SNS: Sequential Normal Scores

In LuisBenavides/SNS: Sequential Normal Scores in Statistical Process Management

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 + kσ, LCL = mu - kσ. 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.

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)

LuisBenavides/SNS documentation built on April 11, 2021, 3:50 p.m.