Target Reliability Tool - Revision history

Lisa Hacker at 19:12, 15 September 2023

2023-09-15T19:12:34Z

← Older revision		Revision as of 19:12, 15 September 2023
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	{{Template:~~LDABOOK_SUB~~\|Additional Reliability Analysis Tools\|Target Reliability Tool}}		{{Template:LDABOOK\|Additional Reliability Analysis Tools\|Target Reliability Tool}}
	Product reliability affects total product costs in multiple ways. Increasing reliability increases the initial cost of production but decreases other costs incurred over the life of the product. For example, increased reliability results in lower warranty and replacement costs for defective products. Increased reliability also results in greater market share because satisfied customers typically become repeat customers and recommend reliable products to others. A minimal total product cost can be determined by calculating the optimum reliability for such a product. The Target Reliability tool in Weibull++ does this by minimizing the sum of lost sales costs, warranty costs and manufacturing costs.		Product reliability affects total product costs in multiple ways. Increasing reliability increases the initial cost of production but decreases other costs incurred over the life of the product. For example, increased reliability results in lower warranty and replacement costs for defective products. Increased reliability also results in greater market share because satisfied customers typically become repeat customers and recommend reliable products to others. A minimal total product cost can be determined by calculating the optimum reliability for such a product. The Target Reliability tool in Weibull++ does this by minimizing the sum of lost sales costs, warranty costs and manufacturing costs.

Nicolette Young: /* Total Cost */

2015-12-23T22:27:09Z

Total Cost

← Older revision		Revision as of 22:27, 23 December 2015
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	The production cost is a pre-shipping cost, whereas the warranty and lost sales costs are incurred after a product is shipped. These pre- and post-shipping costs can be seen in the figure below.		The production cost is a pre-shipping cost, whereas the warranty and lost sales costs are incurred after a product is shipped. These pre- and post-shipping costs can be seen in the figure below.

	[[Image:Chart_totalcost.jpg\|center\|~~350px~~\| ]]		[[Image:Chart_totalcost.jpg\|center\|550px\| ]]

	The reliability value resulting in the lowest total cost will be the target reliability for the product.		The reliability value resulting in the lowest total cost will be the target reliability for the product.

Harry Guo at 16:09, 28 January 2013

2013-01-28T16:09:22Z

← Older revision		Revision as of 16:09, 28 January 2013
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	<center><font size="3">		<center><font size="3">
	''Sales Revenue'' (''R'') = ''~~Total~~ Market ~~Value~~'' x ''Market Share'' (''R'') x ''Unit Price'' (''R'')		''Sales Revenue'' (''R'') = ''Maximum Market Potential'' x ''Market Share'' (''R'') x ''Unit Price'' (''R'')
	</font></center>		</font></center>

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	<center><font size="3">		<center><font size="3">
	''Warranty Cost'' (''R'') = ''~~Total~~ Market ~~Value~~'' x ''Market Share'' (''R'') x (1 - ''R'') x ''Cost Per Failure'' (''R'')		''Warranty Cost'' (''R'') = ''Maximum Market Potential'' x ''Market Share'' (''R'') x (1 - ''R'') x ''Cost Per Failure'' (''R'')
	</font></center>		</font></center>

Richard House at 18:48, 26 September 2012

2012-09-26T18:48:32Z

← Older revision		Revision as of 18:48, 26 September 2012
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	Calculating sales revenue requires knowledge of market share and unit sale price. The function for '''market share''' is given by the equation:		Calculating sales revenue requires knowledge of market share and unit sale price. The function for '''market share''' is given by the equation:

	<center><math>{{f}_{Market\_Share}}(R)=1-{{e}^{-{{\left( \frac{R}{a} \right)}^{b}}}}</math></center>		<center><math>{{f}_{Market\_Share}}(R)=1-{{e}^{-{{\left( \frac{R}{a} \right)}^{b}}}}\,\!</math></center>

	where ''a'' and ''b'' are parameters fitted to market share data, and ''R'' is the product reliability.		where ''a'' and ''b'' are parameters fitted to market share data, and ''R'' is the product reliability.
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	<center>		<center>
	<math> f_{Sale\_Price}\left(R\right)=b\times e^{a\cdot R} </math>		<math> f_{Sale\_Price}\left(R\right)=b\times e^{a\cdot R} \,\!</math>
	</center>		</center>

