Template:Example: Warranty Analysis Prediction Example - Revision history

Lisa Hacker: Redirected page to Warranty Data Analysis

2012-08-13T02:48:28Z

Redirected page to Warranty Data Analysis

← Older revision		Revision as of 02:48, 13 August 2012
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	[[~~Category: For Deletion~~]]		#REDIRECT [[Warranty_Data_Analysis]]

Kate Racaza: content moved to page: Warranty_Data_Analysis#Warranty_Prediction

2012-07-26T06:22:50Z

content moved to page: Warranty_Data_Analysis#Warranty_Prediction

← Older revision		Revision as of 06:22, 26 July 2012
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	~~'''Warranty Analysis Prediction Example'''~~		[[Category: For Deletion]]

	~~Using the data from~~ [[~~Warranty Analysis Nevada Format Example\|Example 1]], predict the number of warranty returns for October for each of the three shipment periods.~~


	~~'''Solution'''~~

	~~We use the Weibull parameter estimates found in [[Warranty Analysis Nevada Format Example\|Example 1~~]] to determine the conditional probability of failure for each shipment time period, and then multiply that probability with the number of units that are at risk for that period as follows. The equation for the conditional probability of failure is given by:

	~~::<math>Q(t\|T)=1-R(t\|T)=1-\frac{R(T+t)}{R(T)}</math>~~

	For the June shipment, there are 89 units that have successfully operated until the end of September ( <math>T=3</math> <math>months)</math> . The probability of one of these units failing in the next month ( <math>t=1</math> <math>month)</math> is then given by:

	~~::<math>Q(1\|3)=1-\frac{R(4)}{R(3)}=1-\frac{{{e}^{-{{\left( \tfrac{4}{6.70} \right)}^{2.49}}}}}{{{e}^{-{{\left( \tfrac{3}{6.70} \right)}^{2.49}}}}}=1-\frac{0.7582}{0.8735}=0.132</math>~~

	Once the probability of failure for an additional month of operation is determined, the expected number of failed units during the next month, from the June shipment, is the product of this probability and the number of units at risk ( <math>{{S}_{JUN,3}}=89)</math> or:

	~~::<math>{{\widehat{F}}_{JUN,4}}=89\cdot 0.132=11.748\text{, or 12 units}</math>~~

	~~This is then repeated for the July shipment, where there were 134 units operating at the end of September, with an exposure time of two months. The probability of failure in the next month is:~~

	~~::<math>Q(1\|2)=1-\frac{R(3)}{R(2)}=1-\frac{0.8735}{0.9519}=0.0824</math>~~

	~~This value is multiplied by <math>{{S}_{JUL,2}}=134</math> to determine the number of failures, or:~~

	~~::<math>{{\widehat{F}}_{JUL,3}}=134\cdot 0.0824=11.035\text{, or 11 units}</math>~~

	~~For the August shipment, there were 146 units operating at the end of September, with an exposure time of one month. The probability of failure in the next month is:~~

	~~::<math>Q(1\|1)=1-\frac{R(2)}{R(1)}=1-\frac{0.9519}{0.9913}=0.0397</math>~~

	~~This value is multiplied by <math>{{S}_{AUG,1}}=146</math> to determine the number of failures, or:~~

	~~::<math>{{\widehat{F}}_{AUG,2}}=146\cdot 0.0397=5.796\text{, or 6 units}</math>~~

	Thus, the total expected returns from all shipments for the next month is the sum of the above, or 29 units. This method can be easily repeated for different future sales periods, and utilizing projected shipments. If the user lists the number of units that are expected be sold or shipped during future periods, then these units are added to the number of units at risk whenever they are introduced into the field. The warranty analysis tool in Weibull++ performs this type of analysis for you.

	~~Note that Weibull++ can perform this step automatically by using the '''Generate Forecast''' functionality.~~

Harry Guo at 23:52, 21 February 2012

2012-02-21T23:52:00Z

← Older revision		Revision as of 23:52, 21 February 2012
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	'''Solution'''		'''Solution'''

	We use the Weibull parameter estimates found in Example 2 to determine the conditional probability of failure for each shipment time period, and then multiply that probability with the number of units that are at risk for that period as follows. The equation for the conditional probability of failure is given by:		We use the Weibull parameter estimates found in [[Warranty Analysis Nevada Format Example\|Example 1]] to determine the conditional probability of failure for each shipment time period, and then multiply that probability with the number of units that are at risk for that period as follows. The equation for the conditional probability of failure is given by:

	::<math>Q(t\|T)=1-R(t\|T)=1-\frac{R(T+t)}{R(T)}</math>		::<math>Q(t\|T)=1-R(t\|T)=1-\frac{R(T+t)}{R(T)}</math>

Harry Guo at 22:43, 21 February 2012

2012-02-21T22:43:59Z

← Older revision		Revision as of 22:43, 21 February 2012
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	'''Warranty Analysis Prediction Example'''		'''Warranty Analysis Prediction Example'''

	Using the data from Example 1, predict the number of warranty returns for October for each of the three shipment periods.		Using the data from [[Warranty Analysis Nevada Format Example\|Example 1]], predict the number of warranty returns for October for each of the three shipment periods.

