Type: Package
Title: Sequential Normal Scores in Statistical Process Management
Version: 1.4.0
Author: Victor Tercero [aut], Luis Benavides [aut, cre], Jorge Merlo [ctb]
Maintainer: Luis Benavides <luisbv@tec.mx>
Description: The methods discussed in this package are new non-parametric methods based on sequential normal scores 'SNS' (Conover et al (2017) <doi:10.1080/07474946.2017.1360091>), designed for sequences of observations, usually time series data, which may occur singly or in batches, and may be univariate or multivariate. These methods are designed to detect changes in the process, which may occur as changes in location (mean or median), changes in scale (standard deviation, or variance), or other changes of interest in the distribution of the observations, over the time observed. They usually apply to large data sets, so computations need to be simple enough to be done in a reasonable time on a computer, and easily updated as each new observation (or batch of observations) becomes available. Some examples and more detail in 'SNS' is presented in the work by Conover et al (2019) <doi:10.48550/arXiv.1901.04443>.
Depends: R (≥ 2.10)
License: MIT + file LICENSE
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.1
Imports: parallel, stats, MASS
Suggests: testthat, knitr, rmarkdown
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2021-04-05 18:22:03 UTC; L03099908
Repository: CRAN
Date/Publication: 2021-04-07 08:40:15 UTC

Multivariate Normal Scores

Description

Get conditional or unconditional multivariate normal score (NS) of observations (X) relative to previous observations (Y).

Usage

MNS(
  X,
  Y = NULL,
  theta = NULL,
  Ftheta = NULL,
  scoring = "Z",
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE
)

Arguments

X

matrix or data.frame. New observations to obtain the normal scores.

Y

matrix or data.frame. If Y is not defined (no previous observation available, NULL), NS is relative to X. Default NULL.

theta

vector. Value corresponding with the Ftheta quantile.

Ftheta

vector. Quantile of the data distribution. The values that take are between (0,1).

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

Value

Multiple output. Select by output$

Examples

Y <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
Y = matrix(Y, ncol=2)
X <- c(30, 35, 45, 30, 35, 45)
X = matrix(X, ncol=2)
theta <- c(40, 40)
Ftheta <- c(0.5, 0.5)
# EXAMPLE CONDITIONAL
MNS(X = X, Y = Y, theta = theta, Ftheta = Ftheta)

Multivariate Sequential Normal Scores

Description

Transform a matrix X into SNS using initial observations Y if available SNS follow the order of X.

Usage

MSNS(
  X,
  X.id,
  Y = NULL,
  theta = NULL,
  Ftheta = NULL,
  scoring = "Z",
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  chart = "T2",
  chart.par = c(0.005),
  null.dist = "Chi",
  isFixed = FALSE,
  omit.id = NULL,
  auto.omit.alarm = TRUE
)

Arguments

X

matrix or data.frame. New observations to obtain the normal scores.

X.id

vector. The id of each column (variable) of the matrix X.

Y

matrix or data.frame. If Y is not defined (no previous observation available, NULL), NS is relative to X. Default NULL.

theta

vector. Value corresponding with the Ftheta quantile.

Ftheta

vector. Quantile of the data distribution. The values that take are between (0,1).

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

chart

character string. Selected type of chart. One option available: "T2".

T2 scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

chart.par

vector. Control limit and other parameters of the selected chart.

null.dist

character string. It is the null distribution choose from "Chi" or "F".

isFixed

logical. If TRUE the reference sample does not update, otherwise the reference sample is updated when the batch is in control.

omit.id

vector. Elements of the vector are the id which are omitted in the analysis.

auto.omit.alarm

logical. Determine if OC signals are added (or not) to reference sample. By default is set to TRUE.

Value

Multiple output. Select by output$

Comments

If ties, average ranks are used.

See Also

MNS for multivariate normal scores

Examples

X = cbind(example91$X1, example91$X2)
X.id = example91$X.id
msns = MSNS(X, X.id)

Normal Scores

Description

Get conditional or unconditional normal score (NS) of observations (X) relative to previous observations (Y).

Usage

NS(
  X,
  Y = NULL,
  theta = NULL,
  Ftheta = NULL,
  scoring = "Z",
  Chi2corrector = "None",
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE
)

Arguments

X

vector. New observations to obtain the N¡normal scores.

Y

vector. If Y is not defined (no previous observation available, NULL), NS is relative to X. Default NULL.

theta

scalar. Value corresponig with the Ftheta quantile.

Ftheta

scalar. Quantile of the data distribution. The values that take are between (0,1).

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

Chi2corrector

character string. Only when scoring is Z-SQ. Select from

  • "approx: Z^2*(m + 1 + 1.3)/(m+1).

  • "exact": Z^2/mean(Z).

  • "none": Z^2.

If "approx" () (default). If "exact" (normal scores squared).

