Comparing Life Data Sets - Revision history

Lisa Hacker at 19:12, 15 September 2023

2023-09-15T19:12:11Z

← Older revision		Revision as of 19:12, 15 September 2023
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	{{Template:~~LDABOOK_SUB~~\|Additional Reliability Analysis Tools\|Comparing Life Data Sets}}		{{Template:LDABOOK\|Additional Reliability Analysis Tools\|Comparing Life Data Sets}}
	It is often desirable to be able to compare two sets of reliability or life data in order to determine which of the data sets has a more favorable life distribution. The data sets could be from two alternate designs, manufacturers, lots, assembly lines, etc. Many methods are available in statistical literature for doing this when the units come from a ''complete'' sample (i.e., a sample with no censoring). This process becomes a little more difficult when dealing with data sets that have censoring, or when trying to compare two data sets that have different distributions. In general, the problem boils down to that of being able to determine any statistically significant difference between the two samples of potentially censored data from two possibly different populations. This section discusses some of the methods available in Weibull++ that are applicable to censored data.		It is often desirable to be able to compare two sets of reliability or life data in order to determine which of the data sets has a more favorable life distribution. The data sets could be from two alternate designs, manufacturers, lots, assembly lines, etc. Many methods are available in statistical literature for doing this when the units come from a ''complete'' sample (i.e., a sample with no censoring). This process becomes a little more difficult when dealing with data sets that have censoring, or when trying to compare two data sets that have different distributions. In general, the problem boils down to that of being able to determine any statistically significant difference between the two samples of potentially censored data from two possibly different populations. This section discusses some of the methods available in Weibull++ that are applicable to censored data.

Kate Racaza: /* Life Comparison Tool */

2014-05-12T23:26:16Z

Life Comparison Tool

← Older revision		Revision as of 23:26, 12 May 2014
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	Sometimes we may need to compare the life when one of the distributions is truncated. For example, if the random variable from the first distribution is truncated with a range of [L, U}, then the comparison with truncated distribution should be used. For ~~detail~~, please see [[Stress-Strength Analysis]].		Sometimes we may need to compare the life when one of the distributions is truncated. For example, if the random variable from the first distribution is truncated with a range of [L, U}, then the comparison with the truncated distribution should be used. For details, please see [[Stress-Strength Analysis]].

Harry Guo: /* Life Comparison Tool */

2014-05-05T21:54:54Z

Life Comparison Tool

← Older revision		Revision as of 21:54, 5 May 2014
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	where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.		where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.


	Sometimes we may need to compare the life when one of the distributions is truncated. For example, if the random variable from the first distribution is truncated with a range of [L, U}, then the comparison with truncated distribution should be used. For detail, please see [[Stress-Strength Analysis]].		Sometimes we may need to compare the life when one of the distributions is truncated. For example, if the random variable from the first distribution is truncated with a range of [L, U}, then the comparison with truncated distribution should be used. For detail, please see [[Stress-Strength Analysis]].

Harry Guo: /* Life Comparison Tool */

2014-05-05T21:54:29Z

Life Comparison Tool

← Older revision		Revision as of 21:54, 5 May 2014
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	where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.		where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.

			Sometimes we may need to compare the life when one of the distributions is truncated. For example, if the random variable from the first distribution is truncated with a range of [L, U}, then the comparison with truncated distribution should be used. For detail, please see [[Stress-Strength Analysis]].


	Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t\,\!</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:		Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t\,\!</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:
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	:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.		:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.
	:*If <math>P<0.50\,\!</math> or, for example, <math>P=0.10\,\!</math>, then <math>P=1-0.10=0.90\,\!</math>, or Y is better than X with a 90% probability.		:*If <math>P<0.50\,\!</math> or, for example, <math>P=0.10\,\!</math>, then <math>P=1-0.10=0.90\,\!</math>, or Y is better than X with a 90% probability.


	'''Example:'''{{:Life Comparison Wizard}}		'''Example:'''{{:Life Comparison Wizard}}

Harry Guo: /* Life Comparison Tool */

2014-05-05T21:50:21Z

Life Comparison Tool

← Older revision		Revision as of 21:50, 5 May 2014
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	Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:		Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:

	::<math>P\left[ {{t}_{2}}\ge {{t}_{1}} \right]=\~~mathop{}_~~{0}^{\infty }{{f}_{1}}(t)\cdot {{R}_{2}}(t)\cdot dt\,\!</math>		::<math>P\left[ {{t}_{2}}\ge {{t}_{1}} \right]=\int_{0}^{\infty }{{f}_{1}}(t)\cdot {{R}_{2}}(t)\cdot dt\,\!</math>

	where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.		where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.

