norm_HD

norm_HD is used to derive the narrowest interval of a predetermined coverage from a Normal distribution, containing the Highest Density (HD) values.

The R-package bayespm implements Bayesian Statistical Process Control and Monitoring (SPC/M) methodology. These methods utilize available prior information and/or historical data, providing efficient online quality monitoring of a process, in terms of identifying moderate/large transient shifts (i.e., outliers) or persistent shifts of medium/small size in the process. These self-starting, sequentially updated tools can also run under complete absence of any prior information. The Predictive Control Charts (PCC) are introduced for the quality monitoring of data from any discrete or continuous distribution that is a member of the regular exponential family. The Predictive Ratio CUSUMs (PRC) are introduced for the Binomial, Poisson and Normal data (a later version of the library will cover all the remaining distributions from the regular exponential family). The PCC targets transient process shifts of typically large size (a.k.a. outliers), while PRC is focused in detecting persistent (structural) shifts that might be of medium or even small size. Apart from monitoring, both PCC and PRC provide the sequentially updated posterior inference for the monitored parameter. Bourazas K., Kiagias D. and Tsiamyrtzis P. (2022) "Predictive Control Charts (PCC): A Bayesian approach in online monitoring of short runs" <doi:10.1080/00224065.2021.1916413>, Bourazas K., Sobas F. and Tsiamyrtzis, P. 2023. "Predictive ratio CUSUM (PRC): A Bayesian approach in online change point detection of short runs" <doi:10.1080/00224065.2022.2161434>, Bourazas K., Sobas F. and Tsiamyrtzis, P. 2023. "Design and properties of the predictive ratio cusum (PRC) control charts" <doi:10.1080/00224065.2022.2161435>.

Dimitrios Kiagias

bayespm

Bayesian Statistical Process Monitoring

Konstantinos Bourazas

Panagiotis Tsiamyrtzis

norm_HD function

<dl> <dt>cover</dt>
<dd>scalar (between 0 and 1); The coverage (probability) of the Highest Density (HD).</dd> <dt>mu</dt>
<dd>scalar (real); It is the mean of the Normal distribution and needs to be a number.</dd> <dt>sdv</dt>
<dd>scalar (positive); It is the standand deviation of the Normal distribution and needs to be a number.</dd> <dt>plot</dt>
<dd>logical; if TRUE, the plot of the HD region is displayed. It is FALSE by default.</dd> <dt>xlab, ylab</dt>
<dd>The titles of the x-axis and y-axis for the HD plot. The default values are "x" and "Density".</dd></dl>

Arguments

The Highest Density (HD) interval of Normal distribution. — norm_HD

<dl>

 <dt>cover</dt>
<dd>scalar (between 0 and 1); The coverage (probability) of the Highest Density (HD).</dd>

 <dt>mu</dt>
<dd>scalar (real); It is the mean of the Normal distribution and needs to be a number.</dd>

 <dt>sdv</dt>
<dd>scalar (positive); It is the standand deviation of the Normal distribution and needs to be a number.</dd>

 <dt>plot</dt>
<dd>logical; if TRUE, the plot of the HD region is displayed. It is FALSE by default.</dd>

 <dt>xlab, ylab</dt>
<dd>The titles of the x-axis and y-axis for the HD plot. The default values are "x" and "Density".</dd>

</dl>

norm_HD: The Highest Density (HD) interval of Normal distribution.

Description

Usage

Value

Arguments

Details

Examples