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	Production cost is a function of total market value, market share and manufacturing cost per unit. The function for '''production cost per unit''' is given by:		Production cost is a function of total market value, market share and manufacturing cost per unit. The function for '''production cost per unit''' is given by:

	<center> <math>f_{Production\_Cost} (R)=b\times e^{\frac{a}{\left(1-R\right)}}</math> </center>		<center> <math>f_{Production\_Cost} (R)=b\times e^{\frac{a}{\left(1-R\right)}}\,\!</math> </center>

	where ''a'' and ''b'' are parameters fitted to data, and ''R'' is the product reliability.		where ''a'' and ''b'' are parameters fitted to data, and ''R'' is the product reliability.

	Using the substitution of variable <math> R'=\frac{1}{1-R} </math> results in the equation:		Using the substitution of variable <math> R'=\frac{1}{1-R} \,\!</math> results in the equation:

	<center> <math> f_{Production\_Cost}\left(R'\right)=b\times e^{a\cdot R'} </math> </center>		<center> <math> f_{Production\_Cost}\left(R'\right)=b\times e^{a\cdot R'} \,\!</math> </center>

	for which the parameters ''a'' and ''b'' can be determined using simple regression tools such as the functions in the [[Degradation Data Analysis]] in Weibull++.		for which the parameters ''a'' and ''b'' can be determined using simple regression tools such as the functions in the [[Degradation Data Analysis]] in Weibull++.
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	Warranty cost is a function of total market value, market share, reliability and cost per failure. The function of '''cost per failure''' is given by:		Warranty cost is a function of total market value, market share, reliability and cost per failure. The function of '''cost per failure''' is given by:

	<center> <math>f_{Failure\_Cost}(R)=b\times e^{a\cdot R}</math> </center>		<center> <math>f_{Failure\_Cost}(R)=b\times e^{a\cdot R}\,\!</math> </center>

	where ''a'' and ''b'' are parameters fitted to data. For a given reliability value, ''R'', the '''warranty cost''' is given by:		where ''a'' and ''b'' are parameters fitted to data. For a given reliability value, ''R'', the '''warranty cost''' is given by:
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	First, consider that traditional Return On Investment (ROI) is a performance measure used to evaluate the efficiency of an investment, or to compare the efficiency of a number of different investments. In general to calculate ROI, the benefit (return) of an investment is divided by the cost of the investment; and the result is expressed as a percentage or a ratio. The following equation illustrates this.		First, consider that traditional Return On Investment (ROI) is a performance measure used to evaluate the efficiency of an investment, or to compare the efficiency of a number of different investments. In general to calculate ROI, the benefit (return) of an investment is divided by the cost of the investment; and the result is expressed as a percentage or a ratio. The following equation illustrates this.
	<center>		<center>
	<math>ROI=\frac{\text{Gain from Investment - Cost of Investment}}{\text{Cost of Investment}}</math></center>		<math>ROI=\frac{\text{Gain from Investment - Cost of Investment}}{\text{Cost of Investment}}\,\!</math></center>

	In this formula, ''Gains from Investment'' refers to the revenue or proceeds obtained due to the investment of interest.		In this formula, ''Gains from Investment'' refers to the revenue or proceeds obtained due to the investment of interest.
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	R3OI considers the cost and return due to the product reliability. As we discussed before, high reliability will reduce the unreliability cost, but will increase the sales revenue and production cost. A balanced reliability target should be determined based on all of the costs involved. For a given initial investment value, the R3OI is calculated by:		R3OI considers the cost and return due to the product reliability. As we discussed before, high reliability will reduce the unreliability cost, but will increase the sales revenue and production cost. A balanced reliability target should be determined based on all of the costs involved. For a given initial investment value, the R3OI is calculated by:
	<center>		<center>
	<math>R3OI=\frac{\text{Profit(R)-Initial Investment }}{\text{Initial Investment}}</math>		<math>R3OI=\frac{\text{Profit(R)-Initial Investment }}{\text{Initial Investment}}\,\!</math>
	</center>		</center>

