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xshewhartrunsrules.matrix <- function(mu, c=1, type="12") {
# Shewhart chart
if (type=="1") {
p0 <- pnorm( 3*c, mean=mu ) - pnorm( -3*c, mean=mu)
Q <- p0
}
# 2 of 3 beyond +-2 sigma
if (type=="12") {
dimQ <- 7
pl <- pnorm( -2*c, mean=mu ) - pnorm( -3*c, mean=mu)
p0 <- pnorm( 2*c, mean=mu ) - pnorm( -2*c, mean=mu)
pr <- pnorm( 3*c, mean=mu ) - pnorm( 2*c, mean=mu)
# 1 2 3 4 5 6 7
# 0000 1000 0100 0010 0001 1001 0110
# 1 0000 p0 pl 0 pr 0 0 0
# 2 1000 0 0 p0 0 0 0 pr
# 3 0100 p0 0 0 pr 0 0 0
# 4 0010 0 0 0 0 p0 pl 0
# 5 0001 p0 pl 0 0 0 0 0
# 6 1001 0 0 p0 0 0 0 0
# 7 0110 0 0 0 0 p0 0 0
Q <- diag(0,dimQ)
Q[1,2] <- pl; Q[1,1] <- p0; Q[1,4] <- pr
Q[2,3] <- p0; Q[2,7] <- pr
Q[3,1] <- p0; Q[3,4] <- pr
Q[4,6] <- pl; Q[4,5] <- p0
Q[5,2] <- pl; Q[5,1] <- p0
Q[6,3] <- p0
Q[7,5] <- p0
}
# 4 of 5 beyond +-1 sigma
if (type=="13") {
dimQ <- 29
pl <- pnorm( -c, mean=mu ) - pnorm( -3*c, mean=mu)
p0 <- pnorm( c, mean=mu ) - pnorm( -c, mean=mu)
pr <- pnorm( 3*c, mean=mu ) - pnorm( c, mean=mu)
Q <- diag(0,dimQ)
Q[ 1, 2] <- pl; Q[ 1, 1] <- p0; Q[ 1,11] <- pr
Q[ 2, 4] <- pl; Q[ 2, 3] <- p0; Q[ 2,12] <- pr
Q[ 3, 5] <- pl; Q[ 3, 1] <- p0; Q[ 3,11] <- pr
Q[ 4, 7] <- pl; Q[ 4, 6] <- p0; Q[ 4,13] <- pr
Q[ 5, 8] <- pl; Q[ 5, 3] <- p0; Q[ 5,12] <- pr
Q[ 6, 9] <- pl; Q[ 6, 1] <- p0; Q[ 6,11] <- pr
Q[ 7,10] <- p0; Q[ 7,14] <- pr
Q[ 8, 6] <- p0; Q[ 8,13] <- pr
Q[ 9, 3] <- p0; Q[ 9,12] <- pr
Q[10, 1] <- p0; Q[10,11] <- pr
Q[11,16] <- pl; Q[11,15] <- p0; Q[11,19] <- pr
Q[12,17] <- pl; Q[12,15] <- p0; Q[12,19] <- pr
Q[13,18] <- pl; Q[13,15] <- p0; Q[13,19] <- pr
Q[14,15] <- p0; Q[14,19] <- pr
Q[15, 2] <- pl; Q[15, 1] <- p0; Q[15,20] <- pr
Q[16, 4] <- pl; Q[16, 3] <- p0; Q[16,21] <- pr
Q[17, 8] <- pl; Q[17, 3] <- p0; Q[17,21] <- pr
Q[18, 3] <- p0; Q[18,21] <- pr
Q[19,23] <- pl; Q[19,22] <- p0; Q[19,24] <- pr
Q[20,16] <- pl; Q[20,15] <- p0; Q[20,25] <- pr
Q[21,17] <- pl; Q[21,15] <- p0; Q[21,25] <- pr
Q[22, 2] <- pl; Q[22, 1] <- p0; Q[22,26] <- pr
Q[23, 4] <- pl; Q[23, 3] <- p0; Q[23,27] <- pr
Q[24,29] <- pl; Q[24,28] <- p0
