calibrateControlLimit: Calibration of the control limit for the selected chart

In SNSchart: Sequential Normal Scores in Statistical Process Management

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 + 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
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
)

SNSchart documentation built on April 7, 2021, 9:07 a.m.