Template:ReliaSoft's Alternate Ranking Method - Revision history

Kate Racaza: Redirected page to Appendix: Special Analysis Methods#ReliaSoft Ranking Method

2012-08-10T04:08:34Z

Redirected page to Appendix: Special Analysis Methods#ReliaSoft Ranking Method

Kate Racaza: /* Initial Parameter Estimation */

2012-05-25T18:22:19Z

Initial Parameter Estimation

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	\|colspan="8" style="text-align:center"\|Table B.6- Increments Solved Numerically Along with the Sum of Each Row.		\|colspan="8" style="text-align:center"\|Table B.6- Increments Solved Numerically, Along with the Sum of Each Row.
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	!Number of items		!Number of items

Kate Racaza: /* Initial Parameter Estimation */

2012-05-25T18:14:44Z

Initial Parameter Estimation

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	{\|style= align="center" border="1"		{\|style= align="center" border="1"
	\|colspan="5" style="text-align:center"\|Table B.3- The Union of Exact ~~times~~-to-~~failure~~ with the "~~midpoint~~" of the ~~interval failures~~, ~~based~~ upon the ~~parameters~~ <math>\beta</math> and <math>\eta</math>.		\|colspan="5" style="text-align:center"\|Table B.3- The Union of Exact Times-to-Failure with the "Midpoint" of the Interval Failures, Based upon the Parameters <math>\beta</math> and <math>\eta</math>.
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	!Number of Items		!Number of Items
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	{\|style= align="center" border="1"		{\|style= align="center" border="1"
	\|colspan="2"\|Table B.4- The Union of Exact ~~times~~-to-~~failure~~ with the "~~midpoint~~" of the ~~interval failures~~, in ~~ascending order~~.		\|colspan="2"\|Table B.4- The Union of Exact Times-to-Failure with the "Midpoint" of the Interval Failures, in Ascending Order.
	\|-align="center"		\|-align="center"
	!Number of Items		!Number of Items
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	\|colspan="7" style="text-align:center"\|Table B.5- Computation of ~~increments,~~ in a ~~matrix format,~~ for ~~computing~~ a ~~revised~~ Mean Order Number.		\|colspan="7" style="text-align:center"\|Table B.5- Computation of Increments in a Matrix Format for Computing a Revised Mean Order Number.
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	!Number of items		!Number of items
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	\|colspan="8" style="text-align:center"\|Table B.6- Increments ~~solved numberically, along~~ with the ~~sum~~ of ~~each row~~.		\|colspan="8" style="text-align:center"\|Table B.6- Increments Solved Numerically Along with the Sum of Each Row.
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	!Number of items		!Number of items
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	{\|style= align="center" border="1"		{\|style= align="center" border="1"
	\|colspan="3" style="text-align:center"\|Table B.8- Mean Order Numbers with ~~their ranks~~ for a ~~sample size~~ of 13 ~~units~~.		\|colspan="3" style="text-align:center"\|Table B.8- Mean Order Numbers with Their Ranks for a Sample Size of 13 Units.
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	!Time		!Time

Kate Racaza: /* Initial Parameter Estimation */

2012-05-25T18:12:12Z

Initial Parameter Estimation

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	{\|style= align="center" border="1"		{\|style= align="center" border="1"
	\|colspan="4" style="text-align:center"\|Table B.2- The Union of Exact ~~times~~-to-~~failure~~ with the "~~midpoint~~" of the ~~interval failures~~		\|colspan="4" style="text-align:center"\|Table B.2- The Union of Exact Times-to-Failure with the "Midpoint" of the Interval Failures
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	!Number of Items		!Number of Items

Kate Racaza: /* Step-by-Step Example */

2012-05-25T18:11:48Z

Step-by-Step Example

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	\|colspan="4" style="text-align:center"\|Table B.1- The ~~test data~~		\|colspan="4" style="text-align:center"\|Table B.1- The Test Data
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	\|1\|\|Left Censored\|\|0\|\|100		\|1\|\|Left Censored\|\|0\|\|100
	\|}		\|}