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

Value

Multiple output. Select by output$

Examples

Y <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
X <- c(30, 35, 45)
theta <- 40
Ftheta <- 0.5
# EXAMPLE CONDITIONAL
NS(X = X, Y = Y, theta = theta, Ftheta = Ftheta)

# EXAMPLE UNCONDITIONAL
theta <- NULL
Ftheta <- NULL
NS(X = X, Y = Y, theta = theta, Ftheta = Ftheta)

Sequential Normal Scores

Description

Transform a vector X into SNS using initial observations Y if available SNS follow the order of X.

Usage

SNS(
  X,
  X.id,
  Y = NULL,
  theta = NULL,
  Ftheta = NULL,
  scoring = "Z",
  Chi2corrector = "None",
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  chart = "Shewhart",
  chart.par = c(3),
  snsRaw = FALSE,
  isFixed = FALSE,
  omit.id = NULL,
  auto.omit.alarm = TRUE
)

Arguments

X

vector. New observations to obtain the N¡normal scores.

X.id

vector. The id of the vector X.

Y

vector. If Y is not defined (no previous observation available, NULL), NS is relative to X. Default NULL.

theta

scalar. Value corresponig with the Ftheta quantile.

Ftheta

scalar. Quantile of the data distribution. The values that take are between (0,1).

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

Chi2corrector

character string. Only when scoring is Z-SQ. Select from

  • "approx: Z^2*(m + 1 + 1.3)/(m+1).

  • "exact": Z^2/mean(Z).

  • "none": Z^2.

If "approx" () (default). If "exact" (normal scores squared).

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

chart

character string. Selected type of chart. Three options are available: Shewhart, CUSUM, EWMA

chart.par

vector. The size depends on the selected chart:

Shewhart scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

CUSUM scheme:

is c(k, h, t) where k is the reference value and h is the control limit, and t is the type of the chart (1:positive, 2:negative, 3:two sides)

EWMA scheme:

is c(lambda, L), where lambda is the smoothing constant and L multiplies standard deviation to get the control limit

snsRaw

logical. If TRUE return also the sns for each observation in vector X.

isFixed

logical. If TRUE the reference sample does not update, otherwise the reference sample is updated whenever the batch is in control.

omit.id

vector. Elements of the vector are the id which are omitted in the analysis.

auto.omit.alarm

logical. Determine if OC signals are added (or not) to reference sample. By default is set to TRUE.

Value

Multiple output. Select by output$

Comments

If ties occur, average ranks are used.

See Also

NS for normal scores

Examples

# EXAMPLE CONDITIONAL WITH REFERENCE SAMPLE
Y <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
X <- c(30, 35, 45)
theta <- 40
Ftheta <- 0.5
sample.id <- c("a", "b", "c")
SNS(X = X, X.id = sample.id, Y = Y, theta = theta, Ftheta = Ftheta)

# EXAMPLE CONDITIONAL WITH REFERENCE SAMPLE
Y <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
X <- c(30, 35, 45)
theta <- 40
Ftheta <- 0.5
sample.id <- c("a", "b", "c")
SNS(X = X, X.id = sample.id, Y = Y, theta = theta, Ftheta = Ftheta)

# EXAMPLE UNCONDITIONAL WITH REFERENCE SAMPLE
Y <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
X <- c(30, 35, 45)
theta <- NULL
Ftheta <- NULL
sample.id <- c("a", "b", "c")
SNS(X = X, X.id = sample.id, Y = Y, theta = theta, Ftheta = Ftheta)

# EXAMPLE CONDITIONAL WITHOUT REFERENCE SAMPLE
Y <- NULL # c(10,20,30,40,50,60,70,80,90,100)
X <- c(30, 35, 45)
theta <- 40
Ftheta <- 0.5
sample.id <- c("a", "b", "c")
SNS(X = X, X.id = sample.id, Y = Y, theta = theta, Ftheta = Ftheta)

# EXAMPLE UNCONDITIONAL WITHOUT REFERENCE SAMPLE
Y <- NULL
X <- c(30, 35, 45)
theta <- NULL
Ftheta <- NULL
sample.id <- c("a", "b", "c")
SNS(X = X, X.id = sample.id, Y = Y, theta = theta, Ftheta = Ftheta)

Calibration of the control limit for the selected chart

Description

The methodology used to calibrate the control limit for the SNS chart depending on the selected chart

Usage

calibrateControlLimit(
  targetARL = NULL,
  targetMRL = NULL,
  n,
  m,
  theta = NULL,
  Ftheta = NULL,
  scoring = "Z",
  Chi2corrector = "None",
  dist,
  mu,
  sigma,
  dist.par = c(0, 1, 1),
  chart,
  chart.par,
  replicates = 50000,
  isParallel = TRUE,
  maxIter = 20,
  progress = TRUE,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  isFixed = FALSE,
  rounding.factor = NULL
)

Arguments

targetARL

scalar. is the target ARL to calibrate. By default is set to NULL

targetMRL

scalar. is the target ARL to calibrate. By default is set to NULL

n

scalar. Subroup size

m

scalar. Reference sample size

theta

scalar. Value corresponig with the Ftheta quantile.

Ftheta

scalar. Quantile of the data distribution. The values that take are between (0,1).

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

Chi2corrector

character string. Only when scoring is Z-SQ. Select from

  • "approx: Z^2*(m + 1 + 1.3)/(m+1).

