1 Select Help > Sample Data Library and open Reliability/Appliance.jmp.
 2 Select Analyze > Reliability and Survival > Life Distribution.
 3 Select Time Cycles and click Y, Time to Event.
 4 Select Cause Code and click Failure Cause.
 5 Select Likelihood as the Confidence Interval Method.
 6 Select Allow failure mode to use fixed parameter models.
 7 Click OK.
Fixed Parameter Model with Cause 1 Omitted
 8 Open the Individual Causes report for Cause 1. The report is called Life Distribution - Failure Cause: 1 Failure Counts: 1.
 9 Select Fix Parameter from the red triangle next to Parametric Estimate - Weibull.
 10 Select Weibull beta and type 2.
 11 Click Update.
Fixed Parameter Model with Weibull Beta Specified
In the Parametric Estimate - Weibull report, assuming β equals 2, the alpha parameter is estimated to be 22463.391. Now you can use this for the failure distribution for Cause=1.
 12 Scroll up to Cause Combination at the top of the report window.
 13 Deselect Omit for Cause 1.
 14 For the distribution for Cause 1, select Fixed Parameter Weibull.
 15 Click Update Model.
Updated Model Showing Cause 1
The steps for specifying a Bayesian model for a cause are similar to those described in Specify a Fixed Parameter Model as a Distribution for a Cause. Define the model in the desired Bayesian Estimation report found in the corresponding Parametric Estimate outline under Statistics in the Life Distribution report for the individual cause. See Bayesian Estimation - <Distribution Name>.
 • A parametric bootstrap is performed for the first Weibull, yielding random samples from the asymptotic distribution of the maximum likelihood estimate . Denote a sampled value from the asymptotic distribution of by .
 • A sample is drawn from the posterior distribution of θ2, denoted by .
 • For each set of values and , an estimate of , denoted by , is obtained.
 •
The steps for specifying a Weibayes model for a cause are similar to those described in Specify a Fixed Parameter Model as a Distribution for a Cause. Select the Fix Parameter option in the Parametric Estimate - Weibull outline under Statistics in the Life Distribution report for the cause. In the Fix Parameter report, check the Weibayes option. The Weibayes model is treated as a Bayesian model and a bootstrap sample is drawn from the posterior distribution of the parameter alpha. See Liu and Wang (2013).
To obtain an estimate of the mean remaining life at time t, m samples are drawn from the aggregated distribution conditioned on survival to time t. Their average is computed.
To compute the confidence interval, n samples of parameter estimates are drawn from either the asymptotic distributions of the MLEs, or the posterior distributions derived using Bayesian inference. For each sample of parameter values, an aggregated distribution is formed, from which m samples are drawn to compute a mean remaining life. The samples of n mean remaining life values are used to construct the confidence interval.
 – If the observation y is not censored, the saved value is given by
 – If the observation is censored, the saved value is obtained by replacing the estimated density values in the formula for an uncensored observation by the following:

Help created on 9/19/2017