	=== Initial Parameter Estimation===		=== Initial Parameter Estimation===

Kate Racaza: /* ReliaSoft's Alternate Ranking Method (RRM) */

2012-05-25T18:09:55Z

ReliaSoft's Alternate Ranking Method (RRM)

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	{{template:LDAOtherSections\|\|}}		{{template:LDAOtherSections\|\|}}
	= ReliaSoft's ~~Alternate~~ Ranking Method (RRM) =		= ReliaSoft's Ranking Method (RRM) =
	In probability plotting or rank regression analysis of interval or left censored data, difficulties arise when attempting to estimate the exact time within the interval when the failure actually occurs, especially when an overlap on the intervals is present. In this case, the ''standard ranking method'' (SRM) is not applicable when dealing with interval data; thus, ReliaSoft has formulated a more sophisticated methodology to allow for more accurate probability plotting and regression analysis of data sets with interval or left censored data. This method utilizes the traditional rank regression method and iteratively improves upon the computed ranks by parametrically recomputing new ranks and the most probable failure time for interval data. A step-by-step example of this method follows.		In probability plotting or rank regression analysis of interval or left censored data, difficulties arise when attempting to estimate the exact time within the interval when the failure actually occurs, especially when an overlap on the intervals is present. In this case, the ''standard ranking method'' (SRM) is not applicable when dealing with interval data; thus, ReliaSoft has formulated a more sophisticated methodology to allow for more accurate probability plotting and regression analysis of data sets with interval or left censored data. This method utilizes the traditional rank regression method and iteratively improves upon the computed ranks by parametrically recomputing new ranks and the most probable failure time for interval data. A step-by-step example of this method follows.

Kate Racaza: /* Step-by-Step Example */

2012-05-25T18:07:02Z

Step-by-Step Example

← Older revision		Revision as of 18:07, 25 May 2012
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	In probability plotting or rank regression analysis of interval or left censored data, difficulties arise when attempting to estimate the exact time within the interval when the failure actually occurs, especially when an overlap on the intervals is present. In this case, the ''standard ranking method'' (SRM) is not applicable when dealing with interval data; thus, ReliaSoft has formulated a more sophisticated methodology to allow for more accurate probability plotting and regression analysis of data sets with interval or left censored data. This method utilizes the traditional rank regression method and iteratively improves upon the computed ranks by parametrically recomputing new ranks and the most probable failure time for interval data. A step-by-step example of this method follows.		In probability plotting or rank regression analysis of interval or left censored data, difficulties arise when attempting to estimate the exact time within the interval when the failure actually occurs, especially when an overlap on the intervals is present. In this case, the ''standard ranking method'' (SRM) is not applicable when dealing with interval data; thus, ReliaSoft has formulated a more sophisticated methodology to allow for more accurate probability plotting and regression analysis of data sets with interval or left censored data. This method utilizes the traditional rank regression method and iteratively improves upon the computed ranks by parametrically recomputing new ranks and the most probable failure time for interval data. A step-by-step example of this method follows.

	= Step-by-Step Example=		=== Step-by-Step Example===
	This section illustrates the ReliaSoft ranking method (RRM), which is an iterative improvement on the standard ranking method (SRM). Although this method is illustrated by the use of the two-parameter Weibull distribution, it can be easily generalized for other models.		This section illustrates the ReliaSoft ranking method (RRM), which is an iterative improvement on the standard ranking method (SRM). Although this method is illustrated by the use of the two-parameter Weibull distribution, it can be easily generalized for other models.

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	== Initial Parameter Estimation==		=== Initial Parameter Estimation===
	As a preliminary step, we need to provide a crude estimate of the Weibull parameters for this data. To begin, we will extract the exact times-to-failure (10, 40, and 50) and the midpoints of the interval failures. The midpoints are 50 (for the interval of 20 to 80) and 47.5 (for the interval of 10 to 85). Next, we group together the items that have the same failure times, as shown in Table B.2.		As a preliminary step, we need to provide a crude estimate of the Weibull parameters for this data. To begin, we will extract the exact times-to-failure (10, 40, and 50) and the midpoints of the interval failures. The midpoints are 50 (for the interval of 20 to 80) and 47.5 (for the interval of 10 to 85). Next, we group together the items that have the same failure times, as shown in Table B.2.

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	Return and repeat the process from Step 1 until an acceptable convergence is reached on the parameters (i.e., the parameter values stabilize).		Return and repeat the process from Step 1 until an acceptable convergence is reached on the parameters (i.e., the parameter values stabilize).

	==Results==		===Results===
	The results of the first five iterations are shown in Table B.10.		The results of the first five iterations are shown in Table B.10.
	Using Weibull++ with rank regression on X yields:		Using Weibull++ with rank regression on X yields:

Kate Racaza at 18:03, 25 May 2012

2012-05-25T18:03:47Z

← Older revision		Revision as of 18:03, 25 May 2012
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	{{template:LDAOtherSections\|\|}}		{{template:LDAOtherSections\|\|}}
			= ReliaSoft's Alternate Ranking Method (RRM) =
	In probability plotting or rank regression analysis of interval or left censored data, difficulties arise when attempting to estimate the exact time within the interval when the failure actually occurs, especially when an overlap on the intervals is present. In this case, the ''standard ranking method'' (SRM) is not applicable when dealing with interval data; thus, ReliaSoft has formulated a more sophisticated methodology to allow for more accurate probability plotting and regression analysis of data sets with interval or left censored data. This method utilizes the traditional rank regression method and iteratively improves upon the computed ranks by parametrically recomputing new ranks and the most probable failure time for interval data. A step-by-step example of this method follows.		In probability plotting or rank regression analysis of interval or left censored data, difficulties arise when attempting to estimate the exact time within the interval when the failure actually occurs, especially when an overlap on the intervals is present. In this case, the ''standard ranking method'' (SRM) is not applicable when dealing with interval data; thus, ReliaSoft has formulated a more sophisticated methodology to allow for more accurate probability plotting and regression analysis of data sets with interval or left censored data. This method utilizes the traditional rank regression method and iteratively improves upon the computed ranks by parametrically recomputing new ranks and the most probable failure time for interval data. A step-by-step example of this method follows.

	= ~~ReliaSoft's Alternate Ranking Method (RRM)~~ Step-by-Step Example=		= Step-by-Step Example=
	This section illustrates the ReliaSoft ranking method (RRM), which is an iterative improvement on the standard ranking method (SRM). Although this method is illustrated by the use of the two-parameter Weibull distribution, it can be easily generalized for other models.		This section illustrates the ReliaSoft ranking method (RRM), which is an iterative improvement on the standard ranking method (SRM). Although this method is illustrated by the use of the two-parameter Weibull distribution, it can be easily generalized for other models.

Harry Guo: /* Initial Parameter Estimation */

2012-03-16T23:00:14Z

Initial Parameter Estimation

← Older revision		Revision as of 23:00, 16 March 2012
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	In general, for left censored data:		In general, for left censored data:

	:• The increment term for <math>n</math> left censored items at time <math>={{t}_{0}},</math> with a time-to-failure of .. when <math>{{t}_{0}}\le {{t}_{i-1}}</math> is zero.		:• The increment term for <math>n</math> left censored items at time <math>={{t}_{0}},</math> with a time-to-failure of <math>{{t}_{i}}</math> when <math>{{t}_{0}}\le {{t}_{i-1}}</math> is zero.
	:• When <math>{{t}_{0}}>{{t}_{i-1}},</math> the contribution is:		:• When <math>{{t}_{0}}>{{t}_{i-1}},</math> the contribution is:

Kate Racaza: /* Initial Parameter Estimation */

2012-03-16T21:46:50Z

Initial Parameter Estimation

← Older revision		Revision as of 21:46, 16 March 2012
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	'''Step 8'''		'''Step 8'''
	Return and repeat the process from Step 1 until an acceptable convergence is reached on the parameters (i.e. the parameter values stabilize).		Return and repeat the process from Step 1 until an acceptable convergence is reached on the parameters (i.e., the parameter values stabilize).

	==Results==		==Results==