Weibull++ SimuMatic Example

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Example of Using Weibull++ SimuMatic

SimuMatic is a simulation tool in Weibull++. It can be used to design life tests, reliability demonstration tests, and study the effect of sample size.

Assume an engineer wants to design a test to estimate the B10 life a product. He knows large test sample size will provide more confidence on the analysis results from the test outcome. In other words, large sample size will narrow the confidence interval of the estimated B10 life. If he wants the ratio of the estimated one-sided upper and lower confidence bounds at a confidence level of 90% to be less than 1.5, how many samples he need to test?

The needed sample size can be found using SimuMatic in Weibull++.

Step 1: To use Simumatic, select Add Weibull++ SimuMatic from the Tools from the Project Explore.

Select SimuMatic.png

Step 2: In order to simulate random data, a distribution must be assumed. This is set in the following window.

SimuMatic Setup Distribution.png

The engineer knows that by time 200, probably 1 out of 100 test units will fail; by time 300, probably 4 out of 100 test units will fail. Based on this information, the Quick Parameter Estimator can generate the parameters for a specified distribution.

Click on the Quick Parameter Estimator, enter the above information, and calculated the distribution parameters. The result is given at:


SimuMatic Setup Parameter Estimator.png


Click on Update, the solved parameters become the inputs for the SimuMatic:

SimuMatic Setup Distribution updated.png

Step 3: Set up the rest inputs for SimuMatic using the following settings.

SimuMatic Setup censoring.png
SimuMatic Setup Number of points.png

Initially, we used 5 as the initial guess for the sample size. This value should be adjusted based on calculated confidence bound ratio. If the ratio is bigger than the required value of 1.5, we should increase it; if the ratio is smaller than the required value of 1.5, we should decrease it. By trial and error, we can find the most appropriate value for sample size.

SimuMatic Setup Analysis.png
SimuMatic Setup Test Design.png
SimuMatic Setup Reliability and Times.png

In the above figure, we set Reliability value = 0.9 because we need to estimate the B10 life of the product.

Step 4: Click on Generate to generate the data and review the results. Two sheets were generated for the results. In the Simulation Sheet, the estimated results for each generated data set were given. In the Sorted sheet, results are sorted. It is shown below.


SimuMatic Setup Sorted 10.png

In above figure, the 10% percentile of the calculated B10 life (Reliability = 0.9). From the above result, we can see the lower bound of the B10 life is 289.41. Similarly, we can find the upper bound to be:

SimuMatic Setup Sorted 90.png

The ratio of these two bounds is 598.31/289.41 = 2.07, which is bigger than the required value of 1.5. Therefore, we need to increase the sample size. The simulation result and the confidence bounds are also can be viewed at the following plot.

SimuMatic First Plot.png

Step 5: Increase sample size and calculate the confidence bound ratio until find an appropriate sample size. When the sample size is 18, the calculated bound ratio is 1.502. The results are:

SimuMatic Setup Sorted 10 sample size 18.png
SimuMatic Setup Sorted 90 sample size 18.png

The plot is:

SimuMatic Second Plot sample size 18.png

Compare this figure with the plot for sample size of 5, it can be seen that the confidence interval is much narrow.

Therefore, using SimuMatic we found the suitable sample size of 18. There are many other results in SimuMatic. Click on the 'Summary… button, you can view the summary.

SimuMatic Summary.png