Richard House at 19:38, 26 September 2012

2012-09-26T19:38:40Z

← Older revision		Revision as of 19:38, 26 September 2012
Line 13:		Line 13:
	Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:		Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:

	::<math>P\left[ {{t}_{2}}\ge {{t}_{1}} \right]=\mathop{}_{0}^{\infty }{{f}_{1}}(t)\cdot {{R}_{2}}(t)\cdot dt</math>		::<math>P\left[ {{t}_{2}}\ge {{t}_{1}} \right]=\mathop{}_{0}^{\infty }{{f}_{1}}(t)\cdot {{R}_{2}}(t)\cdot dt\,\!</math>

	where <math>{{f}_{1}}(t)~~\,\!~~\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.		where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.

	Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t\,\!</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:		Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t\,\!</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:

	:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.		:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.
	:*If <math>P<0.50\,\!</math> or, for example, <math>P=0.10\,\!</math>, then <math>P=1-0.10=0.90\,\!</math> , or Y is better than X with a 90% probability.		:*If <math>P<0.50\,\!</math> or, for example, <math>P=0.10\,\!</math>, then <math>P=1-0.10=0.90\,\!</math>, or Y is better than X with a 90% probability.

	'''Example:'''{{:Life Comparison Wizard}}		'''Example:'''{{:Life Comparison Wizard}}

Richard House: /* Life Comparison Tool */

2012-09-05T16:28:44Z

Life Comparison Tool

← Older revision		Revision as of 16:28, 5 September 2012
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	where <math>{{f}_{1}}(t)\,\!\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.		where <math>{{f}_{1}}(t)\,\!\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.

	Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:		Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t\,\!</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:

	:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.		:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.

Richard House at 04:53, 24 August 2012

2012-08-24T04:53:07Z

← Older revision		Revision as of 04:53, 24 August 2012
Line 1:		Line 1:
	{{Template:LDABOOK_SUB\|Additional Reliability Analysis Tools\|Comparing Life Data Sets}}		{{Template:LDABOOK_SUB\|Additional Reliability Analysis Tools\|Comparing Life Data Sets}}
	It is often desirable to be able to compare two sets of reliability or life data in order to determine which of the data sets has a more favorable life distribution. The data sets could be from two alternate designs, manufacturers, lots, assembly lines, etc. Many methods are available in statistical literature for doing this when the units come from a ''complete'' sample (i.e., a sample with no censoring). This process becomes a little more difficult when dealing with data sets that have censoring, or when trying to compare two data sets that have different distributions. In general, the problem boils down to that of being able to determine any statistically significant difference between the two samples of potentially censored data from two possibly different populations. This section discusses some of the methods available in Weibull++ that are applicable to censored data.		It is often desirable to be able to compare two sets of reliability or life data in order to determine which of the data sets has a more favorable life distribution. The data sets could be from two alternate designs, manufacturers, lots, assembly lines, etc. Many methods are available in statistical literature for doing this when the units come from a ''complete'' sample (i.e., a sample with no censoring). This process becomes a little more difficult when dealing with data sets that have censoring, or when trying to compare two data sets that have different distributions. In general, the problem boils down to that of being able to determine any statistically significant difference between the two samples of potentially censored data from two possibly different populations. This section discusses some of the methods available in Weibull++ that are applicable to censored data.


	==Simple Plotting==		==Simple Plotting==
	One popular graphical method for making this determination involves plotting the data with confidence bounds and seeing whether the bounds overlap or separate at the point of interest. This can be easily done using the Overlay Plot feature in Weibull++. This approach can be effective for comparisons at a given point in time or a given reliability level, but it is difficult to assess the overall behavior of the two distributions because the confidence bounds may overlap at some points and be far apart at others.		One popular graphical method for making this determination involves plotting the data with confidence bounds and seeing whether the bounds overlap or separate at the point of interest. This can be easily done using the Overlay Plot feature in Weibull++. This approach can be effective for comparisons at a given point in time or a given reliability level, but it is difficult to assess the overall behavior of the two distributions because the confidence bounds may overlap at some points and be far apart at others.


