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soerp_examples.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Jun 24 17:13:42 2013
@author: tisimst
"""
import math
import os,sys
pwd = r'/'.join(os.path.dirname(os.path.abspath(__file__)).split('/')[:-1])
if pwd not in sys.path:
sys.path.append(pwd)
from soerp import *
import soerp.umath as umath
print 'UNCERTAIN DISTRIBUTION TEST FUNCTIONS USING GIVEN MOMENTS'
print '*'*80
print 'Example of a three part assembly'
x1 = uv([24,1,0,3,0,15,0,105]) # normally distributed
x2 = uv([37,16,0,3,0,15,0,105]) # normally distributed
x3 = uv([0.5,0.25,2,9,44,265,1854,14833]) # exponentially distributed
Z = (x1*x2**2)/(15*(1.5+x3))
print 'Results should be about:'
print ' > Mean................... 1176.45'
print ' > Variance............... 99699.682'
print ' > Skewness Coefficient... 0.70801305'
print ' > Kurtosis Coefficient... 6.1632855'
print Z
print '*'*80
print 'Example of volumetric gas flow through orifice meter'
H = uv([64,0.25,0,3,0,15,0,105]) # normally distributed
M = uv([16,0.01,0,3,0,15,0,105]) # normally distributed
P = uv([361, 4,0,3,0,15,0,105]) # normally distributed
t = uv([165,0.25,0,3,0,15,0,105]) # normally distributed
C = 38.4
Q = C*umath.sqrt((520*H*P)/(M*(t + 460)))
print 'Results should be about:'
print ' > Mean................... 1330.9997'
print ' > Variance............... 58.210763'
print ' > Skewness Coefficient... 0.010942207'
print ' > Kurtosis Coefficient... 3.0003269'
print Q
print '*'*80
print 'Example of manufacturing tolerance stackup'
x = uv([1.5,0.25,2/3.,11/3.,0,0,0,0]) # gamma distributed
y = uv([1.5,0.25,2/3.,11/3.,0,0,0,0]) # gamma distributed
z = uv([1.5,0.25,2/3.,11/3.,0,0,0,0]) # gamma distributed
w = x+y+z
print 'Results should be about:'
print ' > Mean................... 4.5'
print ' > Variance............... 0.75'
print ' > Skewness Coefficient... 0.385'
print ' > Kurtosis Coefficient... 3.22'
print w
print '*'*80
print 'Example of scheduling facilities (six stations)'
s1 = uv([10,1,0,3,0,0,0,0]) # normal distributed
s2 = uv([20,2,0,3,0,0,0,0]) # normal distributed
s3 = uv([1.5,0.25,0.67,3.67,0,0,0,0]) # gamma distributed
s4 = uv([10,10,0.63,3.6,0,0,0,0]) # gamma distributed
s5 = uv([0.2,0.04,2,9,0,0,0,0]) # exponental distributed
s6 = uv([10,20,0.89,4.2,0,0,0,0]) # chi-square distributed
T = s1 + s2 + s3 + s4 + s5 + s6
print 'Results should be about:'
print ' > Mean................... 51.7'
print ' > Variance............... 33.3'
print ' > Skewness Coefficient... 0.52'
print ' > Kurtosis Coefficient... 3.49'
print T
###############################################################################
try:
import scipy.stats as ss
except ImportError:
pass
else:
print '*'*80
print 'SAME TEST FUNCTIONS USING DERIVED MOMENTS FROM SCIPY DISTRIBUTIONS'
print '*'*80
print 'Example of a three part assembly'
x1 = uv(rv=ss.norm(loc=24, scale=1)) # normally distributed
x2 = uv(rv=ss.norm(loc=37, scale=4)) # normally distributed
x3 = uv(rv=ss.expon(scale=1/2.)) # exponentially distributed
Z = (x1*x2**2)/(15*(1.5 + x3))
print 'Results should be about:'
print ' > Mean................... 1176.45'
print ' > Variance............... 99699.682'
print ' > Skewness Coefficient... 0.70801305'
print ' > Kurtosis Coefficient... 6.1632855'
print Z
print '*'*80
print 'Example of volumetric gas flow through orifice meter'
H = uv(rv=ss.norm(loc=64, scale=0.5))
M = uv(rv=ss.norm(loc=16, scale=0.1))
P = uv(rv=ss.norm(loc=361, scale=2))
t = uv(rv=ss.norm(loc=165, scale=0.5))
C = 38.4
Q = C*umath.sqrt((520*H*P)/(M*(t + 460)))
print 'Results should be about:'
print ' > Mean................... 1330.9997'
print ' > Variance............... 58.210763'
print ' > Skewness Coefficient... 0.010942207'
print ' > Kurtosis Coefficient... 3.0003269'
print Q
print '*'*80
print 'Example of manufacturing tolerance stackup'
# for a gamma distribution we need the following conversions:
# scale = var/mean
# shape = mean**2/var
mn = 1.5
vr = 0.25
scale = vr/mn
shape = mn**2/vr
x = uv(rv=ss.gamma(shape, scale=scale))
y = uv(rv=ss.gamma(shape, scale=scale))
z = uv(rv=ss.gamma(shape, scale=scale))
w = x + y + z
print 'Results should be about:'