  • "exact": Z^2/mean(Z).

  • "none": Z^2.

If "approx" () (default). If "exact" (normal scores squared).

dist

character string. Select from:

  • "Uniform: Continuous Uniform distribution .

  • "Normal": Normal distribution (default).

  • "Normal2": Squared Normal distribution (also known as Chi-squared).

  • "DoubleExp": Double exponential distribution (also known as Laplace distribution).

  • "DoubleExp2": Double exponential squared distribution from a DoubleExp(0,1).

  • "LogNormal": Lognormal distribution.

  • "Gamma": Gamma distribution.

  • "Weibull": Weibull distribution.

  • "t": Student-t distribution.

mu

vector. Two elements, the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.

sigma

vector. Two elements, the first one is the sd of the reference sample and the second one is the sd of the monitoring sample.

dist.par

vector. Distribution parameters. c(par.a, par.b). Default c(0,1).

chart

character string. Selected type of chart. Three options are available: Shewhart, CUSUM, EWMA

chart.par

vector. The size depends on the selected chart:

Shewhart scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

CUSUM scheme:

is c(k, h, t) where k is the reference value and h is the control limit, and t is the type of the chart (1:positive, 2:negative, 3:two sides)

EWMA scheme:

is c(lambda, L), where lambda is the smoothing constant and L multiplies standard deviation to get the control limit

replicates

scalar. Number of replicates to get the ARL

isParallel

logical. If TRUE the code runs in parallel according to the number of cores in the computer,otherwise the code runs sequentially. Default TRUE.

maxIter

scalar. is a numeric. The maximum number of iteration to take the calibration before stops

progress

logical. If TRUE it shows the progress in the console.

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

isFixed

logical. If TRUE the reference sample does not update, otherwise the reference sample is updated whenever the batch is in control.

rounding.factor

scalar. positive value that determine the range between two consecutive rounded values.

Value

Multiple output. Select by output$

Note

The argument chart.par in this function correspond to the initial parameters to start the calibration.

Examples

n <- 2 # subgroup size
m <- 30 # reference-sample size
dist <- "Normal" # distribution
mu <- c(0, 0) # c(reference sample mean, monitoring sample mean)
sigma <- c(1, 1) # c(reference sample sd, monitoring sample sd)

#### Distribution parameters
dist.par <- c(0, 1) # c(location, scale)

#### Other Parameters
replicates <- 2
targetARL <- 370
isParallel = FALSE

#### Control chart parameters
chart <- "Shewhart"
chart.par <- c(3)
shewhart <- calibrateControlLimit(
  targetARL = targetARL, targetMRL = NULL, n = n, m = m, theta = NULL,
  Ftheta = NULL, dist = dist, mu = mu, sigma = sigma, dist.par = dist.par, chart.par = chart.par,
  replicates = replicates, chart = chart, isParallel = isParallel
)

chart <- "CUSUM"
chart.par <- c(0.5, 2.5, 3)
cusum <- calibrateControlLimit(
  targetARL = targetARL, targetMRL = NULL, n = n, m = m, theta = NULL,
  Ftheta = NULL, dist = dist, mu = mu, sigma = sigma, dist.par = dist.par, chart.par = chart.par,
  replicates = replicates, chart = chart, isParallel = isParallel
)

chart <- "EWMA"
chart.par <- c(0.2, 2.962)
ewma <- calibrateControlLimit(
  targetARL = targetARL, targetMRL = NULL, n = n, m = m, theta = NULL,
  Ftheta = NULL, dist = dist, mu = mu, sigma = sigma, dist.par = dist.par, chart.par = chart.par,
  replicates = replicates, chart = chart, isParallel = isParallel
)

Alignment of the data

Description

Align the monitoring sample X and the reference sample Y.

Usage

dataAlignment(
  X,
  Y,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE
)

Arguments

X

vector. Monitoring sample.

Y

vector. Reference sample.

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

Value

Multiple output. Select by output$

Examples

X = c(30, 45, 50)
Y = c(20, 22, 25, 30, 70)
dataAlignment(X,Y)

Data from Example 4.9 Qiu (2014).

Description

A dataset containing the data set used in Example 4.9 of Qiu (2014).

Usage

example49

Format

A data frame with 50 rows and 6 columns:

Y1

Reference sample of the first data set. 10 batches are N(0,1)

X1

Monitoring sample of the first data set. 10 batches are N(1,1).

Y2

Reference sample of the second data set. 10 batches are N(0,1)

X2

Monitoring sample of the second data set. 10 batches are N(0,2^2).

X.id

id of each observation of the batch for the second data set.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example49.dat

Data from Example 6.5 on page 246 Qiu (2014).

Description

A dataset containing the data set used in Example 6.5 on page 246 of Qiu (2014).

Usage

example65

Format

A data frame with 30 rows and 5 columns:

x

first 9 observations are the reference sample. Batch size equals to 1.

Wn

Wn

Sn2

Sn2

Bmax

Bmax

hn

hn

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example65.dat

Data from Example 7.1 Qiu (2014).