	==Contour Plots==<!-- THIS SECTION HEADER IS LINKED TO: Contour Plot Example. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->		==Contour Plots==<!-- THIS SECTION HEADER IS LINKED TO: Contour Plot Example. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->
	To determine whether two data sets are significantly different and at what confidence level, one can utilize the contour plots provided in Weibull++. By overlaying two contour plots from two different data sets at the same confidence level, one can visually assess whether the data sets are significantly different at that confidence level if there is no overlap on the contours. The disadvantage of this method is that the same distribution must be fitted to both data sets.		To determine whether two data sets are significantly different and at what confidence level, one can utilize the contour plots provided in Weibull++. By overlaying two contour plots from two different data sets at the same confidence level, one can visually assess whether the data sets are significantly different at that confidence level if there is no overlap on the contours. The disadvantage of this method is that the same distribution must be fitted to both data sets.


	'''Example:'''{{:Contour Plot Example}}		'''Example:'''{{:Contour Plot Example}}


	==Life Comparison Tool==<!-- THIS SECTION HEADER IS LINKED TO: Life Comparison Wizard. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->		==Life Comparison Tool==<!-- THIS SECTION HEADER IS LINKED TO: Life Comparison Wizard. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->

Richard House: /* Life Comparison Tool */

2012-08-24T04:52:49Z

Life Comparison Tool

← Older revision		Revision as of 04:52, 24 August 2012
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	==Life Comparison Tool==<!-- THIS SECTION HEADER IS LINKED TO: Life Comparison Wizard. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->		==Life Comparison Tool==<!-- THIS SECTION HEADER IS LINKED TO: Life Comparison Wizard. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->
	Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:		Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:


	::<math>P\left[ {{t}_{2}}\ge {{t}_{1}} \right]=\mathop{}_{0}^{\infty }{{f}_{1}}(t)\cdot {{R}_{2}}(t)\cdot dt</math>		::<math>P\left[ {{t}_{2}}\ge {{t}_{1}} \right]=\mathop{}_{0}^{\infty }{{f}_{1}}(t)\cdot {{R}_{2}}(t)\cdot dt</math>

			where <math>{{f}_{1}}(t)\,\!\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.
	where <math>{{f}_{1}}(t)\,\!</math> is the ''pdf '' of the first distribution and <math>{{R}_{2}}(t)\,\!</math> is the reliability function of the second distribution. The evaluation of the superior data set is based on whether this probability is smaller or greater than 0.5. If the probability is equal to 0.5, then it is equivalent to saying that the two distributions are identical.


	Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:		Consider two product designs where X and Y represent the life test data from two different populations. If we simply wanted to determine which component has a higher reliability, we would simply compare the reliability estimates of both components at a time <math>t</math>. But if we wanted to determine which product will have a longer life, we would want to calculate the probability that the distribution of one product is better than the other. Using the equation given above, the probability that X is greater than or equal to Y can be interpreted as follows:

	:*If <math>P=0.50</math>, then lives of both X and Y are equal.		:*If <math>P=0.50\,\!</math>, then lives of both X and Y are equal.
	:*If <math>P<0.50</math> or, for example, <math>P=0.10</math>, then <math>P=1-0.10=0.90</math> , or Y is better than X with a 90% probability.		:*If <math>P<0.50\,\!</math> or, for example, <math>P=0.10\,\!</math>, then <math>P=1-0.10=0.90\,\!</math> , or Y is better than X with a 90% probability.


	'''Example:'''{{:Life Comparison Wizard}}		'''Example:'''{{:Life Comparison Wizard}}

Kate Racaza at 06:31, 15 August 2012

2012-08-15T06:31:36Z

← Older revision		Revision as of 06:31, 15 August 2012
Line 7:		Line 7:


	==Contour Plots==		==Contour Plots==<!-- THIS SECTION HEADER IS LINKED TO: Contour Plot Example. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->
	To determine whether two data sets are significantly different and at what confidence level, one can utilize the contour plots provided in Weibull++. By overlaying two contour plots from two different data sets at the same confidence level, one can visually assess whether the data sets are significantly different at that confidence level if there is no overlap on the contours. The disadvantage of this method is that the same distribution must be fitted to both data sets.		To determine whether two data sets are significantly different and at what confidence level, one can utilize the contour plots provided in Weibull++. By overlaying two contour plots from two different data sets at the same confidence level, one can visually assess whether the data sets are significantly different at that confidence level if there is no overlap on the contours. The disadvantage of this method is that the same distribution must be fitted to both data sets.

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	==Life Comparison Tool==		==Life Comparison Tool==<!-- THIS SECTION HEADER IS LINKED TO: Life Comparison Wizard. IF YOU RENAME THE SECTION, YOU MUST UPDATE THE LINK. -->
	Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by:		Another methodology, suggested by Gerald G. Brown and Herbert C. Rutemiller, is to estimate the probability of whether the times-to-failure of one population are better or worse than the times-to-failure of the second. The equation used to estimate this probability is given by: