Crow Extended - Continuous Evaluation - Revision history

David J. Groebel: /* Discrete Data */

2014-06-03T22:36:09Z

Discrete Data

← Older revision		Revision as of 22:36, 3 June 2014
Line 183:		Line 183:
	{{:Multi-Phase_Example}}		{{:Multi-Phase_Example}}

	==~~Discrete~~ Data==		==Mixed Data==
	The Crow Extended - Continuous Evaluation model also can be applied for discrete data from one-shot (success/failure) testing. In the RGA software, you can create a multi-phase data sheet that is configured for mixed data to accommodate data from tests where a single unit is tested for each successive configuration (individual trial-by-trial), where multiple units are tested for each successive configuration (configurations in groups) or a combination of both.		The Crow Extended - Continuous Evaluation model also can be applied for discrete data from one-shot (success/failure) testing. In the RGA software, you can create a multi-phase data sheet that is configured for mixed data to accommodate data from tests where a single unit is tested for each successive configuration (individual trial-by-trial), where multiple units are tested for each successive configuration (configurations in groups) or a combination of both.

David J. Groebel: /* Average vs. Demonstrated Failure Intensities Test */

2014-06-03T22:35:07Z

Average vs. Demonstrated Failure Intensities Test

← Older revision		Revision as of 22:35, 3 June 2014
Line 292:		Line 292:
	Because 0.058 is lower than 0.10, the conclusion is that at the 10% significance level of the the average failure intensity for phase 2 is statistically less than the average failure intensity for phase 1. The conclusion would be different for a different significance level. For example, at the 5% significance level, since 0.058 is not lower than 0.05, we fail to reject the null hypothesis. In other words, we cannot statistically prove any significant difference between the average failure intensities at the 5% level.		Because 0.058 is lower than 0.10, the conclusion is that at the 10% significance level of the the average failure intensity for phase 2 is statistically less than the average failure intensity for phase 1. The conclusion would be different for a different significance level. For example, at the 5% significance level, since 0.058 is not lower than 0.05, we fail to reject the null hypothesis. In other words, we cannot statistically prove any significant difference between the average failure intensities at the 5% level.

	==Average vs. Demonstrated Failure Intensities Test==		===Average vs. Demonstrated Failure Intensities Test===
	The purpose of this test is to compare the average failure intensity during phase 2 with the Crow-AMSAA (NHPP) instantaneous (demonstrated) failure intensity at the end of phase 1.		The purpose of this test is to compare the average failure intensity during phase 2 with the Crow-AMSAA (NHPP) instantaneous (demonstrated) failure intensity at the end of phase 1.

David J. Groebel: /* Discrete Data */

2014-06-03T22:34:37Z

Discrete Data

← Older revision		Revision as of 22:34, 3 June 2014
Line 183:		Line 183:
	{{:Multi-Phase_Example}}		{{:Multi-Phase_Example}}

	=Discrete Data=		==Discrete Data==
	The Crow Extended - Continuous Evaluation model also can be applied for discrete data from one-shot (success/failure) testing. In the RGA software, you can create a multi-phase data sheet that is configured for mixed data to accommodate data from tests where a single unit is tested for each successive configuration (individual trial-by-trial), where multiple units are tested for each successive configuration (configurations in groups) or a combination of both.		The Crow Extended - Continuous Evaluation model also can be applied for discrete data from one-shot (success/failure) testing. In the RGA software, you can create a multi-phase data sheet that is configured for mixed data to accommodate data from tests where a single unit is tested for each successive configuration (individual trial-by-trial), where multiple units are tested for each successive configuration (configurations in groups) or a combination of both.

Line 190:		Line 190:
	Note that for calculation purposes, it is required to have at least three failures in the first interval. If that is not the case, then the data set needs to be grouped until this requirement is met before calculating. The RGA software performs this operation in the background.		Note that for calculation purposes, it is required to have at least three failures in the first interval. If that is not the case, then the data set needs to be grouped until this requirement is met before calculating. The RGA software performs this operation in the background.

	==Example - Multi-Phase Discrete Data==		===Example - Multi-Phase Discrete Data===
	{{:Multi-Phase_-_Mixed_Data}}		{{:Multi-Phase_-_Mixed_Data}}

David J. Groebel: /* Statistical Tests for Effectiveness of Corrective Actions */

2014-06-03T22:33:51Z

Statistical Tests for Effectiveness of Corrective Actions

← Older revision		Revision as of 22:33, 3 June 2014
Line 193:		Line 193:
	{{:Multi-Phase_-_Mixed_Data}}		{{:Multi-Phase_-_Mixed_Data}}

	=Statistical Tests for Effectiveness of Corrective Actions=		==Statistical Tests for Effectiveness of Corrective Actions==
	The purpose of the statistical tests is to explore the effectiveness of corrective actions during or at the end of a phase. Say we have two phases, phase 1 and phase 2. Suppose that corrective actions are incorporated during or at the end of phase 1. The system is then operated during phase 2. The general question is whether or not the corrective actions have been effective.		The purpose of the statistical tests is to explore the effectiveness of corrective actions during or at the end of a phase. Say we have two phases, phase 1 and phase 2. Suppose that corrective actions are incorporated during or at the end of phase 1. The system is then operated during phase 2. The general question is whether or not the corrective actions have been effective.

Line 202:		Line 202:
	Question 2. Is the average failure intensity for phase 2 statistically less than the Crow-AMSAA (NHPP) instantaneous failure intensity at the end of phase 1?		Question 2. Is the average failure intensity for phase 2 statistically less than the Crow-AMSAA (NHPP) instantaneous failure intensity at the end of phase 1?

	==Average Failure Intensities Test==		===Average Failure Intensities Test===
	The purpose of this test is to compare the average failure intensity during phase 2 with the average failure intensity during phase 1.		The purpose of this test is to compare the average failure intensity during phase 2 with the average failure intensity during phase 1.

Line 244:		Line 244:
	which gives the probability that the test failures, <math>f\,\!</math>, are less than or equal to the number of allowable failures, or acceptance number <math>k\,\!</math> in <math>N\,\!</math> trials, when each trial has a probability of succeeding of <math>P\,\!</math>.		which gives the probability that the test failures, <math>f\,\!</math>, are less than or equal to the number of allowable failures, or acceptance number <math>k\,\!</math> in <math>N\,\!</math> trials, when each trial has a probability of succeeding of <math>P\,\!</math>.

	===Example===		====Example====
	Suppose a test is being conducted and is divided into two phases. The test time for the first phase is <math>{{T}_{1}}=27\,\!</math> days, and the test time for the second phase is <math>{{T}_{2}}=18\,\!</math> days. The number of failures during phase 1 is <math>{{N}_{1}}=11\,\!</math>, and the number of failures during phase 2 is <math>{{N}_{2}}=2.\,\!</math>		Suppose a test is being conducted and is divided into two phases. The test time for the first phase is <math>{{T}_{1}}=27\,\!</math> days, and the test time for the second phase is <math>{{T}_{2}}=18\,\!</math> days. The number of failures during phase 1 is <math>{{N}_{1}}=11\,\!</math>, and the number of failures during phase 2 is <math>{{N}_{2}}=2.\,\!</math>

Line 330:		Line 330:
	\end{matrix} \right){{P}^{f}}{{\left( 1-P \right)}^{N-f}}\,\!</math>		\end{matrix} \right){{P}^{f}}{{\left( 1-P \right)}^{N-f}}\,\!</math>

	===Example===		====Example====
	Suppose a test is being conducted and is divided into two phases. The test time for the first phase is <math>T_{1}=21\,\!</math> days, and the test time for the second phase is <math>T_{2} = 18\,\!</math> days. The number of failures during phase 1 is <math>N_{1}=11\,\!</math> and the number of failures during phase 2 is <math>N_{2}=2\,\!</math>. The Crow-AMSAA (NHPP) parameters for the first phase are <math>\beta = 0.7189\,\!</math> and <math>\lambda = 1.0288\,\!</math>.		Suppose a test is being conducted and is divided into two phases. The test time for the first phase is <math>T_{1}=21\,\!</math> days, and the test time for the second phase is <math>T_{2} = 18\,\!</math> days. The number of failures during phase 1 is <math>N_{1}=11\,\!</math> and the number of failures during phase 2 is <math>N_{2}=2\,\!</math>. The Crow-AMSAA (NHPP) parameters for the first phase are <math>\beta = 0.7189\,\!</math> and <math>\lambda = 1.0288\,\!</math>.

David J. Groebel: /* Multi-Phase Discrete Data Example */

2014-06-03T22:09:02Z

Multi-Phase Discrete Data Example

← Older revision		Revision as of 22:09, 3 June 2014
Line 190:		Line 190:
	Note that for calculation purposes, it is required to have at least three failures in the first interval. If that is not the case, then the data set needs to be grouped until this requirement is met before calculating. The RGA software performs this operation in the background.		Note that for calculation purposes, it is required to have at least three failures in the first interval. If that is not the case, then the data set needs to be grouped until this requirement is met before calculating. The RGA software performs this operation in the background.

	==Multi-Phase Discrete Data ~~Example~~==		==Example - Multi-Phase Discrete Data==
	{{:Multi-Phase_-_Mixed_Data}}		{{:Multi-Phase_-_Mixed_Data}}

David J. Groebel at 22:08, 3 June 2014

2014-06-03T22:08:28Z

← Older revision		Revision as of 22:08, 3 June 2014
Line 356:		Line 356:

	:<math>T_{1}^{}= \frac{N_{1}^{}}{\hat{r}(T_{1})}= \frac{5.5}{0.2929}= 18.78</math>		:<math>T_{1}^{}= \frac{N_{1}^{}}{\hat{r}(T_{1})}= \frac{5.5}{0.2929}= 18.78</math>


	Concerning the total test time, we have:		Concerning the total test time, we have:
Line 406:		Line 405:
	Since 0.201 is greater than 0.10, the conclusion is that at the 10% significance level the average failure intensity for phase 2 is not statistically different compared to the demonstrated failure intensity at the end of phase 1.		Since 0.201 is greater than 0.10, the conclusion is that at the 10% significance level the average failure intensity for phase 2 is not statistically different compared to the demonstrated failure intensity at the end of phase 1.

	Using the [[Crow_Extended_-_Continuous_Evaluation#~~Example_with_Six_Phases~~\|example with the six phases]] that was given earlier in this chapter, the following figure shows the application of the two statistical tests in RGA.		Using the [[Crow_Extended_-_Continuous_Evaluation#Example_-_Six_Phases\|example with the six phases]] that was given earlier in this chapter, the following figure shows the application of the two statistical tests in RGA.

	[[Image:TestForFixEffectiveness.png\|center\|~~403px~~]]		[[Image:TestForFixEffectiveness.png\|center\|450px]]

David J. Groebel: /* Example with Six Phases */

2014-06-03T22:06:38Z

Example with Six Phases

← Older revision		Revision as of 22:06, 3 June 2014
Line 180:		Line 180:
	{{:Crow_Extended_-_Continuous_Evaluation_Model_Example}}		{{:Crow_Extended_-_Continuous_Evaluation_Model_Example}}

	=Example ~~with~~ Six Phases=<!-- THIS SECTION HEADER IS LINKED FROM ANOTHER SECTION IN THIS PAGE. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK(S). -->		==Example - Six Phases==<!-- THIS SECTION HEADER IS LINKED FROM ANOTHER SECTION IN THIS PAGE. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK(S). -->
	{{:Multi-Phase_Example}}		{{:Multi-Phase_Example}}

David J. Groebel: /* Example with One Phase */

2014-06-03T22:06:09Z

Example with One Phase

← Older revision		Revision as of 22:06, 3 June 2014
Line 177:		Line 177:
	In terms of confidence intervals and goodness-of-fit tests, the calculations are the same as for the [[Crow Extended\|Crow Extended model]].		In terms of confidence intervals and goodness-of-fit tests, the calculations are the same as for the [[Crow Extended\|Crow Extended model]].

	=Example ~~with One~~ Phase=		==Example - Single Phase==
	{{:Crow_Extended_-_Continuous_Evaluation_Model_Example}}		{{:Crow_Extended_-_Continuous_Evaluation_Model_Example}}

