Template:Estimating equation using the cw - Revision history

Richard House: Redirected page to Comparing Life Data Sets

2012-08-13T06:33:57Z

Redirected page to Comparing Life Data Sets

← Older revision		Revision as of 06:33, 13 August 2012
Line 1:		Line 1:
	~~===Using the Life Comparison Tool===~~		#REDIRECT [[Comparing_Life_Data_Sets]]
	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:


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


	where <math>{{f}_{1}}(t)</math> is the <math>pdf</math> 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, that is equivalent to saying the two distributions are identical.


	If given two alternate designs with life test data (where X and Y represent the life test data from two different populations), and if we simply wanted to choose the component at time <math>t</math> with the higher reliability, one choice would be to select the component with the higher reliability at time <math>t</math>. However, if we wanted to design a product as long-lived as possible, we would want to calculate the probability that the entire distribution of one product is better than the other and choose X or Y when this probability is above or below 0.50, respectively.


	~~The statement that the probability that X is greater than or equal to Y can be interpreted as follows:~~

	~~:• If <math>P=0.50</math> , then the statement is equivalent to saying that both X and Y are equal.~~
	~~:• If <math>P<0.50</math> or, for example, <math>P=0.10</math> , then the statement is equivalent to saying that <math>P=1-0.10=0.90</math> , or Y is better than X with a 90% probability.~~


	Weibull++'s Life Comparison tool allows you to perform such calculations. The disadvantage of this method is that the sample sizes are not taken into account, thus one should avoid using this method of comparison when the sample sizes are different.


	~~'''Example 2:'''~~
	~~{{Example: Life Comparison-Compare Two Designs Using Comparison Wizard}}~~

Lisa Hacker: /* Using the Life Comparison Tool */

2012-03-30T18:36:15Z

Using the Life Comparison Tool

← Older revision		Revision as of 18:36, 30 March 2012
Line 7:		Line 7:

	where <math>{{f}_{1}}(t)</math> is the <math>pdf</math> 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, that is equivalent to saying the two distributions are identical.		where <math>{{f}_{1}}(t)</math> is the <math>pdf</math> 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, that is equivalent to saying the two distributions are identical.


	If given two alternate designs with life test data (where X and Y represent the life test data from two different populations), and if we simply wanted to choose the component at time <math>t</math> with the higher reliability, one choice would be to select the component with the higher reliability at time <math>t</math>. However, if we wanted to design a product as long-lived as possible, we would want to calculate the probability that the entire distribution of one product is better than the other and choose X or Y when this probability is above or below 0.50, respectively.		If given two alternate designs with life test data (where X and Y represent the life test data from two different populations), and if we simply wanted to choose the component at time <math>t</math> with the higher reliability, one choice would be to select the component with the higher reliability at time <math>t</math>. However, if we wanted to design a product as long-lived as possible, we would want to calculate the probability that the entire distribution of one product is better than the other and choose X or Y when this probability is above or below 0.50, respectively.


	The statement that the probability that X is greater than or equal to Y can be interpreted as follows:		The statement that the probability that X is greater than or equal to Y can be interpreted as follows:
Line 14:		Line 16:
	:• If <math>P=0.50</math> , then the statement is equivalent to saying that both X and Y are equal.		:• If <math>P=0.50</math> , then the statement is equivalent to saying that both X and Y are equal.
	:• If <math>P<0.50</math> or, for example, <math>P=0.10</math> , then the statement is equivalent to saying that <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 the statement is equivalent to saying that <math>P=1-0.10=0.90</math> , or Y is better than X with a 90% probability.


	Weibull++'s Life Comparison tool allows you to perform such calculations. The disadvantage of this method is that the sample sizes are not taken into account, thus one should avoid using this method of comparison when the sample sizes are different.		Weibull++'s Life Comparison tool allows you to perform such calculations. The disadvantage of this method is that the sample sizes are not taken into account, thus one should avoid using this method of comparison when the sample sizes are different.

Lisa Hacker: /* Estimating P\left[ {{t}_{2}}\ge {{t}_{1}} \right] Using the Comparison Wizard */

2012-03-30T18:35:37Z