Description

A dataset containing the data set used in Example 7.1 of Qiu (2014).

Usage

example71

Format

The data (X1,X2,X3) consist of 30 observations each variable.

X

1st batch.

X.1

2nd batch.

X.2

3rd batch.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example71.dat

Data from Example 7.4(a) Qiu (2014).

Description

A dataset containing the data set used in Example 7.4(a) of Qiu (2014).

Usage

example74a

Format

The data (X1,X2,X3) consist of 30 observations each variable.

X

1st batch.

X.1

2nd batch.

X.2

3rd batch.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example74a.dat

Data from Example 7.4(b) Qiu (2014).

Description

A dataset containing the data set used in Example 7.4(b) of Qiu (2014).

Usage

example74b

Format

The data (X1,X2,X3) consist of 30 observations each variable.

X

1st batch.

X.1

2nd batch.

X.2

3rd batch.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example74b.dat

Data from Example 7.4(c) Qiu (2014).

Description

A dataset containing the data set used in Example 7.4(c) of Qiu (2014).

Usage

example74c

Format

The data (X1,X2,X3) consist of 30 observations each variable.

X

1st batch.

X.1

2nd batch.

X.2

3rd batch.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example74c.dat

Data from Example 8.1 on page 319 Qiu (2014).

Description

A dataset containing the data set used in Example 8.1 on page 319 of Qiu (2014).

Usage

example81

Format

A data frame with 300 rows (30 batches of size equals to 10)

X

observations of all batches

X.id

id of each observation of the batch

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example81.dat

Data from Example 8.2 Qiu (2014).

Description

A dataset containing the data set used in Example 8.2 on page 323 of Qiu (2014).

Usage

example82

Format

A data frame with 150 rows (30 batches of size equals to 5)

X

observations of all batches

X.id

id of each observation of the batch

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example82.dat

Data from Example 8.3 on page 326 Qiu (2014).

Description

A dataset containing the data set used in Example 8.3 on page 326 of Qiu (2014).

Usage

example83

Format

A data frame with 180 rows (30 batches of size equals to 6)

X

observations of all batches

X.id

id of each observation of the batch

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example81.dat

Data from Example 8.4 Qiu (2014).

Description

A dataset containing the data set used in Example 8.4 of Qiu (2014).

Usage

example84

Format

A data frame with 150 rows (30 batches of size equals to 5)

X

observations of all batches

X.id

id of each observation of the batch

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example84.dat

Data from Example 8.5 Qiu (2014).

Description

A dataset containing the data set used in Example 8.5 of Qiu (2014).

Usage

example85

Format

A data frame with 300 rows (30 batches of size equals to 10)

X

observations of all batches

X.id

id of each observation of the batch

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example85.dat

Data from Example 8.7 on page 339 Qiu (2014).

Description

A dataset containing the data set used in Example 8.7 on page 339 of Qiu (2014).

Usage

example87

Format

A data frame with 86 rows (86 batches of size equals to 1)

X

observations of all batches

X.id

id of each observation of the batch

Y

reference sample of size equals to 14

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example87.dat

Data from Example 9.1 on page 369 Qiu (2014).

Description

A dataset containing the data set used in Example 9.1 on page 369 of Qiu (2014).

Usage

example91

Format

The data (X,Y) consist of 20 batches with 50 observations in each batch.

V1

1st batch.

V2

2nd batch.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example91.dat

Data from Example 9.3 Qiu (2014).

Description

A dataset containing the data set used in Example 9.3 of Qiu (2014).

Usage

example93

Format

The data (X,Y) consist of 20 batches with 10 observations in each batch.

X

1st batch.

X.1

2nd batch.

Source

https://users.phhp.ufl.edu/pqiu/research/book/spc/data/example93.dat

Average Run Length (ARL)

Description

Get the ARL getRL

Usage

getARL(
  n,
  m,
  theta = NULL,
  Ftheta = NULL,
  dist,
  mu,
  sigma,
  dist.par = c(0, 1, 1),
  chart,
  chart.par,
  scoring = "Z",
  Chi2corrector = "None",
  replicates = 10000,
  isParallel = TRUE,
  print.RL = FALSE,
  progress = FALSE,
  calibrate = FALSE,
  arl0 = 370,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  isFixed = FALSE,
  rounding.factor = NULL
)

Arguments

n

scalar. Subroup size

m

scalar. Reference sample size

theta

scalar. Value corresponig with the Ftheta quantile.

Ftheta

scalar. Quantile of the data distribution. The values that take are between (0,1).

dist

character string. Select from:

  • "Uniform: Continuous Uniform distribution .

  • "Normal": Normal distribution (default).

  • "Normal2": Squared Normal distribution (also known as Chi-squared).

  • "DoubleExp": Double exponential distribution (also known as Laplace distribution).

  • "DoubleExp2": Double exponential squared distribution from a DoubleExp(0,1).

  • "LogNormal": Lognormal distribution.

  • "Gamma": Gamma distribution.

  • "Weibull": Weibull distribution.