Harry Guo at 20:50, 21 February 2012

2012-02-21T20:50:59Z

← Older revision		Revision as of 20:50, 21 February 2012
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	Thus, the total expected returns from all shipments for the next month is the sum of the above, or 29 units. This method can be easily repeated for different future sales periods, and utilizing projected shipments. If the user lists the number of units that are expected be sold or shipped during future periods, then these units are added to the number of units at risk whenever they are introduced into the field. The warranty analysis tool in Weibull++ performs this type of analysis for you.		Thus, the total expected returns from all shipments for the next month is the sum of the above, or 29 units. This method can be easily repeated for different future sales periods, and utilizing projected shipments. If the user lists the number of units that are expected be sold or shipped during future periods, then these units are added to the number of units at risk whenever they are introduced into the field. The warranty analysis tool in Weibull++ performs this type of analysis for you.

	Note that Weibull++ can perform this step automatically by using the `Generate Forecast' functionality.		Note that Weibull++ can perform this step automatically by using the '''Generate Forecast''' functionality.

Harry Guo at 20:50, 21 February 2012

2012-02-21T20:50:20Z

← Older revision		Revision as of 20:50, 21 February 2012
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	Using the data from Example 1, predict the number of warranty returns for October for each of the three shipment periods.		Using the data from Example 1, predict the number of warranty returns for October for each of the three shipment periods.


	'''Solution'''		'''Solution'''

Harry Guo: Created page with ''''Warranty Analysis Prediction Example''' Using the data from Example 1, predict the number of warranty returns for October for each of the three shipment periods. '''Solution…'

2012-02-21T20:50:12Z

Created page with ''''Warranty Analysis Prediction Example''' Using the data from Example 1, predict the number of warranty returns for October for each of the three shipment periods. '''Solution…'

New page

'''Warranty Analysis Prediction Example'''

Using the data from Example 1, predict the number of warranty returns for October for each of the three shipment periods.

'''Solution'''

We use the Weibull parameter estimates found in Example 2 to determine the conditional probability of failure for each shipment time period, and then multiply that probability with the number of units that are at risk for that period as follows. The equation for the conditional probability of failure is given by:

::<math>Q(t|T)=1-R(t|T)=1-\frac{R(T+t)}{R(T)}</math>

For the June shipment, there are 89 units that have successfully operated until the end of September ( <math>T=3</math> <math>months)</math> . The probability of one of these units failing in the next month ( <math>t=1</math> <math>month)</math> is then given by:

::<math>Q(1|3)=1-\frac{R(4)}{R(3)}=1-\frac{{{e}^{-{{\left( \tfrac{4}{6.70} \right)}^{2.49}}}}}{{{e}^{-{{\left( \tfrac{3}{6.70} \right)}^{2.49}}}}}=1-\frac{0.7582}{0.8735}=0.132</math>

Once the probability of failure for an additional month of operation is determined, the expected number of failed units during the next month, from the June shipment, is the product of this probability and the number of units at risk ( <math>{{S}_{JUN,3}}=89)</math> or:

::<math>{{\widehat{F}}_{JUN,4}}=89\cdot 0.132=11.748\text{, or 12 units}</math>

This is then repeated for the July shipment, where there were 134 units operating at the end of September, with an exposure time of two months. The probability of failure in the next month is:

::<math>Q(1|2)=1-\frac{R(3)}{R(2)}=1-\frac{0.8735}{0.9519}=0.0824</math>

This value is multiplied by <math>{{S}_{JUL,2}}=134</math> to determine the number of failures, or:

::<math>{{\widehat{F}}_{JUL,3}}=134\cdot 0.0824=11.035\text{, or 11 units}</math>

For the August shipment, there were 146 units operating at the end of September, with an exposure time of one month. The probability of failure in the next month is:

::<math>Q(1|1)=1-\frac{R(2)}{R(1)}=1-\frac{0.9519}{0.9913}=0.0397</math>

This value is multiplied by <math>{{S}_{AUG,1}}=146</math> to determine the number of failures, or:

::<math>{{\widehat{F}}_{AUG,2}}=146\cdot 0.0397=5.796\text{, or 6 units}</math>

Thus, the total expected returns from all shipments for the next month is the sum of the above, or 29 units. This method can be easily repeated for different future sales periods, and utilizing projected shipments. If the user lists the number of units that are expected be sold or shipped during future periods, then these units are added to the number of units at risk whenever they are introduced into the field. The warranty analysis tool in Weibull++ performs this type of analysis for you.

Note that Weibull++ can perform this step automatically by using the `Generate Forecast' functionality.