Simulation Based Bounds Example

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.

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.