Template:Mixed data camsaa-cd: Difference between revisions

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===Mixed Data===
#REDIRECT [[Crow-AMSAA - NHPP]]
<br>
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 section 5.3 for the Crow-AMSAA grouped data.
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====Example====
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Table 5.7 shows the number of fai
<math>\widehat{\beta }=0.7950</math>
lures 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.
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{|style= align="center" border="2"
|+'''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
|}
 
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Using RGA 7, the parameters of the Crow-AMSAA model are estimated as follows:
 
:and:
 
::<math>\widehat{\lambda }=0.5588</math>
 
As we have seen, the Crow-AMSAA instantaneous failure intensity,  <math>{{\lambda }_{i}}(T)</math> , is defined as:
 
::<math>{{\lambda }_{i}}(T)=\lambda \beta {{T}^{\beta -1}},\text{with }T>0,\text{ }\lambda >0\text{ and }\beta >0</math>
 
Using the above parameter estimates, we can calculate the or instantaneous unreliability at the end of the test, or  <math>T=68.</math>
 
::<math>{{R}_{i}}(68)=0.5588\cdot 0.7950\cdot {{68}^{0.7950-1}}=0.1871</math>
 
This result that can be obtained from the Quick Calculation Pad (QCP), for  <math>T=68,</math>  as seen in Figure Mixednst.FI.
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[[Image:rga5.18.png|thumb|center|400px|Instantaneous unreliability at the end of the test.]]
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The instantaneous reliability can then be calculated as:
 
::<math>{{R}_{inst}}=1-0.1871=0.8129</math>
 
The average unreliability is calculated as:
 
::<math>\text{Average Unreliability }({{t}_{1,}}{{t}_{2}})=\frac{\lambda t_{2}^{\beta }-\lambda t_{1}^{\beta }}{{{t}_{2}}-{{t}_{1}}}</math>
 
and the average reliability is calculated as:
 
::<math>\text{Average Reliability }({{t}_{1,}}{{t}_{2}})=1-\frac{\lambda t_{2}^{\beta }-\lambda t_{1}^{\beta }}{{{t}_{2}}-{{t}_{1}}}</math>
 
====Bounds on Average Failure Probability for Mixed Data====
The process to calculate the average unreliability confidence bounds for mixed data is as follows:
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:1) Calculate the average failure probability    .
:2) There will exist a  <math>{{t}^{*}}</math>  between  <math>{{t}_{1}}</math>  and  <math>{{t}_{2}}</math>  such that the instantaneous unreliability at  <math>{{t}^{*}}</math>  equals the average unreliability    . The confidence intervals for the instantaneous unreliability at  <math>{{t}^{*}}</math>  are the confidence intervals for the average unreliability    .
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<br>
====Bounds on Average Reliability for Mixed Data====
The process to calculate the average reliability confidence bounds for mixed data is as follows:
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:1) Calculate confidence bounds for average unreliability    as described above.
:2) The confidence bounds for reliability are 1 minus these confidence bounds for average unreliability.

Latest revision as of 12:40, 23 August 2012

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