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	Monte Carlo and SimuMatic Weibull++ Monte Carlo Utility

ALTA Monte Carlo Utility

The ALTA Monte Carlo utility uses Monte Carlo simulation to generate a single data set containing values that are distributed according to a specified model. The software uses the cdf (cumulative distribution function) of the relevant model to solve for time given an unreliability value chosen from a uniform random distribution. The process is repeated with new random unreliability values until the desired number of data points is obtained. The data set is then automatically placed in a ALTA standard folio, where it can be analyzed like any other data set.

To access ALTA’s Monte Carlo utility choose Home > ALTA Monte Carlo.

The setup window will appear. Follow the steps outlined below to set up the simulation:

1. On the Main tab of the window, select a model, enter its required parameter values and select the time units (e.g., hours) for the failures/suspensions in the data set. In addition, please note the following:

   • If the estimated values of the distribution parameters are not available, you can use the Quick Parameter Estimator button to solve for them.

   • If you select a proportional hazards (PPH), general log-linear (GLL) or cumulative damage (CD) model, you will have the option to change the number of stress columns in the data sheet. When this option is available, the Number of Stress Columns area, shown next, will be enabled.

   

   Every additional stress column represents an additional stress type. So, for example, a data sheet with two stress columns would be used to simulate data obtained from a two-stress test. The different rows would then be used to represent different stress value combinations for the two stresses.

   • If you select a cumulative damage (CD) model, then you will have the option to create a new time-dependent stress profile or open an existing one from this window. You can create a new profile by choosing <Add New> from the Stress Profiles drop-down list and then clicking the Create/View Profile icon next to the list. You can open an existing profile by choosing it from the drop-down list (as shown next) and then clicking the icon.

   

2. On the Stress tab, enter the appropriate Use Level stress value for each stress type. This is the stress level that the product is expected to operate under during normal use conditions. If you have selected to generate a data set with more than one stress type, multiple input fields will be available, where the first input field corresponds to Stress 1, the second to Stress 2, and so forth.

   • If you select a general log-linear (GLL) or cumulative damage (CD) model, you must also select an appropriate option from the Transformation drop-down list for each stress.

   • • Use the None X=V transformation for stress types associated with the exponential life-stress relationship (LSR). This transformation is commonly used for indicator variables (e.g., 0 = on/off and 1 = continuous operation).

     • Use the Reciprocal X=1/V transformation for stress types associated with the Arrhenius LSR. This transformation is commonly used for thermal stresses.

     • Use the Logarithmic X=ln[V] transformation for stress types associated with the inverse power law LSR. This transformation is commonly used for non-thermal stresses.

3. In the data sheet on the right side of the window, specify how many data points you want generated for each stress level, and specify the values for each stress level.

   • For example, if you wanted to generate 30 data points, 10 at 3 different stress levels, you could enter the following.

   

   Each row in the data sheet represents a stress level, and every stress column represents a stress type. For a multi-stress model, the stress level is the combination of stress values that will be applied to each group of tested units. Thus, the first row of the above table would configure the utility to generate 10 data points from 2 stresses, one with a value of 348 and another with a value of 3. The second row would generate an additional 10 data points from a different combination of stress values, and so on.

   • If you select a cumulative damage (CD) model, you will be able to assign time-dependent stress profiles to the stress columns of the data sheet. Click a cell in a stress column and a drop-down list will appear. This list will include all validated stress profiles in your current project.

     

4. Select the appropriate option on the Censoring tab:

   • No censoring: The generated data set will contain only exact failure times (i.e., it will contain no right censored, interval or left censored data).

   • Right censoring after specific number of failures: You specify the number of failures, n, that the generated data set will contain in the Number of Failures field. After the data are generated, the data is sorted. The first n data points will be marked as failures while the remaining data points will be marked as suspensions at a time equal to the time of the nth failure. When used with SimuMatic, this option allows you to simulate a failure-terminated test (i.e., a test that ends after a specified number of failures occur).

     Note: To illustrate how this censoring is performed, suppose you chose to generate 20 data points (e.g., 10 at one stress level and 10 at another) and entered 10 in the Number of Failures field. The software would first generate 20 time values. Then the lowest 10 values across all the stress levels would be marked as failure times. The remaining 10 values would be marked as suspensions.

   • Right censoring after a specific time: You specify a duration in the Time field. All simulated values that do not exceed this time will be marked as failure times. Values that exceed this time will be considered suspensions at the specified time (i.e., units that had not failed by the end of the test). When used with SimuMatic, this option allows you to simulate a time-terminated test (i.e., a test that ends after a specified time).

5. On the Settings tab, specify how you want to generate the data set and where you want the data to be stored.

   • Select the Use Seed check box if you would like to set a consistent starting point from which the random numbers will be generated. Using the same seed value and keeping all other settings the same will allow you to replicate your results.

   • In the Math Precision field, enter the number of decimal places you wish to use for each simulated data point.

   • In the Data Points field, enter the number of data points you wish to generate.

   • In the Folio and the Sheet drop-down lists, choose where to put the simulated data.

   • • If you choose <New Folio> the software will create a new folio to place the data into. If you choose <New Sheet> the software will create a new sheet in a new or existing folio, depending on what you chose in the Folio drop-down list.

     • Click the Active button to select the folio and data sheet that were active when the utility was opened. If you would like the utility to always select the active folio and data sheet, select the check box labeled Select active folio/sheet when loading this window.

After the simulation is set up, click Generate to create a data set according to your specifications. An ALTA standard folio containing the data will appear.