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	& f_{Failure\_Cost}(R)=b\cdot {{e}^{\left( a\cdot R \right)}} \\		& f_{Failure\_Cost}(R)=b\cdot {{e}^{\left( a\cdot R \right)}} \\
	\end{align}		\end{align}
	</math>		\,\!</math>

Lisa Hacker at 04:25, 28 August 2012

2012-08-28T04:25:10Z

← Older revision		Revision as of 04:25, 28 August 2012
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	==Example==		==Example==
	{{:Target Reliability Tool Example}}		{{:Target Reliability Tool Example}}
	~~\begin{equation} \text{Profit}\left(R\right) = \text{Sales Revenue}\left(R\right) - \text{Warranty Cost}\left(R\right) - \text{Production Cost}\left(R\right) \end{equation}~~

Lisa Hacker at 04:24, 28 August 2012

2012-08-28T04:24:36Z

← Older revision		Revision as of 04:24, 28 August 2012
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	==Example==		==Example==
	{{:Target Reliability Tool Example}}		{{:Target Reliability Tool Example}}
			\begin{equation} \text{Profit}\left(R\right) = \text{Sales Revenue}\left(R\right) - \text{Warranty Cost}\left(R\right) - \text{Production Cost}\left(R\right) \end{equation}

Lisa Hacker at 04:17, 28 August 2012

2012-08-28T04:17:25Z

← Older revision		Revision as of 04:17, 28 August 2012
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	Calculating sales revenue requires knowledge of market share and unit sale price. The function for '''market share''' is given by the equation:		Calculating sales revenue requires knowledge of market share and unit sale price. The function for '''market share''' is given by the equation:

	::<math>~~\begin{align}~~		<center><math>{{f}_{Market\_Share}}(R)=1-{{e}^{-{{\left( \frac{R}{a} \right)}^{b}}}}</math></center>
	{{f}_{Market\_Share}}(R)=1-{{e}^{-{{\left( \frac{R}{a} \right)}^{b}}}}
	~~\end{align~~}</math>

	where ''a'' and ''b'' are parameters fitted to market share data, and ''R'' is the product reliability.		where ''a'' and ''b'' are parameters fitted to market share data, and ''R'' is the product reliability.

Lisa Hacker: Undo revision 34183 by Lisa Hacker (Talk)

2012-08-28T04:15:20Z

Undo revision 34183 by Lisa Hacker (Talk)

← Older revision		Revision as of 04:15, 28 August 2012
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	{{Template:LDABOOK_SUB\|Additional Reliability Analysis Tools\|Target Reliability Tool}}		{{Template:LDABOOK_SUB\|Additional Reliability Analysis Tools\|Target Reliability Tool}}

	Product reliability affects total product costs in multiple ways. Increasing reliability increases the initial cost of production but decreases other costs incurred over the life of the product. For example, increased reliability results in lower warranty and replacement costs for defective products. Increased reliability also results in greater market share because satisfied customers typically become repeat customers and recommend reliable products to others. A minimal total product cost can be determined by calculating the optimum reliability for such a product. The Target Reliability tool in Weibull++ does this by minimizing the sum of lost sales costs, warranty costs and manufacturing costs.		Product reliability affects total product costs in multiple ways. Increasing reliability increases the initial cost of production but decreases other costs incurred over the life of the product. For example, increased reliability results in lower warranty and replacement costs for defective products. Increased reliability also results in greater market share because satisfied customers typically become repeat customers and recommend reliable products to others. A minimal total product cost can be determined by calculating the optimum reliability for such a product. The Target Reliability tool in Weibull++ does this by minimizing the sum of lost sales costs, warranty costs and manufacturing costs.

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	Once the total market value and the sales revenue are obtained, they can then be used to calculate the lost sales cost using the formula given at the beginning of this section.		Once the total market value and the sales revenue are obtained, they can then be used to calculate the lost sales cost using the formula given at the beginning of this section.