  • "t": Student-t distribution.

mu

vector. Two elements, the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.

sigma

vector. Two elements, the first one is the sd of the reference sample and the second one is the sd of the monitoring sample.

dist.par

vector. Distribution parameters. c(par.a, par.b). Default c(0,1).

chart

character string. Selected type of chart. Three options are available: Shewhart, CUSUM, EWMA

chart.par

vector. The size depends on the selected chart:

Shewhart scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

CUSUM scheme:

is c(k, h, t) where k is the reference value and h is the control limit, and t is the type of the chart (1:positive, 2:negative, 3:two sides)

EWMA scheme:

is c(lambda, L), where lambda is the smoothing constant and L multiplies standard deviation to get the control limit

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

Chi2corrector

character string. Only when scoring is Z-SQ. Select from

  • "approx: Z^2*(m + 1 + 1.3)/(m+1).

  • "exact": Z^2/mean(Z).

  • "none": Z^2.

If "approx" () (default). If "exact" (normal scores squared).

replicates

scalar. Number of replicates to get the ARL

isParallel

logical. If TRUE the code runs in parallel according to the number of cores in the computer,otherwise the code runs sequentially. Default TRUE.

print.RL

logical. If TRUE return the vectors of RL for each iteration.

progress

logical. If TRUE it shows the progress in the console.

calibrate

logical. If TRUE the RL is limit to 10 times the target ARL.

arl0

scalar. Expected value of the RL. Default 370.

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

isFixed

logical. If TRUE the reference sample does not update, otherwise the reference sample is updated whenever the batch is in control.

rounding.factor

scalar. positive value that determine the range between two consecutive rounded values.

Value

Multiple output. Select by output$

Examples

n <- 5 # subgroup size
m <- 100 # reference-sample size
dist <- "Normal"
mu <- c(0, 0) # c(reference sample mean, monitoring sample mean)
sigma <- c(1, 1) # c(reference sample sd, monitoring sample sd)

#### Normal distribution parameters
dist.par <- c(0, 1) # c(location, scale)

#### Other Parameters
replicates <- 2
print.RL <- TRUE
isParallel <- FALSE
calibrate <- FALSE
progress <- TRUE
arl0 <- 370

#### Control chart parameters
chart <- "Shewhart"
chart.par <- c(3)
shewhart <- getARL(n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, print.RL = print.RL,
  replicates = replicates, isParallel = isParallel,
  calibrate = calibrate, arl0 = arl0
)

chart <- "CUSUM"
chart.par <- c(0.25, 4.4181, 3)
cusum <- getARL(n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, print.RL = print.RL,
  replicates = replicates, isParallel = isParallel,
  calibrate = calibrate, arl0 = arl0
)

chart <- "EWMA"
chart.par <- c(0.2, 2.962)
shewhart <- getARL(n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, print.RL = print.RL,
  replicates = replicates, isParallel = isParallel,
  calibrate = calibrate, arl0 = arl0
)

Random Observations Generator

Description

Random observations generator selected from several distributions with user defined mean and variance.

Usage

getDist(
  n,
  dist,
  mu,
  sigma,
  par.location = 0,
  par.scale = 1,
  par.shape = 1,
  dist.par = NULL,
  rounding.factor = NULL
)

Arguments

n

scalar. Number of observations to be generated.

dist

character string. Select from:

  • "Uniform: Continuous Uniform distribution .

  • "Normal": Normal distribution (default).

  • "Normal2": Squared Normal distribution (also known as Chi-squared).

  • "DoubleExp": Double exponential distribution (also known as Laplace distribution).

  • "DoubleExp2": Double exponential squared distribution from a DoubleExp(0,1).

  • "LogNormal": Lognormal distribution.

  • "Gamma": Gamma distribution.

  • "Weibull": Weibull distribution.

  • "t": Student-t distribution.

mu

scalar. Expected value of the desired distribution.

sigma

scalar. Standard deviation of the desired distribution.

par.location

scalar. Location parameter of the desired distribution. Default 0**.

par.scale

scalar. Scale parameter of the desired distribution. Default 1**.

par.shape

scalar. Shape parameter of the desired distribution, Default 1.

dist.par

vector. Overwrite par.location, par.scale, par.shape. Depends on the distribution (default NULL):

  • "Uniform: no matter how is defined always gives numbers between 0 and 1.

  • "Normal": c(location, scale).

  • "Normal2": c(location, scale).

  • "DoubleExp": c(location, scale).

  • "DoubleExp2": c(location, scale).

  • "LogNormal": c(location, scale).

  • "Gamma": c(scale, shape).

  • "Weibull": c(shape, scale).

  • "t": c(degrees of freedom).

rounding.factor

scalar. positive value that determine the range between two consecutive rounded values.

Value

A vector x with n observations generated following the selected distribution with its parameters.

**Note

Examples

getDist(1, "Normal", 0, 1)

Obtain Quantile from Distribution Function

Description

Get the quantile theta from several distributions with user defined mean and variance.

