
4 |
48 |
0 |
52 |
1 |
53 |
0 |
57 |
1 |
58 |
0 |
62 |
1 |
63 |
0 |
67 |
1 |
68 |
Using RGA 7, the parameters of the Crow-AMSAA model are estimated as follows:
and:
As we have seen, the Crow-AMSAA instantaneous failure intensity, λi(T), is defined as: 
Using the above parameter estimates, we can calculate the instantaneous
unreliability at the end of the test, or T
= 68.
This result that can be obtained from the Quick Calculation Pad (QCP), for T = 68, as seen in Figure 5.18.
Figure 5.18: Instantaneous unreliability at the end of the test |
The instantaneous reliability can then be calculated as:
The average unreliability is calculated as:
and the average reliability is calculated as:
The process to calculate the average failure probability confidence bounds for mixed data is as follows:
between
t1 and t2
such that the instantaneous failure probability at 
equals
the average failure probability (t1, t2). The confidence intervals for the instantaneous
failure probability at 
are the confidence intervals for the average
failure probability (t1, t2).The process to calculate the average reliability confidence bounds for mixed data is as follows:
