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| ===Mixed Data===
| | #REDIRECT [[Crow-AMSAA - NHPP]] |
| <br>
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| 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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| <br>
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| '''Example 9'''
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| <br>
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| Table 5.7 shows the number of fai
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| <math>\widehat{\beta }=0.7950</math>
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| 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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| <br>
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| {|style= align="center" border="2"
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| |+'''Table 5.7 - Mixed data for Example 9'''
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| !Failures in Interval
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| !Cumulative Trials
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| |-
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| |5|| 14
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| |-
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| |3|| 33
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| |-
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| |4|| 48
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| |-
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| |0|| 52
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| |-
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| |1|| 53
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| |-
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| |0|| 57
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| |-
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| |1|| 58
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| |-
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| |0|| 62
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| |-
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| |1|| 63
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| |-
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| |0|| 67
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| |-
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| |1|| 68
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| |}
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| <br>
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| Using RGA 7, the parameters of the Crow-AMSAA model are estimated as follows:
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| :and:
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| ::<math>\widehat{\lambda }=0.5588</math>
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| As we have seen, the Crow-AMSAA instantaneous failure intensity, <math>{{\lambda }_{i}}(T)</math> , is defined as:
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| ::<math>{{\lambda }_{i}}(T)=\lambda \beta {{T}^{\beta -1}},\text{with }T>0,\text{ }\lambda >0\text{ and }\beta >0</math>
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| Using the above parameter estimates, we can calculate the or instantaneous unreliability at the end of the test, or <math>T=68.</math>
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| ::<math>{{R}_{i}}(68)=0.5588\cdot 0.7950\cdot {{68}^{0.7950-1}}=0.1871</math>
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| 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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| <br>
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| [[Image:rga5.18.png|thumb|center|400px|Instantaneous unreliability at the end of the test.]]
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| <br>
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| The instantaneous reliability can then be calculated as:
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| ::<math>{{R}_{inst}}=1-0.1871=0.8129</math>
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| The average unreliability is calculated as:
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| ::<math>\text{Average Unreliability }({{t}_{1,}}{{t}_{2}})=\frac{\lambda t_{2}^{\beta }-\lambda t_{1}^{\beta }}{{{t}_{2}}-{{t}_{1}}}</math>
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| and the average reliability is calculated as:
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| ::<math>\text{Average Reliability }({{t}_{1,}}{{t}_{2}})=1-\frac{\lambda t_{2}^{\beta }-\lambda t_{1}^{\beta }}{{{t}_{2}}-{{t}_{1}}}</math>
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| ====Bounds on Average Failure Probability for Mixed Data====
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| The process to calculate the average unreliability confidence bounds for mixed data is as follows:
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| <br>
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| :1) Calculate the average failure probability .
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| :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>
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| <br>
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| ====Bounds on Average Reliability for Mixed Data====
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| The process to calculate the average reliability confidence bounds for mixed data is as follows:
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| <br>
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| :1) Calculate confidence bounds for average unreliability as described above.
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| :2) The confidence bounds for reliability are 1 minus these confidence bounds for average unreliability.
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