Monte Carlo and SimuMatic

In life data analysis and accelerated life testing analysis, the reliability engineer will typically select a model to fit data obtained from testing or usage in the field. However, in some situations, it is useful to generate simulated data sets containing values that are distributed according to a specified life distribution or model. For example, simulated data could be used to:

  • Test different warranty and maintenance strategies
  • Perform risk analysis
  • Obtain simulation-based confidence bounds
  • Analyze probabilistic design models
  • Design reliability or reliability growth  tests
  • Compare different parameter estimation methods
  • Evaluate the impact of different censoring schemes

When using reliability growth analysis, the engineer will typically fit a reliability growth model to actual data obtained from developmental testing or fielded repairable systems operating in the field. However, in some situations, it may be useful to generate simulated data sets containing values that are distributed according to a specified set of parameters. For example, simulated data could be used to:

  • Design reliability growth tests.
  • Obtain simulation-based confidence bounds.
  • Experiment with the influences of sample sizes and data types on analysis methods.
  • Evaluate the impact of allocated test time.

You can use Monte Carlo simulation to produce data sets based on various user inputs, such as data type, the beta and lambda parameters of the Crow-AMSAA (NHPP) model and sample size. The software will randomly generate input variables that follow a specified probability distribution. In the case of reliability growth and repairable system data analysis, the goal is to generate failure times for systems that are assumed to have specific characteristics. Therefore, the inter-arrival times of the failures will follow a non-homogeneous Poisson process with a Weibull failure intensity (as specified in the Crow-AMSAA model).

Weibull++ offers the following utilities for generating and analyzing simulated data:

  • The Monte Carlo utility (which comes in a life data version, a life-stress version and a reliability growth version) uses Monte Carlo simulation to generate a single data set based on various user inputs, such as distribution type, distribution parameters and sample size. The data set is then automatically placed in an analysis folio, where it can be analyzed like any other data set. For growth analysis, the Repairable Systems Monte Carlo utility uses simulation to generate a single data set containing values that are distributed according to the Crow-AMSAA model with specified beta and lambda parameters. The data set is then automatically placed in a growth data folio, where it can be analyzed like any other data set.
  • SimuMatic (which also comes in a life data version, a life-stress version and a reliability growth version) generates a large number of data sets using Monte Carlo simulation. It then analyzes the group of data sets as a whole. You can use SimuMatic, for example, to find the average reliability at a given time for a thousand simulated data sets. For growth analysis, the Repairable Systems SimuMatic folio generates a large number of data sets using Monte Carlo simulation. It then automatically analyzes the group of data sets as a whole in order to explore a variety of questions. For example, you can use SimuMatic to calculate the simulation-based confidence bounds on the demonstrated MTBF.

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