David J. Groebel: /* Effectiveness Factors */

2014-05-30T17:04:08Z

Effectiveness Factors

← Older revision		Revision as of 17:04, 30 May 2014
Line 59:		Line 59:
	Similar to the Crow Extended model, each BD mode has an effectiveness factor that represents the decrease in failure intensity for that mode once the corrective action has been incorporated into the system. In addition, a delayed fix can be incorporated any time after the first occurrence of the failure mode. Therefore, delayed fixes can be incorporated before the end of the test phase, at the end of the test phase (just like the Crow Extended delayed fixes) or not incorporated at all at the end of the current test phase but postponed for a subsequent test phase. For calculation purposes, any delayed fixes that are incorporated during the test (those with an ''I'' event code) do not need to have an effectiveness factor specified, since the fix is already incorporated in the system. The next figure shows how effectiveness factors are defined in the Crow Extended - Continuous Evaluation model in the RGA software. The figure also shows that you can specify whether the delayed fix was actually implemented at the end of the current test phase, at a later phase or not implemented at all.		Similar to the Crow Extended model, each BD mode has an effectiveness factor that represents the decrease in failure intensity for that mode once the corrective action has been incorporated into the system. In addition, a delayed fix can be incorporated any time after the first occurrence of the failure mode. Therefore, delayed fixes can be incorporated before the end of the test phase, at the end of the test phase (just like the Crow Extended delayed fixes) or not incorporated at all at the end of the current test phase but postponed for a subsequent test phase. For calculation purposes, any delayed fixes that are incorporated during the test (those with an ''I'' event code) do not need to have an effectiveness factor specified, since the fix is already incorporated in the system. The next figure shows how effectiveness factors are defined in the Crow Extended - Continuous Evaluation model in the RGA software. The figure also shows that you can specify whether the delayed fix was actually implemented at the end of the current test phase, at a later phase or not implemented at all.

	[[Image:rga10.3.png\|center\|~~400px\|Effectiveness factors defined for each unique BD mode not corrected during the test. If the fix will be impletmented at the end of a test phase, the phase number is indicated.~~]]		[[Image:rga10.3.png\|center\|450px]]

	For a Type BD failure mode that is not yet corrected but still deferred, the Actual Effectiveness Factor for that mode is zero. The Actual Effectiveness Factor for a deferred Type BD failure mode will stay at zero until the point when the corrective action will be incorporated is reached. At that time, the Actual Effectiveness Factor is changed to equal the Assigned Effectiveness Factor for that mode. At this point, the Nominal Effectiveness Factor (the effectiveness factor, assuming that fixes are implemented at the end of the specific phase) and the Actual Effectiveness Factor are the same. In other words, if a fix is not incorporated for a BD mode, its actual effectiveness for reducing failure intensity is zero, and the assigned effectiveness factor will be used only for projecting the MTBF (or failure intensity). This topic will be discussed in the [[Crow_Extended_-_Continuous_Evaluation#Growth_Potential_and_Projections\|Growth Potential and Projections]] section.		For a Type BD failure mode that is not yet corrected but still deferred, the Actual Effectiveness Factor for that mode is zero. The Actual Effectiveness Factor for a deferred Type BD failure mode will stay at zero until the point when the corrective action will be incorporated is reached. At that time, the Actual Effectiveness Factor is changed to equal the Assigned Effectiveness Factor for that mode. At this point, the Nominal Effectiveness Factor (the effectiveness factor, assuming that fixes are implemented at the end of the specific phase) and the Actual Effectiveness Factor are the same. In other words, if a fix is not incorporated for a BD mode, its actual effectiveness for reducing failure intensity is zero, and the assigned effectiveness factor will be used only for projecting the MTBF (or failure intensity). This topic will be discussed in the [[Crow_Extended_-_Continuous_Evaluation#Growth_Potential_and_Projections\|Growth Potential and Projections]] section.

David J. Groebel at 17:03, 30 May 2014

2014-05-30T17:03:44Z

← Older revision		Revision as of 17:03, 30 May 2014
Line 45:		Line 45:
	The next figure shows an example of a Crow Extended - Continuous Evaluation folio with all of the possible event codes. As you can see, each failure is indicated with A, BC or BD in the '''Classification''' column. In addition, any text can be used to specify the mode. In this figure, failure codes were used in the '''Mode''' column for simplicity, but you could just as easily use Seal Leak, or whatever designation you deem appropriate for the failure mode.		The next figure shows an example of a Crow Extended - Continuous Evaluation folio with all of the possible event codes. As you can see, each failure is indicated with A, BC or BD in the '''Classification''' column. In addition, any text can be used to specify the mode. In this figure, failure codes were used in the '''Mode''' column for simplicity, but you could just as easily use Seal Leak, or whatever designation you deem appropriate for the failure mode.

	[[Image:rga10.2.png~~\|thumb~~\|center\|~~400px\|A Crow Extended- Continuous Evaluation folio with all possible event codes.~~]]		[[Image:rga10.2.png\|center\|600px]]

	===<math>p\,\!</math> Ratio===		===<math>p\,\!</math> Ratio===