Q[25,23] <- pl; Q[25,22] <- p0
Q[26,16] <- pl; Q[26,15] <- p0
Q[27,17] <- pl; Q[27,15] <- p0
Q[28, 2] <- pl; Q[28, 1] <- p0
Q[29, 4] <- pl; Q[29, 3] <- p0
}
# 8 on the same side
if (type=="14") {
dimQ <- 15
pl <- pnorm( 0, mean=mu ) - pnorm( -3*c, mean=mu)
pr <- pnorm( 3*c, mean=mu ) - pnorm( 0, mean=mu)
Q <- diag(0,dimQ)
Q[ 1, 2] <- pl; Q[ 1, 9] <- pr
Q[ 2, 3] <- pl; Q[ 2, 9] <- pr
Q[ 3, 4] <- pl; Q[ 3, 9] <- pr
Q[ 4, 5] <- pl; Q[ 4, 9] <- pr
Q[ 5, 6] <- pl; Q[ 5, 9] <- pr
Q[ 6, 7] <- pl; Q[ 6, 9] <- pr
Q[ 7, 8] <- pl; Q[ 7, 9] <- pr
Q[ 8, 9] <- pr
Q[ 9, 2] <- pl; Q[ 9,10] <- pr
Q[10, 2] <- pl; Q[10,11] <- pr
Q[11, 2] <- pl; Q[11,12] <- pr
Q[12, 2] <- pl; Q[12,13] <- pr
Q[13, 2] <- pl; Q[13,14] <- pr
Q[14, 2] <- pl; Q[14,15] <- pr
Q[15, 2] <- pl;
}
# ... on the same side (general approach)
if ( regexpr("SameSide", type)>0 ) {
anzahl <- as.numeric(gsub("SameSide", "", type))
dimQ <- 2*anzahl - 1
hdQ <- anzahl - 1
pl <- pnorm( 0, mean=mu ) - pnorm( -3*c, mean=mu)
pr <- pnorm( 3*c, mean=mu ) - pnorm( 0, mean=mu)
Q <- diag(0, dimQ)
for ( i in 1:hdQ ) {
Q[i,i+1] <- pl
Q[hdQ+i+1,2] <- pl
Q[i,hdQ+2] <- pr
Q[hdQ+i,hdQ+i+1] <- pr
}
}
# 2 of 2 beyond +-2 sigma
if (type=="15") {
dimQ <- 3
pl <- pnorm( -2*c, mean=mu ) - pnorm( -3*c, mean=mu)
p0 <- pnorm( 2*c, mean=mu ) - pnorm( -2*c, mean=mu)
pr <- pnorm( 3*c, mean=mu ) - pnorm( 2*c, mean=mu)
# 1 2 3
# 00 10 01
# 1 00 p0 pr pl
# 2 10 p0 0 pl
# 3 01 p0 pr 0
Q <- diag(0,dimQ)
Q[1,2] <- pl; Q[1,1] <- p0; Q[1,3] <- pr
Q[2,1] <- p0; Q[2,3] <- pr
Q[3,2] <- pl; Q[3,1] <- p0;
}
# 3 of 3 beyond +-3 sigma
if (type=="19") {
dimQ <- 5
pl <- pnorm( -3*c, mean=mu )
p0 <- pnorm( 3*c, mean=mu ) - pnorm( -3*c, mean=mu)
pr <- 1 - pnorm( 3*c, mean=mu)
# 1 2 3 4 5
# 0000 1000 1100 0010 0011
# 1 0000 p0 pr 0 pl 0
# 2 1000 p0 0 pr pl 0
# 3 1100 p0 0 0 pl 0
# 4 0010 p0 pr 0 0 pl
# 5 0011 p0 pr 0 0 0
Q <- diag(0,dimQ)
Q[1,4] <- pl; Q[1,1] <- p0; Q[1,2] <- pr
Q[2,4] <- pl; Q[2,1] <- p0; Q[2,3] <- pr
Q[3,4] <- pl; Q[3,1] <- p0;
Q[4,5] <- pl; Q[4,1] <- p0; Q[4,2] <- pr
Q[5,1] <- p0; Q[5,2] <- pr
}
Q
}
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