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An R package for batch process control and monitoring using

Dual STATIS-Parallel Coordinates approach

Un paquete de R para control y monitoreo de procesos por

lotes utilizando el enfoque Statis Dual-Coordenadas Paralelas

Ing. José Ascencio-Moreno

josdasce@espol.edu.ec

https://orcid.org/0000-0002-6883-7195

Blga. Miriam Vanessa Hinojosa-Ramos

mvhinojo@espol.edu.ec

https://orcid.org/0000-0002-4100-5284

PhD. Francisco Vera Alcívar

fvera@espol.edu.ec

https://orcid.org/0000-0001-6541-7243

PhD. Omar Ruiz-Barzola

oruiz@espol.edu.ec

https://orcid.org/0000-0001-8206-1744

PhD. María Purificación Galindo-Villardón

pgalindo@usal.es

https://orcid.org/0000-0001-6977-7545

MPC. Miriam Ramos-Barberán

mvramosb@espol.edu.ec

https://orcid.org/0000-0002-8915-6938

Recibido: 1/9/2020, Aceptado: 1/11/2020

RESUMEN

El control estadístico multivariante de procesos para la producción por lotes

generalmente toma en consideración características correlacionadas para la

inspección del desempeño del proceso. En la literatura, los investigadores han

utilizado varias técnicas estadísticas de forma individual para abordar esta

inspección durante las fases de control y seguimiento. Nuevas estrategias han

explorado la posibilidad de combinar dos técnicas con el fin de optimizar el control

y el monitoreo del proceso por lotes, como el enfoque DS-PC. Este enfoque

novedoso se refiere al uso de Statis Dual y Coordenadas Paralelas e implica una

serie de varios pasos de protocolos y aplicaciones de fórmulas que son propensas

a errores y consumen mucho tiempo. Utilizando la metodología que se encuentra

en la literatura, el paquete DSPC para R

se desarrolló con el objetivo de ofrecer una herramienta simple para realizar el

cómputo de Statis Dual rápidamente para las fases de control y seguimiento. Las

Escuela Superior Politécnica del Litoral, Ecuador

Universidad de Salamanca, España

Escuela Superior Politécnica del Litoral, Ecuador

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Ascencio, Hinojosa, Vera, Ruiz. An R package for batch process control

and monitory using dual statis-parallel coordinates approach.

salidas del paquete ofrecen visualizaciones gráficas para detectar

comportamientos inusuales durante la producción a través de gráficos de control

IS (Interestructura) y CO (Intraestructura). La salida también incluye el gráfico de

coordenadas paralelas. Este paquete será útil para los profesionales interesados

en la aplicación del enfoque DS-PC a cualquier industria de proceso por lotes a

través de la automatización sugerida por defecto o la opción personalizada. Para

familiarizar a los usuarios con esta estrategia, el paquete proporciona un conjunto

de datos simulado de fabricación de bolsas de plástico industriales.

Palabras clave: producción por lotes, control, monitoreo, DS-PC, paquete

ABSTRACT

Multivariate statistical process control for batch production usually takes into

consideration correlated characteristics for inspection of process performance. In

literature, researchers have used several statistical techniques individually to

address this inspection during the pilot and the monitoring phases. New strategies

have explored the possibility of combining two techniques in order to optimize

batch process control and monitoring, such as, DS-PC approach. This novel

approach stands for Dual STATIS and Parallel Coordinates and involves a multi-

step series of protocols and formula applications that are error-prone and time

consuming. Using the methodology found in the literature, DSPC package for R

was developed to deliver a simple tool to quickly compute Dual STATIS for pilot

and monitoring phases. Outputs of the package offer graphic displays to detect

unusual behavior during the production through IS (Interstructure) and CO

(Intrastructure) control charts. Output also includes Parallel Coordinates plot. This

package will be useful to practitioners interested in DS-PC approach application to

any batch process industry through suggested automatization by default or the

personalized option. To familiarize users with this strategy, the package provides a

simulated dataset of industrial plastic bags fabrication.

Keywords: batch production, control, monitoring, DS-PC, package

Introduction

Nowadays, several industries rely on batch processing to yield final products. High-

quality products are commonly described by quality characteristics (variables),

each of which must be controlled within specifications to keep customer satisfaction

and to describe the process performance as the batch progresses (Lewis, 2014).

