How to perform a reliability analysis with few or no failures

When you have few or no failures, you can use Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis to get results. The analysis accepts historical values for distribution parameters. With the assumption that the historical values are accurate, you can get lower confidence bounds for these statistics:
  • Parameters
  • Percentiles
  • Probabilities of survival
  • Cumulative probabilities of failure
When you do a distribution analysis with an assumed shape or scale parameter, you are using a technique known as Bayes analysis. In the case of the Weibull model, this technique is more commonly called Weibayes. A Bayes analysis lets you use previous knowledge about your process to make inferences about your current observations. If you collect failure data and have no failures, Minitab can do a Bayes reliability analysis when these four criteria are true:
  • The data come from a Weibull or exponential distribution.
  • The data are right-censored.
  • The maximum likelihood estimation method is used to estimate parameters.
  • You provide a historical value for the shape parameter (Weibull). If your data are from an exponential distribution, Minitab automatically assigns a shape parameter of 1.
Note

If your data come from a 3-parameter Weibull or 2-parameter exponential, you must also provide a historical value for the threshold parameter.

Example of a performing a Weibayes analysis

Suppose you have a reliability data set with no failures. The time values are in C1, the censoring values are in C2, and the data comes from a Weibull distribution. If there are no failures in the data set, follow the steps below to conduct a Weibayes analysis assuming an imminent failure:
  1. Choose Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis.
  2. In Variables, enter C1.
  3. In Assumed distribution, choose Weibull.
  4. Click Censor.
  5. Choose Use censoring columns, and enter C2. Enter the value from your censoring column that indicates a censored observation in Censoring value and click OK.
  6. Click Estimate.
  7. In Estimation Method, choose Maximum Likelihood.
    Note

    The least squares estimation method cannot be used for an analysis with no failures.

  8. Under Bayes Analysis, in Set shape (slope-Weibull) or scale (1/slope-other dists) at, enter the assumed value.
  9. In Confidence level, enter 50.
    Note

    When no failures are in the data, a 50% lower bound is commonly used as an estimate of the scale parameter.

  10. Click OK in each dialog box.
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