Template:Gompertz models (standard and modified) - Revision history

Richard House: Redirected page to Gompertz Models

2012-08-27T02:10:23Z

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	REDIRECT [[Gompertz_Models]]		#REDIRECT [[Gompertz_Models]]

Richard House: Replaced content with 'REDIRECT Gompertz_Models'

2012-08-27T02:09:08Z

Replaced content with 'REDIRECT Gompertz_Models'

← Older revision		Revision as of 02:09, 27 August 2012
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	~~{{standard model overview gompz}}~~		REDIRECT [[Gompertz_Models]]

	~~{{parameter estimation using least squares in nonlinear regression}}~~

	~~{{cumulative reliability gumpz}}~~

	~~{{modified gompertz model}}~~

	~~==General Examples==~~
	~~===Example 4===~~
	~~<br>~~
	A new design is put through a reliability growth test. The requirement is that after the ninth stage the design will exhibit an 85% reliability with a 90% confidence level. Given the data in Table 7.5, do the following:
	~~<br>~~
	~~:1) Estimate the parameters of the Standard Gompertz model.~~
	~~:2) What is the initial reliability at <math>T=0</math> ?~~
	~~:3) Determine the reliability at the end of the ninth stage and check to see if the goal has been met.~~
	~~<br>~~
	~~{\|style= align="center" border="1"~~
	~~\|+'''Table 7.5 - Grouped per configuration data for Example 4'''~~
	~~!Stage~~
	~~!Number of Units~~
	~~!Number of Failures~~
	\|-
	~~\|1\|\| 10\|\| 5~~
	\|-
	~~\|2\|\| 8\|\| 3~~
	\|-
	~~\|3\|\| 9\|\| 3~~
	\|-
	~~\|4\|\| 9\|\| 2~~
	\|-
	~~\|5\|\| 10\|\| 2~~
	\|-
	~~\|6\|\| 10\|\| 1~~
	\|-
	~~\|7\|\| 10\|\| 1~~
	\|-
	~~\|8\|\| 10\|\| 1~~
	\|-
	~~\|9\|\| 10\|\| 1~~
	\|}
	~~<br>~~
	~~====Solution to Example 4====~~
	~~:1) The data is entered in cumulative format and the estimated Standard Gompertz parameters are shown in Figure Gompex4a.~~

	[[~~Image:rga7.6.png\|thumb\|center\|400px\|Entered data and the estimated Standard Gompertz parameters.]]~~

	~~:2) The initial reliability at <math>T=0</math> is equal to:~~

	~~::<math>\begin{align}~~
	~~& {{R}_{T=0}}= & a\cdot b \\~~
	~~& = & 0.9497\cdot 0.5249 \\~~
	~~& = & 0.4985~~
	~~\end{align}</math>~~

	~~:3) The reliability at the ninth stage can be calculated using the Quick Calculation Pad (QCP) as shown in Figure Gompex4b.~~

	~~[[Image:rga7.7.png\|thumb\|center\|400px\|Calculate the reliability at the end of the ninth stage with 90% confidence bounds.]]~~
	~~<br>~~
	The estimated reliability at the end of the ninth stage is equal to 91.92%. However, the lower limit at the 90% 1-sided confidence bound is equal to 82.15%. Therefore, the required goal of 85% reliability at a 90% confidence level has not been met.

	~~===Example 5===~~
	~~Using the data in Table 7.6, determine whether the Standard Gompertz or Modified Gompertz would be better suited for analyzing the given data.~~
	~~<br>~~
	~~{\|style= align="center" border="1"~~
	~~\|+'''Table 7.6 - Reliability data for Example 5'''~~
	~~!Stage~~
	~~!Reliability (%)~~
	\|-
	~~\|0\|\| 36~~
	\|-
	~~\|1\|\| 38~~
	\|-
	~~\|2\|\| 46~~
	\|-
	~~\|3\|\| 58~~
	\|-
	~~\|4\|\| 71~~
	\|-
	~~\|5\|\| 80~~
	\|-
	~~\|6\|\| 86~~
	\|-
	~~\|7\|\| 88~~
	\|-
	~~\|8\|\| 90~~
	\|-
	~~\|9\|\| 91~~
	\|}

	~~====Solution to Example 5====~~
	~~The Standard Gompertz Reliability vs. Time plot is shown in Figure Ex5Std.~~
	The Standard Gompertz seems to do a fairly good job of modeling the data. However, it appears that it is having difficulty modeling the S-shape of the data. The Modified Gompertz Reliability vs. Time plot is shown in Figure Ex5Mod.

	~~The Modified Gompertz, as expected, does a much better job of handling the S-shape presented by the data and provides a better fit for this data.~~


	~~[[Image:rga7.8.png\|thumb\|center\|400px\|Standard Gompertz Reliability vs. Time plot]]~~
	~~<br>~~
	~~<br>~~
	~~[[Image:rga7.9.png\|thumb\|center\|400px\|Modified Gompertz Reliability vs. Time plot.~~]]

Lisa Hacker at 00:32, 23 August 2012

2012-08-23T00:32:10Z

← Older revision		Revision as of 00:32, 23 August 2012
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	~~=Gompertz Models (Standard and Modified)=~~

	{{standard model overview gompz}}		{{standard model overview gompz}}

Nicolette Young: /* Modified Gompertz Model */

2012-01-10T20:33:59Z

Modified Gompertz Model

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Nicolette Young: /* Cumulative Reliability */

2012-01-10T20:32:24Z

Cumulative Reliability

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 {{parameter estimation using least squares in nonlinear regression}}
-==Cumulative Reliability==
+{{cumulative reliability gumpz}}
 ==Modified Gompertz Model==

Nicolette Young: /* Parameter Estimation Using Least Squares in Nonlinear Regression */

2012-01-10T20:29:18Z

Parameter Estimation Using Least Squares in Nonlinear Regression

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Nicolette Young: /* Standard Model Overview */

2012-01-10T18:35:59Z

Standard Model Overview

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 =Gompertz Models (Standard and Modified)=
-==Standard Model Overview==
+{{standard model overview gompz}}
 ==Parameter Estimation Using Least Squares in Nonlinear Regression==

Nicolette Young: Created page with '=Gompertz Models (Standard and Modified)= ==Standard Model Overview== The Gompertz reliability growth model is often used when analyzing reliability data. It is most applicable …'

2012-01-10T18:35:33Z

Created page with '=Gompertz Models (Standard and Modified)= ==Standard Model Overview== The Gompertz reliability growth model is often used when analyzing reliability data. It is most applicable …'

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