Confidence Bounds - Revision history

Kate Racaza: Replaced content with '{{template:LDABOOK|6|Confidence Bounds}} {{:Introduction to Confidence Bounds}}'

2012-07-23T05:19:17Z

Replaced content with '{{template:LDABOOK|6|Confidence Bounds}} {{:Introduction to Confidence Bounds}}'

Lisa Hacker at 10:32, 20 July 2012

2012-07-20T10:32:45Z

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	SimuMatic generates confidence bounds and assists in visualizing and understanding them. In addition, it allows one to determine the adequacy of certain parameter estimation methods (such as rank regression on X, rank regression on Y and maximum likelihood estimation) and to visualize the effects of different data censoring schemes on the confidence bounds.		SimuMatic generates confidence bounds and assists in visualizing and understanding them. In addition, it allows one to determine the adequacy of certain parameter estimation methods (such as rank regression on X, rank regression on Y and maximum likelihood estimation) and to visualize the effects of different data censoring schemes on the confidence bounds.



	'''Example 4:'''		'''Example 4:'''
			{{Example: Comparing Parameter Estimation Methods Using Simulation Based Bounds}}
	{{:~~ABC~~}}

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Lisa Hacker at 06:09, 20 July 2012

2012-07-20T06:09:25Z

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	~~{{Example: Comparing Parameter Estimation Methods Using Simulation Based Bounds}}~~

			{{:ABC}}

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	<!--The following section applies only to Weibull++-->		<!--The following section applies only to Weibull++-->
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Kate Racaza: All the sections in this article, except the last one (Confidence Bounds for Exponentially Distributed Data), also appear in the appendix of the Accelerated Life Testing Data Analysis Reference book

2012-07-05T11:30:05Z

All the sections in this article, except the last one (Confidence Bounds for Exponentially Distributed Data), also appear in the appendix of the Accelerated Life Testing Data Analysis Reference book

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Lisa Hacker at 22:42, 30 March 2012

2012-03-30T22:42:50Z

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	~~[[Category: Completed Theoretical Review]]~~

Harry Guo at 17:25, 29 February 2012

2012-02-29T17:25:58Z

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	{{What are Confidence Bounds}}		{{What are Confidence Bounds}}
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			[[Category: Completed Theoretical Review]]

Harry Guo at 23:15, 9 February 2012

2012-02-09T23:15:10Z

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			{{Likelihood Ratio Confidence Bounds}}

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Harry Guo at 21:58, 8 February 2012

2012-02-08T21:58:02Z

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	{{Stubs}} {{template:LDABOOK\|6\|Confidence Bounds}}		{{Stubs}} {{template:LDABOOK\|6\|Confidence Bounds}}

	~~= Confidence Bounds =~~

	{{What are Confidence Bounds}}		{{What are Confidence Bounds}}




	{{Fisher Matrix Confidence Bounds}}		{{Fisher Matrix Confidence Bounds}}

Nicolette Young: /* Simulation Based Bounds */

2012-01-04T00:06:03Z

Simulation Based Bounds

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	== Simulation Based Bounds ==		{{Simulation Based Bounds}}

	The SimuMatic tool in Weibull++ can be used to perform a large number of reliability analyses on data sets that have been created using Monte Carlo simulation. This utility can assist the analyst to a) better understand life data analysis concepts, b) experiment with the influences of sample sizes and censoring schemes on analysis methods, c) construct simulation-based confidence intervals, d) better understand the concepts behind confidence intervals and e) design reliability tests. This section describes how to use simulation for estimating confidence bounds. <br> SimuMatic generates confidence bounds and assists in visualizing and understanding them. In addition, it allows one to determine the adequacy of certain parameter estimation methods (such as rank regression on X, rank regression on Y and maximum likelihood estimation) and to visualize the effects of different data censoring schemes on the confidence bounds.

	~~=== Example 4 ===~~

	The purpose of this example is to determine the best parameter estimation method for a sample of ten units following a Weibull distribution with <math>\beta =2</math> and <math>\eta =100</math> and with complete time-to-failure data for each unit (i.e. no censoring). The number of generated data sets is set to 10,000. The SimuMatic inputs are shown next.

	~~[[Image:Weibulltoolssimumatic.png\|thumb\|center\|300px]]~~

	~~{\| align="center" border="1"~~
	\|-
	~~\| [[Image:Weibullsimumatic.png\|thumb\|center\|300px]]~~
	~~\| [[Image:Weibullsimumatic2.png\|thumb\|center\|300px]]~~
	\|-
	~~\| [[Image:Weibullsimumatic3.png\|thumb\|center\|300px]]~~
	~~\| [[Image:Weibullsimumatic4.png\|thumb\|center\|300px]]~~
	\|-
	~~\| [[Image:Weibullsimumatic5.png\|thumb\|center\|300px]]~~
	~~\| [[Image:Weibullsimumatic6.png\|thumb\|center\|300px]]~~
	\|}

	~~The parameters are estimated using RRX, RRY and MLE. The plotted results generated by SimuMatic are shown next.~~

	~~:Using RRX:~~

	~~[[Image:Probabilityweibull.gif\|thumb\|center\|300px]]~~

	~~<br>~~

	~~:Using RRY:~~

	~~<br> [[Image:Probabilityweibull2.gif\|thumb\|center\|300px]]~~

	~~<br>~~

	~~:Using MLE:~~

	~~<br> [[Image:Probabilityweibull3.gif\|thumb\|center\|300px]]~~

	<br> The results clearly demonstrate that the median RRX estimate provides the least deviation from the truth for this sample size and data type. However, the MLE outputs are grouped more closely together, as evidenced by the bounds. The previous figures also show the simulation-based bounds, as well as the expected variation due to sampling error.

	<br> This experiment can be repeated in SimuMatic using multiple censoring schemes (including Type I and Type II right censoring as well as random censoring) with various distributions. Multiple experiments can be performed with this utility to evaluate assumptions about the appropriate parameter estimation method to use for data sets.

Nicolette Young: /* Bayesian Confidence Bounds */

2012-01-04T00:05:05Z

Bayesian Confidence Bounds

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