Usage

getQuantile(
  Ftheta,
  mu,
  sigma,
  dist,
  par.location = 0,
  par.scale = 1,
  par.shape = 1,
  dist.par = NULL
)

Arguments

Ftheta

scalar. Quantile of the data distribution. The values that take are between (0,1).

mu

scalar. Expected value of the desired distribution.

sigma

scalar. Standard deviation of the desired distribution.

dist

character string. Select from:

  • "Uniform: Continuous Uniform distribution .

  • "Normal": Normal distribution (default).

  • "Normal2": Squared Normal distribution (also known as Chi-squared).

  • "DoubleExp": Double exponential distribution (also known as Laplace distribution).

  • "DoubleExp2": Double exponential squared distribution from a DoubleExp(0,1).

  • "LogNormal": Lognormal distribution.

  • "Gamma": Gamma distribution.

  • "Weibull": Weibull distribution.

  • "t": Student-t distribution.

par.location

scalar. Location parameter of the desired distribution. Default 0**.

par.scale

scalar. Scale parameter of the desired distribution. Default 1**.

par.shape

scalar. Shape parameter of the desired distribution, Default 1.

dist.par

vector. Overwrite par.location, par.scale, par.shape. Depends on the distribution (default NULL):

  • "Uniform: no matter how is defined always gives numbers between 0 and 1.

  • "Normal": c(location, scale).

  • "Normal2": c(location, scale).

  • "DoubleExp": c(location, scale).

  • "DoubleExp2": c(location, scale).

  • "LogNormal": c(location, scale).

  • "Gamma": c(scale, shape).

  • "Weibull": c(shape, scale).

  • "t": c(degrees of freedom).

Value

A quantile theta of the selected Ftheta distribution with its parameters.

Examples

getQuantile(0.5, 0, 1, "Normal")

Run Length

Description

Get the run length

Usage

getRL(
  replica = 1,
  n,
  m,
  theta = NULL,
  Ftheta = NULL,
  dist,
  mu,
  sigma,
  dist.par = c(0, 1, 1),
  scoring = "Z",
  chart,
  chart.par,
  calibrate = FALSE,
  arl0 = 370,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  isFixed = FALSE,
  Chi2corrector = "None",
  rounding.factor = NULL
)

Arguments

replica

scalar. It is used for the parallel version of the function (parallel=TRUE). Default 1.

n

scalar. Subroup size

m

scalar. Reference sample size

theta

scalar. Value corresponig with the Ftheta quantile.

Ftheta

scalar. Quantile of the data distribution. The values that take are between (0,1).

dist

character string. Select from:

  • "Uniform: Continuous Uniform distribution .

  • "Normal": Normal distribution (default).

  • "Normal2": Squared Normal distribution (also known as Chi-squared).

  • "DoubleExp": Double exponential distribution (also known as Laplace distribution).

  • "DoubleExp2": Double exponential squared distribution from a DoubleExp(0,1).

  • "LogNormal": Lognormal distribution.

  • "Gamma": Gamma distribution.

  • "Weibull": Weibull distribution.

  • "t": Student-t distribution.

mu

vector. Two elements, the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.

sigma

vector. Two elements, the first one is the sd of the reference sample and the second one is the sd of the monitoring sample.

dist.par

vector. Distribution parameters. c(par.a, par.b). Default c(0,1).

scoring

character string. If "Z" (normal scores) (default). If "Z-SQ" (normal scores squared).

chart

character string. Selected type of chart. Three options are available: Shewhart, CUSUM, EWMA

chart.par

vector. The size depends on the selected chart:

Shewhart scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

CUSUM scheme:

is c(k, h, t) where k is the reference value and h is the control limit, and t is the type of the chart (1:positive, 2:negative, 3:two sides)

EWMA scheme:

is c(lambda, L), where lambda is the smoothing constant and L multiplies standard deviation to get the control limit

calibrate

logical. If TRUE the RL is limit to 10 times the target ARL.

arl0

scalar. Expected value of the RL. Default 370.

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

isFixed

logical. If TRUE the reference sample does not update, otherwise the reference sample is updated whenever the batch is in control.

Chi2corrector

character string. Only when scoring is Z-SQ. Select from

  • "approx: Z^2*(m + 1 + 1.3)/(m+1).

  • "exact": Z^2/mean(Z).

  • "none": Z^2.

If "approx" () (default). If "exact" (normal scores squared).

rounding.factor

scalar. positive value that determine the range between two consecutive rounded values.

Value

RL vector. The run length of the chart for the parameter setting.

