# dfphase1-package: Phase I Control Charts (with Emphasis on Distribution-Free... In dfphase1: Phase I Control Charts (with Emphasis on Distribution-Free Methods)

 dfphase1-package R Documentation

## Phase I Control Charts (with Emphasis on Distribution-Free Methods)

### Description

Statistical methods for retrospectively detecting changes in location and/or dispersion of univariate and multivariate variables. Data values are assumed to be independent, can be individual (one observation at each instant of time) or subgrouped (more than one observation at each instant of time). Control limits are computed, often using a permutation approach, so that a prescribed false alarm probability is guaranteed without making any parametric assumptions on the stable (in-control) distribution.

### Details

The main functions are:

• `shewhart` and `mshewhart`: univariate and multivariate Shewhart-type control charts based either on the original observations or on a rank transformation. These functions are particularly useful for detecting isolated shifts in the mean and/or variance of subgrouped observations. Functions `shewhart` and `mshewhart` also allow the simultaneously use of two control charts originally designed to detect separately location and scale shifts. In particular, note that when more than one critical values are needed, the false alarm probability is “balanced” between the separate control charts as discussed by Capizzi (2015).

• `changepoint` and `mchangepoint`: univariate or multivariate control charts useful for detecting sustained (and other patterned) mean and/or variance shifts. The control statistic is based on a generalized likelihood ratio test computed under a Gaussian assumption. However, the control limits are computed by permutation. An optional preliminary rank transformation can be used to improve the performance in the case of nonnormal data.

• `rsp` and `mphase1`: the univariate and multivariate methods introduced by Capizzi and Masarotto (2013) and (2017) to detect multiple isolated or step shifts in individual or subgrouped data.

The use of distribution-free control limits is emphasized. However, the package also includes some functions for computing normal-based control limits. As noted in the individual help pages, these limits can also be suitable for some non-normal distributions (e.g., applying a multivariate rank.-transformation, normal-based control limits mantain the desired false alarm probability in the class of the multivariate elliptical distributions). Nevertheless, their use is not generally recommended.

The data should be organized as follows:

• Univariate control charts: an nxm matrix, where n and m are the size of each subgroup and the number of subgroups, respectively. A vector of length m is accepted in the case of individual data, i.e., when n=1.

• Multivariate control charts: a pxnxm array, where p denotes the number of monitored variables. A p x m matrix is accepted in the case of individual data.

Functions `phase1Plot` and `mphase1Plot` can be used for plotting the data.

### Author(s)

Giovanna Capizzi and Guido Masarotto (maintainer: Giovanna Capizzi <giovanna.capizzi@unipd.it>).

### References

G. Capizzi (2015) “Recent advances in process monitoring: Nonparametric and variable-selection methods for Phase I and Phase II (with discussion)”. Quality Engineering, 27, pp. 44–80, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/08982112.2015.968046")}.

G. Capizzi and G. Masarotto (2013), “Phase I Distribution-Free Analysis of Univariate Data”. Journal of Quality Technology, 45, pp. 273–284, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00224065.2013.11917938")}.

G. Capizzi and G. Masarotto (2017), Phase I Distribution-Free Analysis of Multivariate Data, Technometrics, 59, pp. 484–495, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00401706.2016.1272494")}.

G. Capizzi and G. Masarotto (2018), “Phase I Distribution-Free Analysis with the R Package `dfphase1`”. Frontiers in Statistical Quality Control 12, eds. S. Knoth and W. Schmid, pp. 3–19, Springer, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-319-75295-2_1")}

`shewhart`, `shewhart.normal.limits`, `mshewhart`, `mshewhart.normal.limits`, `changepoint`, `changepoint.normal.limits`, `mchangepoint`, `mchangepoint.normal.limits`, `rsp`, `mphase1`, `phase1Plot`, `mphase1Plot`.