print ' > Mean................... 4.5'
print ' > Variance............... 0.75'
print ' > Skewness Coefficient... 0.385'
print ' > Kurtosis Coefficient... 3.22'
print w
print '*'*80
print 'Example of scheduling facilities (six stations)'
s1 = uv(rv=ss.norm(loc=10, scale=1))
s2 = uv(rv=ss.norm(loc=20, scale=2**0.5))
mn1 = 1.5
vr1 = 0.25
scale1 = vr1/mn1
shape1 = mn1**2/vr1
s3 = uv(rv=ss.gamma(shape1,scale=scale1))
mn2 = 10
vr2 = 10
scale2 = vr2/mn2
shape2 = mn2**2/vr2
s4 = uv(rv=ss.gamma(shape2, scale=scale2))
s5 = uv(rv=ss.expon(scale=0.2))
s6 = uv(rv=ss.chi2(10))
T = s1 + s2 + s3 + s4 + s5 + s6
print 'Results should be about:'
print ' > Mean................... 51.7'
print ' > Variance............... 33.3'
print ' > Skewness Coefficient... 0.52'
print ' > Kurtosis Coefficient... 3.49'
print T
print '*'*80
print 'Example of two-bar truss'
H = uv(rv=ss.norm(loc=30, scale=5/3.), tag='H')
B = uv(rv=ss.norm(loc=60, scale=0.5/3.), tag='B')
d = uv(rv=ss.norm(loc=3, scale=0.1/3), tag='d')
t = uv(rv=ss.norm(loc=0.15, scale=0.01/3), tag='t')
E = uv(rv=ss.norm(loc=30000, scale=1500/3.), tag='E')
rho = uv(rv=ss.norm(loc=0.3, scale=0.01/3.), tag='rho')
P = uv(rv=ss.norm(loc=66, scale=3/3.), tag='P')
pi = math.pi
wght = 2*pi*rho*d*t*umath.sqrt((B/2)**2 + H**2)
strs = (P*umath.sqrt((B/2)**2 + H**2))/(2*pi*d*t*H)
buck = (pi**2*E*(d**2 + t**2))/(8*((B/2)**2 + H**2))
defl = (P*((B/2)**2 + H**2)**(1.5))/(2*pi*d*t*H**2*E)
print 'wght:', wght
print 'strs:', strs
print 'buck:', buck
print 'defl:', defl
wght.error_components(pprint=True)
###############################################################################
print '*'*80
print 'SAME TEST FUNCTIONS USING EASY DISTRIBUTION CONSTRUCTORS'
print '*'*80
print 'Example of a three part assembly'
x1 = N(24, 1) # normally distributed
x2 = N(37, 4) # normally distributed
x3 = Exp(2) # exponentially distributed
Z = (x1*x2**2)/(15*(1.5 + x3))
print 'Results should be about:'
print ' > Mean................... 1176.45'
print ' > Variance............... 99699.682'
print ' > Skewness Coefficient... 0.70801305'
print ' > Kurtosis Coefficient... 6.1632855'
print Z
print '*'*80
print 'Example of volumetric gas flow through orifice meter'
H = N(64, 0.5)
M = N(16, 0.1)
P = N(361, 2)
t = N(165, 0.5)
C = 38.4
Q = C*umath.sqrt((520*H*P)/(M*(t + 460)))
print 'Results should be about:'
print ' > Mean................... 1330.9997'
print ' > Variance............... 58.210763'
print ' > Skewness Coefficient... 0.010942207'
print ' > Kurtosis Coefficient... 3.0003269'
print Q
print '*'*80
print 'Example of manufacturing tolerance stackup'
# for a gamma distribution we need the following conversions:
# scale = var/mean
# shape = mean**2/var
mn = 1.5
vr = 0.25
scale = vr/mn
shape = mn**2/vr
x = Gamma(shape, scale)
y = Gamma(shape, scale)
z = Gamma(shape, scale)
w = x + y + z
print 'Results should be about:'
print ' > Mean................... 4.5'
print ' > Variance............... 0.75'
print ' > Skewness Coefficient... 0.385'
print ' > Kurtosis Coefficient... 3.22'
print w
print '*'*80
print 'Example of scheduling facilities (six stations)'
s1 = N(10, 1)
s2 = N(20, 2**0.5)
mn1 = 1.5
vr1 = 0.25
scale1 = vr1/mn1
shape1 = mn1**2/vr1
s3 = Gamma(shape1, scale1)
mn2 = 10
vr2 = 10
scale2 = vr2/mn2
shape2 = mn2**2/vr2
s4 = Gamma(shape2, scale2)
s5 = Exp(5)
s6 = Chi2(10)
T = s1 + s2 + s3 + s4 + s5 + s6
print 'Results should be about:'
print ' > Mean................... 51.7'
print ' > Variance............... 33.3'
print ' > Skewness Coefficient... 0.52'
print ' > Kurtosis Coefficient... 3.49'
print T
print '*'*80
print 'Example of two-bar truss'
H = N(30, 5/3., tag='H')
B = N(60, 0.5/3., tag='B')
d = N(3, 0.1/3, tag='d')
t = N(0.15, 0.01/3, tag='t')
E = N(30000, 1500/3., tag='E')
rho = N(0.3, 0.01/3., tag='rho')
P = N(66, 3/3., tag='P')
pi = math.pi
wght = 2*pi*rho*d*t*umath.sqrt((B/2)**2 + H**2)
strs = (P*umath.sqrt((B/2)**2 + H**2))/(2*pi*d*t*H)
buck = (pi**2*E*(d**2 + t**2))/(8*((B/2)**2 + H**2))
defl = (P*((B/2)**2 + H**2)**(1.5))/(2*pi*d*t*H**2*E)
print 'wght:', wght
print 'strs:', strs
print 'buck:', buck
print 'defl:', defl
wght.error_components(pprint=True)