Examples

n <- 5 # subgroup size
m <- 100 # reference-sample size
dist <- "Normal"
mu <- c(0, 0) # c(reference sample mean, monitoring sample mean)
sigma <- c(1, 1) # c(reference sample sd, monitoring sample sd)

#### Distribution parameters
dist.par <- c(0, 1, 1) # c(location, scale, shape)

#### Other Parameters
replicates <- 2
print.RL <- TRUE
calibrate <- FALSE
progress <- TRUE
arl0 <- 370

#### Control chart parameters
chart <- "Shewhart"
chart.par <- c(3)
shewhart <- getRL(1, n, m,
  theta = NULL, Ftheta = NULL,dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, calibrate = calibrate, arl0 = arl0
)

chart <- "CUSUM"
chart.par <- c(0.25, 4.4181, 3)
cusum <- getRL(1, n, m,
  theta = NULL, Ftheta = NULL, dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, calibrate = calibrate, arl0 = arl0
)

chart <- "EWMA"
chart.par <- c(0.2, 2.962)
shewhart <- getRL(1, n, m,
  theta = NULL, Ftheta = NULL,dist, mu, sigma, dist.par = dist.par,
  chart = chart, chart.par = chart.par, calibrate = calibrate, arl0 = arl0
)

Calibration of the control limit for the selected chart

Description

The methodology used to calibrate the control limit for the SNS chart depending on the selected chart

Usage

mcalibrateControlLimit(
  targetARL = NULL,
  targetMRL = NULL,
  n,
  m,
  nv,
  theta = NULL,
  Ftheta = NULL,
  dists = c("Normal", "Normal"),
  mu = c(0, 0),
  sigma = NULL,
  dists.par = matrix(c(0, 1, 1, 0, 1, 1), ncol = 2),
  correlation = 0,
  chart = "T2",
  chart.par = c(10),
  replicates = 50000,
  isParallel = FALSE,
  maxIter = 20,
  progress = TRUE,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE
)

Arguments

targetARL

scalar. is the target ARL to calibrate. By default is set to NULL

targetMRL

scalar. is the target ARL to calibrate. By default is set to NULL

n

scalar. Subroup size

m

scalar. Reference sample size

nv

scalar. Number of variables to be generated.

theta

vector. Value corresponding with the Ftheta quantile.

Ftheta

vector. Quantile of the data distribution. The values that take are between (0,1).

dists

list. Select the

mu

vector. Two elements of the vector the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.

sigma

scalar. Standard deviation of the desired distribution.

dists.par

matrix For each variable (column), specify

  • par.location: Location parameter of the desired distribution. Default 0.

  • par.scale: Scale parameter of the desired distribution. Default 1.

  • par.shape: Shape parameter of the desired distribution, Default 1.

The number of columns must be the same as the number of variables.

correlation

scalar. Corralation between variables.

chart

character string. Selected type of chart. One option available: "T2".

T2 scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

chart.par

vector. Control limit and other parameters of the selected chart.

replicates

scalar. Number of replicates to get the ARL

isParallel

logical. If TRUE the code runs in parallel according to the number of cores in the computer,otherwise the code runs sequentially. Default TRUE.

maxIter

scalar. is a numeric. The maximum number of iteration to take the calibration before stops

progress

logical. If TRUE it shows the progress in the console.

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

Value

Multiple output. Select by output$

Note

The argument chart.par in this function correspond to the initial parameters to start the calibration.

Examples

n <- 5 # subgroup size
m <- 10 # reference-sample size
dists <- c("Normal", "Normal") # distribution
mu <- c(0, 0) # c(reference sample mean, monitoring sample mean)
nv <- 2 # number of variables
#### Other Parameters
replicates <- 2
targetARL <- 200
isParallel = FALSE
maxIter <- 2
#### Control chart parameters
chart <- "T2"
chart.par <- c(0.005)
t2 <- mcalibrateControlLimit(targetARL = targetARL,n = n, m = m, nv = nv, theta = NULL,
  Ftheta = NULL, dists = dists, mu = mu, chart.par = chart.par,
  replicates = replicates, chart = chart, isParallel = isParallel,
  maxIter = maxIter
)

Multivariate Average Run Length (ARL)

Description

Get the ARL getRL

Usage

mgetARL(
  n,
  m,
  nv,
  theta = NULL,
  Ftheta = NULL,
  dists,
  dists.par = NULL,
  mu,
  sigma = NULL,
  chart = "T2",
  chart.par = c(0.005),
  correlation = 0,
  s = NULL,
  replicates = 10000,
  isParallel = TRUE,
  print.RL = FALSE,
  progress = FALSE,
  calibrate = FALSE,
  arl0 = 370,
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE
)

Arguments

n

scalar. Subroup size

m

scalar. Reference sample size

nv

scalar. Number of variables to be generated.

theta

vector. Value corresponding with the Ftheta quantile.

Ftheta

vector. Quantile of the data distribution. The values that take are between (0,1).

dists

list. Select the

dists.par

matrix For each variable (column), specify

  • par.location: Location parameter of the desired distribution. Default 0.

  • par.scale: Scale parameter of the desired distribution. Default 1.

  • par.shape: Shape parameter of the desired distribution, Default 1.

The number of columns must be the same as the number of variables.

mu

vector. Two elements of the vector the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.

sigma

scalar. Standard deviation of the desired distribution.

chart

character string. Selected type of chart. One option available: "T2".

T2 scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

chart.par

vector. Control limit and other parameters of the selected chart.

correlation

scalar. Corralation between variables.

s

matrix. Correlation matrix of the variables

replicates

scalar. Number of replicates to get the ARL

isParallel

logical. If TRUE the code runs in parallel according to the number of cores in the computer,otherwise the code runs sequentially. Default TRUE.

print.RL

logical. If TRUE return the vectors of RL for each iteration.

progress

logical. If TRUE it shows the progress in the console.

calibrate

logical. If TRUE the RL is limit to 10 times the target ARL.

arl0

scalar. Expected value of the RL. It is only used for stop the RL if exceeds 10 times its value. Default 370.

