PROBLEM 4-4

 

Residence Occupancy Period

Weibull, shape 0.8, scale 11

(to get mean 13.2, 95th percentile 41.4)

(sample mean = 12.382, 95th pctile 42.5515)

26 cases with ROP _ 100 were deleted, leaving 10074

(giving sample mean 12.099, 95th pctile 41.7868)

 

 

 

 

 

 

 

 

 

Water Use Rate: (10,074 samples)

Lognormal, mu = 6.14, sigma = 0.33 (for logX)

(To get mean 480, 95th percentile 800)

(sample has mean = 490.59, 95th pctile 798.86,

max 1912.25)

 

 

 

 

 

 

 

 

Exposure Time: 10074 samples,

Lognormal, mu = -2.347, sigma = 0.563 (for logX)

(to get mean 0.13, 95th percentile 0.28

Sample: Mean 0.11, Max 0.72.

What shape should we expect for total exposure?

 

 

 

 

 

 

 

 

 

 

Total exposure simulated as

365 X use rate X exposure time X occupancy period

 

Mean 240,359 (compare with 300,000)

95th percentile: 900,555 (compare with 3,400,000)

 

Correlations

rop wur et

wur 0.001

et 0.005 0.011

totexp 0.735 0.213 0.376

 

 

 

 

NEW GRAPH OF SIMULATED TOTAL EXPOSURE

100 BINS

Q1 33,555 MEDIAN 109,068

Q3 286,610 MAX 4,722,010

166 VALUES (1.65%) > 1,500,000

 

PLOTS OF 2000 SIMULATIONS

TOTAL EXPOSURE VS RESIDENCE OCCUPANCY PERIOD:

TOTAL EXPOSURE VS WATER USE RATE:

TOTAL EXPOSURE VS EXPOSURE TIME

SUMMARY STATISTICS FOR SIMULATION OUTPUT OF TOTAL EXPOSURE

N Mean Median StDev Min Max

10074 240,359 109,068 382,277 3 4,722,010

PERCENTILE LITERS OF WATER

5% 10,027

10% 12,630

25% 33,555

50% 109,068

75% 286,680

90% 1,511,650

95% 1,300,037

99% 1,453,599

 

PLOTS OF LOGS OF 2000 SIMULATIONS

 

LOG TOT EXP VS LOG ROP

 

 

LOG TOT EXP VS LOG WATER USE RATE:

 

 

 

 

LOG TOT EXP VS EXPOSURE TIME

 

 

 

CORRELATIONS OF LOGS

 

Ln ROP ln WUR lncET

lnROP -0.021

ln WUR -0.011 -0.023

ln ET 0.924 0.167 0.319