In this sense, statistical techniques are mandatory in control and monitoring of

industrial processes, involving surveillance of correlated quality-process

characteristics through control charts and other graphical methods (Bersimis et

al., 2007).

First contributions to batch control and monitoring were mostly grounded on

Multiway Partial Least Squares (MPLS) and Multiway Principal Component Analysis

(MPCA) (Kourti et al., 1995; Nomikos & MacGregor, 1994, 1995). From that

moment on, several strategies and methods have been developed in order to meet

statistical assumptions, typical in batch production models (Lewis, 2014).

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Alternative ways included Structuration des tableaux à trois indices de la

Statistique (STATIS), Parallel Factors Analysis (PARAFAC), Tucker3, Multiset

Canonical Correlation Analysis (MCCA), Multiway Independent Component Analysis

(MICA), Multiway Slow Features Analysis (MSFA), and Parallel Coordinates (Dunia

et al., 2012; Escoufier, 1987; Filho & Luna, 2015; Harshman, 1970; Hyvärinen &

Oja, 2000; Inselberg & Dimsdale, 1990; Jiang et al., 2018; Louwerse & Smilde,

2000; Meng et al., 2003; Parra, 2018; Tucker, 1966; Wang et al., 2017; Wiskott

& Sejnowski, 2002; Zhang et al., 2017).

Some recent strategies even contemplate combining more than one technique to

optimize multivariate batch process control under certain conditions, for instance,

DS-PC approach (Dual STATIS-Parallel Coordinates). This nonparametric quality

control strategy based on control charts enables off-line monitoring of batch

processes using Dual STATIS and bagplots for control regions. A complementary

analysis is developed with parallel coordinate plotting to examine tendencies within

out-of-control batches. In this sense, this combined strategy brings on a variable-

wise analysis, leading to support the visual interpretation of out-of-control signals

(Ramos-Barberán et al., 2018).

Although the DS-PC strategy demand data preprocessing along with several

calculations that are not particularly complex, its multi-step approach in which data

set has been collected and cross-referenced in a series of steps that are fairly easy

to mishandle, susceptible to mistakes and tough to replicate.

To facilitate DS-PC strategy application to any practical case, a package for the R

environment (DSPC) was developed to automate the process and

programmatically provide multivariate control charts and descriptive graphics for

batch control and monitoring, without the uncertainty for miscalculation, and with

the convenience and speed that computation provides. Then, industries will be able

to determine if quality specifications are met, resulting in cost and time savings.

Methodology

The package DSPC was written for R, an open source software and programmatic

environment for statistics and graphics. The program runs on the most popular

computer platforms including Windows, MacOS, and UNIX. Since its inception, R

has been used by programmers, scientists, practitioners, and code developers to

create packages that guarantee reproducible code and results (Wickham, 2015).

These packages run customized statistical functions, generate map and graphics,

and allow researchers to import and export from large data sets in the public

domain, among other uses. To date, many thousands of these packages have been

developed in virtually all scientific fields and disciplines (Smith, 2017).

This package was elaborated as a generalization from the DS-PC strategy published

by Ramos-Barberán et al. (2018). Development of the DSPC package followed

coding and compilation guidelines outlined by Kim et al. (2018) and Leisch (2009).

Functions and metadata files for DSPC were created and deposited on Git Hub,

after a substantial testing period that started from 2018. Students at ESPOL

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Ascencio, Hinojosa, Vera, Ruiz. An R package for batch process control

and monitory using dual statis-parallel coordinates approach.

University were required the use of the package as part of an undergraduate class,

and their experiences were used to troubleshoot and debug code.

Results

In this section, the main functions and outputs of the R package DSPC are

presented. The functions of this package allow to perform the DS-PC strategy both

in a step-by-step fashion and automatically. Table 1 shows a brief description for

every function.

Table 1: Functions available in DSPC package

Function Description

TabFactor

Create a Factor from a vector

SeqFactor

Create sequences over a Factor

TableObject

Create a Tables Object ready for Dual STATIS analysis

PreprocessTobj

Suggested preprocessing of the Table Object

DualSTATIS

Dual STATIS analysis for reference data

DualSTATISproje

ction

Dual STATIS projection of new tables

GenBagplots

Bagplots computing for projected tables. The

compute.bagplot function contained in the aplpack

package is used.