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

Value

Multiple output. Select by output$

Examples

mgetARL(replicates=5,n=5,m=100,nv=2,mu=c(0,0),
dists = c("Normal", "Normal"), dists.par = matrix(c(0,1,1,0,1,1), ncol=2),
isParallel=FALSE)

Multivariate Random Observations Generetor

Description

Multivariate Random observations generator selected from several distributions with user defined mean and variance.

Usage

mgetDist(
  n,
  nv,
  mu = 0,
  sigma = NULL,
  correlation = 0,
  s = NULL,
  dists = NULL,
  dists.par = NULL
)

Arguments

n

scalar. Number of observations to be generated.

nv

scalar. Number of variables to be generated.

mu

scalar. Expected value of the desired distribution.

sigma

scalar. Standard deviation of the desired distribution.

correlation

scalar. Corralation between variables.

s

matrix. Correlation matrix of the variables

dists

list. Select the

dists.par

matrix For each variable (column), specify

  • par.location: Location parameter of the desired distribution. Default 0.

  • par.scale: Scale parameter of the desired distribution. Default 1.

  • par.shape: Shape parameter of the desired distribution, Default 1.

The number of columns must be the same as the number of variables.

Value

A matrix x with n observations generated following the selected distribution with its parameters.

Examples

mgetDist(n=5, nv=2, dists=c("Normal", "Normal"),dists.par= matrix(c(0,1,1,0,1,1), ncol=2))

Multivariate Run Length

Description

Get the run length

Usage

mgetRL(
  replica = 1,
  n,
  m,
  nv,
  theta = NULL,
  Ftheta = NULL,
  dists,
  mu,
  sigma = NULL,
  dists.par = NULL,
  correlation = 0,
  s = NULL,
  chart = "T2",
  chart.par = c(0.005),
  null.dist = "Chi",
  alignment = "unadjusted",
  constant = NULL,
  absolute = FALSE,
  calibrate = FALSE,
  arl0 = 370
)

Arguments

replica

scalar. It is used for the parallel version of the function (parallel=TRUE). Default 1.

n

scalar. Subroup size

m

scalar. Reference sample size

nv

scalar. Number of variables to be generated.

theta

vector. Value corresponding with the Ftheta quantile.

Ftheta

vector. Quantile of the data distribution. The values that take are between (0,1).

dists

list. Select the

mu

vector. Two elements of the vector the first one is the mean of the reference sample and the second one is the mean of the monitoring sample.

sigma

scalar. Standard deviation of the desired distribution.

dists.par

matrix For each variable (column), specify

  • par.location: Location parameter of the desired distribution. Default 0.

  • par.scale: Scale parameter of the desired distribution. Default 1.

  • par.shape: Shape parameter of the desired distribution, Default 1.

The number of columns must be the same as the number of variables.

correlation

scalar. Corralation between variables.

s

matrix. Correlation matrix of the variables

chart

character string. Selected type of chart. One option available: "T2".

T2 scheme:

is c(k), where k comes from UCL = mu + k\sigma, LCL = mu - k\sigma.

chart.par

vector. Control limit and other parameters of the selected chart.

null.dist

character string. It is the null distribution choose from "Chi" or "F".

alignment

character string. Aligment of the data X and Y. Select from

  • "unadjusted": nothing is sustracte from X and Y (default).

  • "overallmean": overall mean is sustracted from X and Y.

  • "overallmedian": overall median is sustracted from X and Y.

  • "samplemean": mean from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "samplemedian": median from corresponding group (X and Y) is sustracted from its corresponing vector.

  • "referencemean": mean from Y is subtracted from X and Y.

  • "referencemedian": median from Y is subtracted from X and Y.

  • "constantvalue": a constant value is subtracted from X and Y.

constant

scalar. Only used when the alignment is selected "constantvalue". Default NULL.

absolute

logical. If TRUE, the absolute aligned values are obtained. (Default FALSE)

calibrate

logical. If TRUE the RL is limit to 10 times the target ARL.

arl0

scalar. Expected value of the RL. It is only used for stop the RL if exceeds 10 times its value. Default 370.

Value

RL vector. The run length of the chart for the parameter setting.

Examples

mgetRL(n=5, m=10, nv=2, mu=c(0,0), dists = c("Normal", "Normal"),
dists.par = matrix(c(0,1,1,0,1,1), ncol=2))

Sequential Rank

Description

Get the sequential rank of observations (X) relative to previous observations (Y).

Usage

srank(X, Y = NULL)

Arguments

X

vector. New observations to obtain the N¡normal scores.

Y

vector. If Y is not defined (no previous observation available, NULL), NS is relative to X. Default NULL.

Value

vector. Sequentil Ranks for the X observations. If ties occurs, average of the ranks are used.

Examples

X <- c(30, 35, 45)
srank(X)