	==Production Cost==		==Production Cost==

	Production cost is a function of total market value, market share and manufacturing cost per unit. The function for '''production cost per unit''' is given by:		Production cost is a function of total market value, market share and manufacturing cost per unit. The function for '''production cost per unit''' is given by:

	::<math>~~\begin{align}~~		<center> <math>f_{Production\_Cost} (R)=b\times e^{\frac{a}{\left(1-R\right)}}</math> </center>
	f_{Production\_Cost} (R)=b\times e^{\frac{a}{\left(1-R\right)}}
	~~\end{align~~}</math>

	where ''a'' and ''b'' are parameters fitted to data, and ''R'' is the product reliability.		where ''a'' and ''b'' are parameters fitted to data, and ''R'' is the product reliability.
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	Using the substitution of variable <math> R'=\frac{1}{1-R} </math> results in the equation:		Using the substitution of variable <math> R'=\frac{1}{1-R} </math> results in the equation:

	::<math>~~\begin{align}~~		<center> <math> f_{Production\_Cost}\left(R'\right)=b\times e^{a\cdot R'} </math> </center>
	f_{Production\_Cost}\left(R'\right)=b\times e^{a\cdot R'}
	~~\end{align~~}</math>

	for which the parameters ''a'' and ''b'' can be determined using simple regression tools such as the functions in the [[Degradation Data Analysis]] in Weibull++.		for which the parameters ''a'' and ''b'' can be determined using simple regression tools such as the functions in the [[Degradation Data Analysis]] in Weibull++.


	==Warranty Cost==		==Warranty Cost==

Lisa Hacker: /* Production Cost */

2012-08-28T04:14:16Z

Production Cost

← Older revision		Revision as of 04:14, 28 August 2012
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	Once the total market value and the sales revenue are obtained, they can then be used to calculate the lost sales cost using the formula given at the beginning of this section.		Once the total market value and the sales revenue are obtained, they can then be used to calculate the lost sales cost using the formula given at the beginning of this section.

	==Production Cost==		==Production Cost==

	Production cost is a function of total market value, market share and manufacturing cost per unit. The function for '''production cost per unit''' is given by:		Production cost is a function of total market value, market share and manufacturing cost per unit. The function for '''production cost per unit''' is given by:

	~~<center>~~ <math>f_{Production\_Cost} (R)=b\times e^{\frac{a}{\left(1-R\right)}}</math~~> </center~~>		::<math>\begin{align}
			f_{Production\_Cost} (R)=b\times e^{\frac{a}{\left(1-R\right)}}
			\end{align}</math>

	where ''a'' and ''b'' are parameters fitted to data, and ''R'' is the product reliability.		where ''a'' and ''b'' are parameters fitted to data, and ''R'' is the product reliability.
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	Using the substitution of variable <math> R'=\frac{1}{1-R} </math> results in the equation:		Using the substitution of variable <math> R'=\frac{1}{1-R} </math> results in the equation:

	~~<center>~~ <math> f_{Production\_Cost}\left(R'\right)=b\times e^{a\cdot R'} </math~~> </center~~>		::<math>\begin{align}
			f_{Production\_Cost}\left(R'\right)=b\times e^{a\cdot R'}
			\end{align}</math>

	for which the parameters ''a'' and ''b'' can be determined using simple regression tools such as the functions in the [[Degradation Data Analysis]] in Weibull++.		for which the parameters ''a'' and ''b'' can be determined using simple regression tools such as the functions in the [[Degradation Data Analysis]] in Weibull++.


	==Warranty Cost==		==Warranty Cost==

Lisa Hacker: /* Lost Sales Cost */

2012-08-28T04:13:06Z

Lost Sales Cost

← Older revision		Revision as of 04:13, 28 August 2012
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	::<math>\begin{align}		::<math>\begin{align}
	~~<math>~~{{f}_{Market\_Share}}(R)=1-{{e}^{-{{\left( \frac{R}{a} \right)}^{b}}}}~~</math>~~		{{f}_{Market\_Share}}(R)=1-{{e}^{-{{\left( \frac{R}{a} \right)}^{b}}}}
	\end{align}</math>		\end{align}</math>