predict_prob

This function predicts the (failure) probabilities of a parametric lifetime
distribution using the (log-)location-scale parameterization.

Provides statistical methods and visualizations that are often
used in reliability engineering. Comprises a compact and easily
accessible set of methods and visualization tools that make the
examination and adjustment as well as the analysis and interpretation
of field data (and bench tests) as simple as possible.
Non-parametric estimators like Median Ranks,
Kaplan-Meier (Abernethy, 2006, <ISBN:978-0-9653062-3-2>),
Johnson (Johnson, 1964, <ISBN:978-0444403223>), and Nelson-Aalen
for failure probability estimation within samples that contain
failures as well as censored data are included.
The package supports methods like Maximum Likelihood and Rank Regression,
(Genschel and Meeker, 2010, <DOI:10.1080/08982112.2010.503447>)
for the estimation of multiple parametric lifetime distributions,
as well as the computation of confidence intervals of quantiles and
probabilities using the delta method related to Fisher's confidence
intervals (Meeker and Escobar, 1998, <ISBN:9780471673279>) and the
beta-binomial confidence bounds.
If desired, mixture model analysis can be done with segmented regression
and the EM algorithm.
Besides the well-known Weibull analysis, the package also contains
Monte Carlo methods for the correction and completion of imprecisely
recorded or unknown lifetime characteristics.
(Verband der Automobilindustrie e.V. (VDA), 2016, <ISSN:0943-9412>).
Plots are created statically ('ggplot2') or interactively ('plotly') and
can be customized with functions of the respective visualization package.
The graphical technique of probability plotting as well as the addition
of regression lines and confidence bounds to existing plots are
supported.

Hensel Tim-Gunnar

weibulltools

Statistical Methods for Life Data Analysis

Tim-Gunnar Hensel

David Barkemeyer

predict_prob function

<dl><dt>q</dt>
<dd>A numeric vector of quantiles.</dd>
<dt>dist_params</dt>
<dd>A vector of parameters. An overview of the
distribution-specific parameters can be found in section 'Distributions'.</dd>
<dt>distribution</dt>
<dd>Supposed distribution of the random variable.</dd></dl>

Arguments

The following table summarizes the available distributions and their parameters<ul>
<li>location parameter \(\mu\),</li>
<li>scale parameter \(\sigma\) or \(\theta\) and</li>
<li>threshold parameter \(\gamma\).</li>
</ul>The order within <code>dist_params</code> is given in the table header.<table class="table">
<tr><td><code>distribution</code></td><td><code>dist_params[1]</code></td><td><code>dist_params[2]</code></td><td><code>dist_params[3]</code></td></tr>
<tr><td><code>"sev"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"normal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"logistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"exponential"</code></td><td>\(\theta\)</td><td>-</td><td>-</td></tr>
<tr><td><code>"exponential2"</code></td><td>\(\theta\)</td><td>\(\gamma\)</td><td>-</td></tr>
</table>

Distributions

Prediction of Failure Probabilities for Parametric Lifetime Distributions — predict_prob

<dl>

<dt>q</dt>
<dd>A numeric vector of quantiles.</dd>


<dt>dist_params</dt>
<dd>A vector of parameters. An overview of the
distribution-specific parameters can be found in section 'Distributions'.</dd>


<dt>distribution</dt>
<dd>Supposed distribution of the random variable.</dd>

</dl>

The following table summarizes the available distributions and their parameters<ul>
<li>location parameter \(\mu\),</li>
<li>scale parameter \(\sigma\) or \(\theta\) and</li>
<li>threshold parameter \(\gamma\).</li>
</ul>

The order within <code>dist_params</code> is given in the table header.<table class='table'>
<tr><td><code>distribution</code></td><td><code>dist_params[1]</code></td><td><code>dist_params[2]</code></td><td><code>dist_params[3]</code></td></tr>
<tr><td><code>"sev"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"weibull3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"normal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"lognormal3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"logistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>-</td></tr>
<tr><td><code>"loglogistic3"</code></td><td>\(\mu\)</td><td>\(\sigma\)</td><td>\(\gamma\)</td></tr>
<tr><td><code>"exponential"</code></td><td>\(\theta\)</td><td>-</td><td>-</td></tr>
<tr><td><code>"exponential2"</code></td><td>\(\theta\)</td><td>\(\gamma\)</td><td>-</td></tr>
</table>

predict_prob: Prediction of Failure Probabilities for Parametric Lifetime Distributions

Description

Usage

Value

Arguments

Distributions

Details

Examples

`distribution`	`dist_params[1]`	`dist_params[2]`	`dist_params[3]`
`"sev"`	\(\mu\)	\(\sigma\)	-
`"weibull"`	\(\mu\)	\(\sigma\)	-
`"weibull3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"normal"`	\(\mu\)	\(\sigma\)	-
`"lognormal"`	\(\mu\)	\(\sigma\)	-
`"lognormal3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"logistic"`	\(\mu\)	\(\sigma\)	-
`"loglogistic"`	\(\mu\)	\(\sigma\)	-
`"loglogistic3"`	\(\mu\)	\(\sigma\)	\(\gamma\)
`"exponential"`	\(\theta\)	-	-
`"exponential2"`	\(\theta\)	\(\gamma\)	-