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Table 10.2 shows a Multi-Phase data sheet with failure and fix implementation events.
Table 10.2 - Multi-Phase data for a time terminated test at T = 400 |
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Figure 10.5 shows the Table 10.2 data as entered in RGA 7. Note that since this is a time terminated test with a single phase ending at T = 400, the last event entry is a phase (PH) with time to event = 400.
Figure 10.5: Example 1 data in RGA 7 |
Figure 10.6 shows the effectiveness factors for the unfixed BD modes and information concerning whether the fix will be implemented. Since we have only one test phase for this example, a 1 indicates that the fix will be implemented at the end of the first (and only) phase.
Figure 10.6: Effectiveness factors for the BD modes of Example 1 that were not fixed during the test |
where in this case 
termination time =
400, and n
is the total number of failures. In this example n = 50. Note that there are five
fix implementation events and one event that marks the end of the phase.
These should not be counted as failures.
So in this case we find that β = 0.9866.
Note that here we calculated the biased estimate of β but we could have used the unbiased estimate as presented in the Parameter Estimation for the Crow-AMSAA Model section of this on-line reference. The choice of calculating the biased or unbiased estimate of β can be set in the User Setup in RGA 7.
Then solve for λ based on the Crow-AMSAA (NHPP) equation explained in the Crow-AMSAA (NHPP) section of this on-line reference:
The demonstrated MTBF of the system at time T = 400 is:
The corresponding current demonstrated failure intensity is:
The average actual effectiveness factor at time Τ is given by Eqn. (2):
The total number M of distinct unfixed BD modes at time 400 is M = 12.
dNi is the assigned (nominal) EF for the ith unfixed BD mode at time Tj, (as given in Figure 10.6).
Ni is the total number of failures over (0, 400) for the distinct unfixed BD mode i. This is summarized in Table 10.3.
Table 10.3 - Number of failures for unfixed BD modes |
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Sum = 21 |
Based on the above, the nominal growth potential factor is calculated as: λNGPFactor = 0.0153.
The actual growth potential factor is given by Eqn. (4):
where dAi is the actual EF for the ith unfixed BD mode at time 400, depending on whether a fix was implemented at time 400 or not. Figure 10.7 shows an event report from RGA 7 where it can be seen that the actual EF is zero if a fix was not implemented at 400, or equal to the nominal EF if the fix was implemented at 400.
Figure 10.7 Event report for Example 1 |
Based on the above, the actual growth potential factor is calculated as:
is the unbiased estimated of β for the Crow-AMSAA
(NHPP) model based on the first occurrence of the 17 distinct BD modes
in our example. 
is the unbiased estimate of λ
for the Crow-AMSAA (NHPP) model based on the first occurrence of the
17 distinct BD modes. Figure
10.8 shows the first time to failure for each of the 17 distinct modes
and the results of the analysis using the Crow-AMSAA (NHPP) model
in RGA 7 (note that the calculation settings in the User Setup have
to be set to calculate unbiased β
in this case).
Figure 10.8: First occurrence of each BD mode |
So we have:
and:
The equations used to determine these parameters have been explained in question 1 of this example and are also presented in detail in the Crow-AMSAA (NHPP) section of this on-line reference.
Based on Eqn. (7), the discovery rate function at time 400 is:
This is the failure intensity of the unseen BD modes at time 400. In this case, it means that 0.0257 new BD modes are discovered per hour, or one new BD mode is discovered every 38.9 hours.
This is the minimum attainable failure intensity if all delayed corrective actions are implemented for the modes that have been seen and delayed corrective actions are also implemented for the unseen BD modes, assuming testing would continue until all unseen BD modes are revealed.
From Eqn. (9), the nominal growth potential MTBF is:
This is the maximum attainable MTBF if all delayed corrective actions are implemented for the modes that have been seen and delayed corrective actions are also implemented for the unseen BD modes, assuming testing would continue until all unseen BD modes are revealed.
This is the projected failure intensity assuming all delayed fixes have been implemented for the modes that have been seen.
The nominal projected MTBF at time 400 is:
This is the projected MTBF assuming all delayed fixes have been implemented for the modes that have been seen.
This is the minimum attainable failure intensity based on the current management strategy.
The actual growth potential MTBF is:
This is the maximum attainable MTBF based on the current management strategy.
This is the projected failure intensity based on the current management strategy.
The actual projected MTBF at time 400 is:
This is the projected MTBF based on the current management strategy.
Figure 10.9 demonstrates how we can derive the results of this example by using RGA 7's Quick Calculation Pad (QCP). Here we chose to calculate the actual projected MTBF.
Figure 10.9: Multi-Phase calculations using the QCP |
The Crow Extended - Continuous Evaluation model allows data analysis across multiple phases, up to seven individual phases. Figure 10.10 shows a portion of failure time test results obtained across six phases. Analysis points are specified for continuous evaluation every 1000 hours. The cumulative test times at the end of each test phase are 5000, 15000, 25000, 35000, 45000 and 60000 hours.
Figure 10.10: Portion of test results for a six-phase reliability growth test program |
Figure 10.11 shows the effectiveness factors for the BD modes that do not have an associated fix implementation event. In other words, these are unfixed BD modes. Note that this specifies the phase after which the BD mode will be fixed, if any.
Figure 10.11: Effectiveness factor and phase of implementation for the BD failure modes that were not fixed during a test phase (I events) |
Figure 10.12 shows the overall test results in terms of demonstrated, projected and growth potential MTBF.
Figure 10.12: Demonstrated, projected and growth potential MTBF for the six-phase test program |
Figure 10.13 shows the "Before" and "After" MTBFs for all the individual modes. Note that the "After" MTBFs are calculated by taking into account the respective effectiveness factors for each of the unfixed BD modes.
Figure 10.13: Individual mode MTBF plot for the six-phase test program |
The analysis points are used to track overall growth inside and across phases, at desired intervals. A multi-phase plot can be created by right-clicking Additional Plots in the Project Explorer and selecting Add MultiPhase Plot. The MultiPhase Plot Wizard guides you through the process concerning the data sheet selection. Since the Crow Extended - Continuous Evaluation was used for the six-phase test, we select the Multi-Phase option.
A Multi-Phase data sheet can be associated with the multi-phase plot. Also, if there is an existing Planning folio, the multi-phase plot can bring the test results together with the Planning. This allows you to track the overall reliability program against the goals and set plans at each stage of the test. Additional information on combining a Planning folio and a MultiPhase plot is presented in the Reliability Growth Planning section of this on-line reference.
Figure 10.14 shows the multi-phase plot for the six phases of the reliability growth test program. This plot can be a powerful tool for overall tracking of the reliability growth program. It displays the termination time for each phase of testing along with the demonstrated, projected and growth potential MTBFs at those times. The plot also displays these calculated MTBFs at specified analysis points, which are determined based on the "AP" events in the data sheet.
Figure 10.14: Multi-phase plot with analysis points and phases for the six-phase test |
