odpbc {pbcc}

Optimal design parameters of the Percentile-based control charts

Description

Determine the optimal statistical design parmeters of either individual or joint Shewharts control charts for percentile-based designs (PL) approach with guaranteed in-control and out-of-control performances.

Usage

odpbc(nmax,T1, T2, hv, mat, p1=0.05,p2=0.05, d=1.0, delta=1.5,
type= c("Xbar", "R", "S", "S2", "Xbar-R", "Xbar-S", "Xbar-S2"),pop.size=1000, sided="two")

Arguments

nmax

The maximum possible sample size in each sampling interval (a numeric value).

T1

The desired in-control time to signal (a numeric value).

T2

The desired out-of-control time to signal (a numeric value).

hv

The vector of intersample interval upto maximum T2 (a numeric vector of possible sample intervals).

mat

The matrix of minimum and maximum bounds for optimum parameters sample size and sample interval. The minimum values of n and h are (2,0.5) and maximum value are (nmax, T2).

p1

The probability to signal in-control from a specified number (default value is 5%)

p2

The probability to signal out-of-control from a specified number (default value is 5%)

d

The expected shift size in the process average in term of standrd deviation, i.e. d= |u1-uo|/delta (default value is 1.0). When the process is in-control w.r.t process average, set d=0.

delta

The expected shift size in the process variance (default value is 1.5). When the process is in-control w.r.t process variation, set delta=1.0

type

A character string specifying the type of Shewhart control chart either individual or joint.Available types are; "Xbar", "R", "S", "S2", "Xbar-R", "Xbar-S" and "Xbar-S2".

pop.size

Population size. This is the number of individuals genoud uses to solve the optimization problem for genetic algorithem (default value is 1000).

sided

A character string specifying the calculation of either one-sided or two-sided control limits of Shewhart dispersion charts based on PL approach (default type is two-sided).

Value

Returns the optimal parameters of PL type control chart:

n

The optimal sample size to design the percentile-based either individual or joint control chart.

h

The optimal intersampling interval to design the percentile-based either individual or joint control chart.

k

The optimal control chart constant/multiplier to design the percentile-based xbar control chart.

lp

The optimal lower percentile point of relative sample range/standard deviation/variance distribution to calculate the lower control limits of percentile-based dispersion control chart.

or/and

up

The optimal upper percentile point of relative sample range/standard deviation/variance distribution to calculate the lower control limits of percentile-based dispersion control chart.

Author(s)

Aamir Saghir, Zsolt T. Kosztyan*

e-mail: [e-mail]

References

Faraz A, Saniga E, Montgomery D. (2019). Percentile-based control charts design with an application to Shewhart Xbar and S2 control charts. Quality and Reliability Engineering International, 35(1); 116-126.

See Also

pbcc,summary.pbcc,plot.pbcc.

Examples

# Calculation of optimal parameters of the percentile-based control charts
#using "pbcc"" package.

# Set the maximum possible sample size in each h units is 10.
nmax=10

# Set the process in-control time to signal is at least 100 samples.
T1=100

# Set the control chart time to signal is at most 1 samples
# when shift occur in the process mean or/and std.dev.
T2=3

# Set the sampling intersample intervals to 0.5(0.5) T2 units of time.
hv=seq(0.5, T2, by=0.5)

#Set the lower and upper bounds of parameters(n and h) used in the optimization.
mat=matrix(c(2, nmax, 1, length(hv)), 2,2, byrow=TRUE)
p1=0.05     # Set the probability of guaranteed in-control signals is 5%.
p2=0.05     # Set the probability of guaranteed out-of-control signals is 5%.

# Optimal parameters of two-sided percentile-based Xbar control chart.

d=3             # Set the shift size in the process mean is 3 (large shift).
Q1<- odpbc(nmax, T1, T2, hv, mat, p1, p2, d, delta=1.5, type= "Xbar")

# Optimal parameters of one-sided percentile-based variance control chart.

delta=2   # Set the shift size in the process dispersion is 2 (moderate shift).
Q2<- odpbc(nmax, T1, T2, hv, mat, p1, p2, d=1.0, delta, type= "S2", sided="one")

#Optimal parameters of two-sided percentile-based joint Xbar& S control chart.
d=1.0     # Set the shift size in the process mean is 1 (small shift).
delta=2   # Set the shift size in the process dispersion is 2 (moderate shift).
Q3<- odpbc(nmax, T1, T2, hv, mat, p1, p2, d, delta, type= "Xbar-S")