source('../Chapter6/chap_6_prob_1_data.R')

x_bar = mean(DF$average)
print(sprintf('x_bar= %f', x_bar))
R_bar = mean(DF$range)
print(sprintf('R_bar= %f', R_bar))

n = 5

# From Table C:
#
A2 = 0.577
D3 = 0
D4 = 2.115
d2 = 2.326
LCL_xbar = x_bar - A2*R_bar
UCL_xbar = x_bar + A2*R_bar
cl = c(LCL_xbar, UCL_xbar)
print( sprintf( 'confidence limits xbar= (%f, %f)', cl[1], cl[2] ) )
LCL_range = D3*R_bar
UCL_range = D4*R_bar
cl = c(LCL_range, UCL_range)
print( sprintf( 'confidence limits Rbar= (%f, %f)', cl[1], cl[2] ) )

#postscript("../../WriteUp/Graphics/Chapter6/chap_6_prob_1_plot.eps", onefile=FALSE, horizontal=FALSE)

par(mfrow=c(2,1))

y_lim_min = min( c( DF$average, LCL_xbar, UCL_xbar ) )
y_lim_max = max( c( DF$average, LCL_xbar, UCL_xbar ) )

plot( DF$average, pch=19, ylim=c(y_lim_min, y_lim_max), col='black', ylab='x bars' )
abline(h=x_bar, col='black')
abline(h=c(LCL_xbar, UCL_xbar), col='red')
grid()

y_lim_min = min( c( DF$range, LCL_range, UCL_range ) )
y_1im_max = max( c( DF$range, LCL_range, UCL_range ) )
plot( DF$range, pch=19, ylim=c(y_lim_min, y_lim_max), col='black', ylab='Rs' )
abline(h=R_bar, col='black')
abline(h=c(LCL_range, UCL_range), col='red')
grid()

par(mfrow=c(1,1))

#dev.off()


s = R_bar/d2
print(sprintf('sigma= %f', s))
ll = x_bar - 3*s
ul = x_bar + 3*s
print( sprintf( 'confidence limits x: (%f, %f)', ll, ul ) )


#postscript("../../WriteUp/Graphics/Chapter6/chap_6_prob_1_hist_plot.eps", onefile=FALSE, horizontal=FALSE)

hist( raw_data, breaks=x_breaks )
abline(v=c(x_bar, 4.0), col=c( 'black', 'blue' ) )
abline(v=c(ll, ul), col='red')

#dev.off()