PH1XBAR {PH1XBAR}

Phase I X-bar control chart with a corrected charting constant

Description

Build a Phase I Shewhart control chart for the variance components model if the data are subgrouped or for the basic Shewhart model if the data are individual. The charting constant is correted by this approach.

Usage

PH1XBAR(
  X,
  cc = NULL,
  fap0 = 0.05,
  var.est = c("S", "MR"),
  ub.option = TRUE,
  method = c("exact", "BA"),
  plot.option = TRUE,
  interval = c(1, 5),
  nsim = 10000,
  verbose = FALSE
)

Arguments

X

input and it must be a matrix

cc

nominal Phase I charting constant. If this is given, the function will not recompute the charting constant.

fap0

nominal false Alarm Probabilty in Phase 1

var.est

'S' - use mean-square-based estimator, 'MR' - use moving-range-based estimator

ub.option

TRUE - the standard deviation estimator corrected by a unbiasing constant. For S, it is c4 and for MR, it is d2. FALSE - no unbiasing constant

method

'exact' - calculate results using the exact method, 'BA' - calculate results using the Bonfferoni approximation

plot.option

- draw a plot for the process; FALSE - Not draw a plot for the process

interval

searching range of charting constants for the exact method

nsim

number of simulation for the exact method

verbose

print diagnostic information about fap0 and the charting constant during the simulations for the exact method

Value

CL Object type double - central line

var.est Object type double - variance estimate

ub.cons Object type double - unbiasing constant

cc Object type double - charting constant

m Object type integer - number of observations

nu Object type integer - degrees of freedom

lambda Object type integer - chi-squared unbiasing constant

LCL Object type double - lower charting limit

UCL Object type double - upper charting limit

CS Object type double - charting statistic

References

Champ, C.W., and Jones, L.A. (2004) Designing Phase I X-bar charts with small sample sizes. Quality and Reliability Engineering International. 20(5), 497-510

Yao, Y., Hilton, C.W., and Chakraborti, S. (2017) Designing Phase I Shewhart X-bar charts: Extended tables and software. Quality and Reliability Engineering International. 33(8), 2667-2672.

Yao, Y., and Chakraborti, S. (2021). Phase I monitoring of individual normal data: Design and implementation. Quality Engineering, 33(3), 443-456.

Yao, Y., and Chakraborti, S. (2021). Phase I process monitoring: The case of the balanced one-way random effects model. Quality and Reliability Engineering International, 37(3), 1244-1265.

Examples

set.seed(12345)

# load the data in the package as an example
data(grinder_data)

# An example using a false alarm probability of 0.05, and 10 simulations
PH1XBAR(grinder_data, fap0 = 0.05, nsim=10, verbose=TRUE)