Simulation Based Bounds Example: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 14: Line 14:
:Using RRX:
:Using RRX:


[[Image:SimuMatic RRX.png|thumb|center|400px|'''RRX''']]  
[[Image:SimuMatic RRX.png|thumb|center|250px|'''RRX''']]  


<br>  
<br>  
Line 20: Line 20:
:Using RRY:
:Using RRY:


[[Image:SimuMatic RRY.png|thumb|center|400px|'''RRY''']]  
[[Image:SimuMatic RRY.png|thumb|center|250px|'''RRY''']]  


<br>  
<br>  
Line 26: Line 26:
:Using MLE:
:Using MLE:


<br> [[Image:SimuMatic MLE.png|thumb|center|400px|'''MLE''']]  
<br> [[Image:SimuMatic MLE.png|thumb|center|250px|'''MLE''']]  


<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> 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.
<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.

Revision as of 17:51, 25 April 2012

Comparing Parameter Estimation Methods Using Simulation Based Bounds

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]\displaystyle{ \beta =2 }[/math] and [math]\displaystyle{ \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 1,000. The SimuMatic inputs are shown next.

SimuMatic Parameters.png
SimuMatic Censoring.png
SimuMatic Number of Data Sets.png


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

Using RRX:
RRX


Using RRY:
RRY


Using MLE:


MLE


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.


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.