Template:Mixed data camsaa-cd - Revision history

Lisa Hacker: Redirected page to Crow-AMSAA - NHPP

2012-08-23T12:40:02Z

← Older revision		Revision as of 12:40, 23 August 2012
Line 1:		Line 1:
	~~===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.~~
	~~<br>~~
	~~====Example====~~
	~~<br>~~
	~~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.
	~~<br>~~
	~~{\|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~~
	\|}

	~~<br>~~
	~~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.~~
	~~<br>~~
	~~[[Image:rga5.18.png\|thumb\|center\|400px\|Instantaneous unreliability at the end of the test.~~]]
	~~<br>~~
	~~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:~~
	~~<br>~~
	~~: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 .
	~~<br>~~
	~~<br>~~
	~~====Bounds on Average Reliability for Mixed Data====~~
	~~The process to calculate the average reliability confidence bounds for mixed data is as follows:~~
	~~<br>~~
	~~: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.~~

Lisa Hacker: /* Mixed Data */

2012-08-23T12:38:45Z

Mixed Data

← Older revision		Revision as of 12:38, 23 August 2012
Line 3:		Line 3:
	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.		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.
	<br>		<br>
	~~'''~~Example ~~9'''~~		====Example====
	<br>		<br>
	Table 5.7 shows the number of fai		Table 5.7 shows the number of fai

Nicolette Young: Created page with '===Mixed Data===
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 …'

2012-01-09T17:12:41Z

Created page with '===Mixed Data=== 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 …'

New page

===Mixed Data===
 
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.
 
'''Example 9'''
 
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.
 
{|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
|}

 
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.
 
[[Image:rga5.18.png|thumb|center|400px|Instantaneous unreliability at the end of the test.]]
 
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:
 
: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 .
 
 
====Bounds on Average Reliability for Mixed Data====
The process to calculate the average reliability confidence bounds for mixed data is as follows:
 
: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.

Template:Mixed data camsaa-cd - Revision history

Lisa Hacker: Redirected page to Crow-AMSAA - NHPP

Lisa Hacker: /* Mixed Data */

Nicolette Young: Created page with '===Mixed Data=== 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 …'

Nicolette Young: Created page with '===Mixed Data===
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 …'