## Problem 6.1 is on EPage 182
##
source('../Chapter6/chap_6_prob_1.R')

LS = 0
US = 4

## Compute C_p:
##
C_p = (US-LS) /(6*s)
print(sprintf('C_p= %f', C_p))

## Compute C_{pk}:
##
C_pk = min(c((x_bar - LS)/(3*s), (US - x_bar) /(3*s)))
print(sprintf('x_bar= %f; LS= %f; US= %f; C_pk= %f', x_bar, LS, US, C_pk))

## Compute P_{PK}:
##
sigma_xbar = sd(DF$average)
sigma_x = sigma_xbar*sqrt(n)
P_PK = (US-LS)/(6*sigma_x)
print(sprintf('sigma_xbar= %f; sigma_x= %f; P_PK= %f', sigma_xbar, sigma_x, P_PK))