Parcoord2

Parallel Coordinates Plot. A modification of parcoord

function from MASS package

AutoProcessing

Automatic processing of data using Dual STATIS

AutoPlotting

Automatic plotting of Dual STATIS results and parallel

coordinates

Source: Self Made

Once the package is downloaded from the GitHub repository and ready to use in

the R environment, it is possible to call these functions to perform analysis of

batch processes with the DS-PC approach (Ramos-Barberán, 2020).

Data organization

Original data may be organized in separated multivariate tables with the same

variables. Reference and additional batches data must be stacked separately, as

shown in Figure 1.

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Figure 1: Data organization. Data from batches are organized in multiple tables for

reference and additional testing, then, stacked into two matrices to load them properly to

Source: Self Made

As commented before, two main procedures can be considered: the suggested

automatization and the personalized option. Despite the option preferred, loading

the data tables into the R environment is required.

Suggested use

When a researcher is not familiar with the use of R, it may be overwhelming the

amount of computational knowledge needed for the application of any robust

method to the data available. If that is the case, this package considers a

suggested option which is nearly automatic. To do so, follow these four steps:

1. Prepare. The reference data table must be contained in a csv file with a Factor-

ObservationNames-variables structure, as appears in Figure 2.

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Ascencio, Hinojosa, Vera, Ruiz. An R package for batch process control

and monitory using dual statis-parallel coordinates approach.

Figure 2: Data structure for DSPC package. The structure is organized by a factor to split

the tables stacked, unique names for every observation, and data from every variable.

Source: Self Made

An additional data table, if required for monitoring scheme, must have the same

Factor-ObsNames-variables structure.

2. Load. The reference table must be loaded into the R environment, then, the factor

and names of observations should be extracted from this table. This loading step

also must be done for the Additional table, if needed.

Supposing that Reftable.csv and AddTable.csv are prepared files with the structure

shown in step 1 and placed in the current working directory, they can be loaded as

tables and factors using the following script.

Reference = read.table(file = "Reftable.csv", header = TRUE, sep = ",")

Additional = read.table(file = "Addtable.csv", header = TRUE, sep = ",")

RefFactor = factor(Reference[,1])

RefTable = as.data.frame(Reference[,c(-1,-2)])

rownames(RefTable) = Reference[,2]

AddFactor = factor(Additional[,1])

AddTable = as.data.frame(Additional[,c(-1,-2)])

rownames(AddTable) = Additional[,2]

The separator character used in the function read.table may change. If the loaded

table has not the correct format, it can be necessary to used “;” instead of “,”.

3. Compute. Performing of Dual STATIS analysis is achieved using the

AutoProcessing function in the pilot phase (just reference) or the monitoring phase

(additional batches are considered).

#Pilot phase

res_Ref = AutoProcessing( RefTable, RefFactor )

#Monitoring phase

res_Ref = AutoProcessing( RefTable, RefFactor, AddTable, AddFactor)

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4. Plot. The Interstructure, Intrastructure and Parallel Coordinates plots must be

drawn using the AutoPlotting function and the Dual STATIS results derived from the

step 3.

#Analysis mode

AutoPlotting( REF = res_Ref$REF, BPS = res_Ref$BPS )

#Monitoring mode

AutoPlotting( REF = res_RefAdd$REF,

ADD = res_RefAdd$ADD,

BPS = res_Ref$BPS )

Personalized use

When the data is organized as a Reftable and Addtable, both can be loaded to the R

environment, and then use the available functions of the package to compute the

elements according to the following:

1. If RefFactor is not already loaded, it should be created from Reftable using the

TabFactor function.

2. Optionally, if not available, names can be easily assigned to every observation in

Reftable using the SeqFactor function on RefFactor.

3. Creating of a table object (Tobj) using the TableObject function with the items

Reftable and RefFactor.

4. The preprocessing of matrices contained in Tobj$Xk_data is suggested via scaling,

centering and normalizing. The PreprocessTobj function allows to perform

preprocessing on Tobj easily.

