Package 'SNSchart' reference manual

Title:	Sequential Normal Scores in Statistical Process Management
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) <arXiv:1901.04443>.
Authors:	Victor Tercero [aut], Luis Benavides [aut, cre], Jorge Merlo [ctb]
Maintainer:	Luis Benavides <[email protected]>
License:	MIT + file LICENSE
Version:	1.4.0
Built:	2024-11-23 05:03:21 UTC
Source:	https://github.com/luisbenavides/snschart

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
)
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$

objective.function: scalar. The best solution obtained, in terms of the target ARL or MRL
par.value: scalar. Which parameter of the chart reach this best solution
iter: scalar. In which iteration is found the objective function.
found: boolean. Is TRUE if in the maxIter is reached the desired +-5

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
)
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
)
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$

X: vector. Monitor sample with the alignment selected.
Y: vector. Reference sample with the alignment selected.

Examples

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

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
)
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$

ARL: scalar. Average Run Length for the RLs of all the replicates.
SDRL: scalar. Standard Deviation Run Length for the RL in all the replicates.
MRL: bolean. Median Run Length for the RLs of all the replicates.
QRL: vector. It retrieve the quantiles (0.05, 0.1, 0.2, 0.25, 0.5, 0.75, 0.8, 0.9, 0.95) for all the RLs.

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
)
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
)
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

For "Lognormal", par.location and par.scale correspond to the location and scale parameters of the normal distribution that generales the lognormal. Hence, in this case they are the logmean and the logsigma parameters
For "Normal2" and "DoubleExp2", par.location and par.scale correspond correspond to the location and scale parameters of the normal and double exponential that are used to generates their squared forms.

Examples

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

objective.function: scalar. The best solution obtained, in terms of the target ARL or MRL
par.value: scalar. Which parameter of the chart reach this best solution
found: boolean. Is TRUE if in the maxIter is reached the desired +-5

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
)

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
)
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$

ARL: scalar. Average Run Length for the RLs of all the replicates.
SDRL: scalar. Standard Deviation Run Length for the RL in all the replicates.
MRL: bolean. Median Run Length for the RLs of all the replicates.
QRL: vector. It retrieve the quantiles (0.05, 0.1, 0.2, 0.25, 0.5, 0.75, 0.8, 0.9, 0.95) for all the RLs.

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)
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
)
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))
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
)
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))
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))

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
)
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$

R: matrix. Multivariate Ranks for the X observations. If ties occurs, average ranks are used.
P: matrix. Multivariate Probability of the ranks for the X observations. Instead of Van Der Waerden normal scores where $P = R/(n+1)$ , $P = (R-0.5)/n$ , where $R$ stands for rank and $P$ for the input evaluated in the inverse of a Standard Normal Distribution.
Z: matrix. Multivariate Normal scores for the X observations. $Z$ if scoring is "Z" and $Z^2$ if scoring is "Z-SQ".

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)
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
)
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$

coefficients: list. Two elements: n the number of observation per group in X and chart the selected chart to perform the analysis.
X: vector. New observations (Monitoring sample) to obtain the SNS.
Z: vector. SNS of the X monitoring sample.
T2: vector. T2 statistic for each of the groups in X.
X.id: vector. The id of each column (variable) of the matrix X.
UCL: vector. Upper control limit for each group in X.

Comments

If ties, average ranks are used.

Examples

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

R: vector. Ranks for the X observations. If ties occurs, average ranks are used.
P: vector. Probability of the ranks for the X observations. Instead of Van Der Waerden normal scores where $P = R/(n+1)$ , $P = (R-0.5)/n$ , where $R$ stands for rank and $P$ for the input evaluated in the inverse of a Standard Normal Distribution.
Z: vector. Normal scores for the X observations. $Z$ if scoring is "Z" and $Z^2$ if scoring is "Z-SQ".

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)
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
)
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$

coefficients: list. Three elements: n the number of observation per group in X, chart the selected chart to perform the analysis, and chart.par the parameters of the selected chart.
R: vector. Ranks for the new observations (Monitoring sample).
X: vector. New observations (Monitoring sample) to obtain the SNS.
Z: vector. SNS of the X monitoring sample.
X.id: vector. The id of each column (variable) of the matrix X.
UCL: vector. Upper control limit for each group in X.
LCL: vector. Lower control limit for each group in X.
scoring: string. Selected score to evaluate SNS.

Comments

If ties occur, average ranks are used.

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)
# 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)

Sequential Rank

Description

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

Usage

srank(X, Y = NULL)
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)
X <- c(30, 35, 45)
srank(X)

Package 'SNSchart'

Help Index

Calibration of the control limit for the selected chart

Description

Usage

Arguments

Value

Note

Examples

Alignment of the data

Description

Usage

Arguments

Value

Examples

Data from Example 4.9 Qiu (2014).

Description

Usage

Format

Source

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

Description

Usage

Format

Source

Data from Example 7.1 Qiu (2014).

Description

Usage

Format

Source

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

Description

Usage

Format

Source

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

Description

Usage

Format

Source

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

Description

Usage

Format

Source

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

Description

Usage

Format

Source

Data from Example 8.2 Qiu (2014).

Description

Usage

Format

Source

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

Description

Usage

Format

Source

Data from Example 8.4 Qiu (2014).

Description

Usage

Format

Source

Data from Example 8.5 Qiu (2014).

Description

Usage

Format

Source

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

Description

Usage

Format

Source

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

Description

Usage

Format

Source