5. Performing of Dual STATIS on Tobj via DualSTATIS function to generate a Dual

STATIS results (Dsr). At this point, the Dsr list contains enough information to

perform Interstructure and Intrastructure analysis. Additionaly, the parcoord2

function allows to visualize all variables using the Tobj$Original_data matrix.

6. Steps 1 to 4 are repeated to obtain a table object (AddTobj) from Addtable. Then,

use the DualSTATISprojection function on this AddTobj, taking Tobj into account, to

obtain a Dual STATIS results list (AddDsr).

7. GenBagplots function is used to create the control regions involved in the

monitoring of additional batches. This completes the required elements for plotting

of batches projections, complementing with parcoord2 function.

A summarization of this scheme is presented in Figure 3.

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Ascencio, Hinojosa, Vera, Ruiz. An R package for batch process control

and monitory using dual statis-parallel coordinates approach.

Figure 3: Personalized use of DSPC package. The flow chart shows the computation

process for applying the DS-PC approach using the functions contained in the DSPC package.

Source: Self Made

Available data

A simulated dataset of industrial plastic bags fabrication is available in this package.

Every batch is represented by a table constituted by 50 observations of 3 process

variables. A factor is associated to each data table. This dataset is coded as

PlasticBags, a list containing 200 reference batches stacked in PlasticBags$Ref$data

and 8 additional testing batches stacked in PlasticBags$Add$data. The testing batches

are conformed by a normal batch and seven anomalous batches, affected by shifts in

mean, standard deviation, and correlation shifts (Ramos-Barberán et al., 2018).

Outputs

Considering the plastic bag data, it is possible to easily generate all the plots

associated, using the following script:

data( PlasticBags )

REFtab = PlasticBags$Ref$data[1:1500,]

ADDtab = PlasticBags$Add$data

REFfac = PlasticBags$Ref$factor[1:1500]

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ADDfac = PlasticBags$Add$factor

DSPCres = AutoProcessing(REFtab, REFfac, ADDtab, ADDfac)

AutoPlotting( DSPCres$REF, DSPCres$ADD, DSPCres$BPS )

Once the code has run, a set of plots is presented as result. These plots are collected

in Figures 4 and 5. On the other hand, if the personalized option is chosen, the

characteristics of the graphs can be modified, as it can be seen in Ramos-Barberán et

al. (2018), section 3.1 Illustrative example.

Figure 4. Control Charts created using the DSPC package. Graphs show the

Interstructure (Left top) and Intrastructure Control Charts created using data and functions

contained in the DSPC package.

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Ascencio, Hinojosa, Vera, Ruiz. An R package for batch process control

and monitory using dual statis-parallel coordinates approach.

Figure 5. Parallel Coordinates plots created using the DSPC package. Graphs show

Parallel Coordinates of reference data (black) and testing batches (blue), each of them,

created using data and functions contained in the DSPC package.

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Discussion

With the release of DSPC package, the authors hope that researchers will not only

benefit from its practicality, but also, that they will explore a tool that conceptualizes

Dual STATIS and Parallel Coordinates strategies under the scope of multivariate

statistical process control and monitoring. Since these strategies have individual

packages already uploaded to R repository in other fields applications (ade4,

MExPosition, MASS), the implementation of this package would address a better

comprehension of its combined potential for batch production application (Chessel et

al., 2004; Chin Fatt et al., 2013; Dray et al., 2007; Venables & Ripley, 2002). It can

also aid in the adoption of uniform historical records that can be used for monitoring

across batches, variables, and time.

One of the conveniences of open-source software is that the original code is freely and

easily available, and may be modified as needed. Future work on this package could

incorporate control charts to handle batches with missing values, which are common

in practice, as well as, other data preprocessing options. While these can be easily

incorporated into this package, we believe it is best to show practical applications in

multivariate statistical process control before it should be coded. In this sense, it is

our hope that future versions of this package can be upgraded with feedback from

researchers around the world.

Conclusions

To sum up, DSPC package is an easy time-saving graphical framework for scientists

and practitioners to control and monitor any batch process data through DS-PC

approach. It implements Dual STATIS computation for pilot and monitoring phases

and offers graphic displays to detect unusual behavior during the production through

IS (Interstructure) and CO (Intrastructure) control charts besides Parallel Coordinates

outputs.

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