hw_1.pdf

Statistical Methods for Reliability Engineering Homework #1

Orlando J. Rivera-Anglero

Exercise 1

a.

b.

c.

d. Starting Cycle

Ending Cycle

f z

0 0

0 20 0.002273 0.002381

20 40 0.004545 0.005263

40 60 0.018182 0.036364

60 80 0.006818 0.01875

80 100 0.006818 0.03

100 120 0.004545 0.033333

120 140 0.004545 0.1

140 160 0.002273

Starting Cycle

Ending Cycle

# Survivors

0 0 22

0 20 21

20 40 19

40 60 11

60 80 8

80 100 5

100 120 3

120 140 1

140 160 0

Starting Cycle

Ending Cycle

R

0 0 1

0 20 0.954545

20 40 0.863636

40 60 0.5

60 80 0.363636

80 100 0.227273

100 120 0.136364

120 140 0.045455

140 160 0

Starting Cycle

Ending Cycle

F

0 0 0

0 20 0.045455

20 40 0.136364

40 60 0.5

60 80 0.636364

80 100 0.772727

100 120 0.863636

120 140 0.954545

140 160 1



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Exercise 2

Based on the chart above and the correlation coefficient, it is determined that a Weibull

distribution provides the best fit for the data.

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St Cycle

Percent

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St Cycle

Percent

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St Cycle

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St Cycle

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Weibull

0.991

Lognormal

0.983

Exponential

*

Loglogistic

0.983

C orrelation C oefficient

Probability Plot for St CycleLSXY Estimates-Arbitrary Censoring

Weibull Lognormal

Exponential Loglogistic

150100500

0.012

0.008

0.004

0.000

St Cycle

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St Cycle

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150100500

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St Cycle

Rate

Shape 2.22947

Scale 82.6234

Mean 73.1777

StDev 34.6962

Median 70.0983

IQR 48.4096

AD* 0.703

C orrelation 0.991

Table of StatisticsProbability Density Function

Surv iv al Function Hazard F unction

Distribution Overview Plot for St CycleLSXY Estimates-Arbitrary Censoring

Weibull



Then a Distribution Overview Plot is created to find the missing parameters of the

Weibull distribution equation. It is found the scale = 82.6234 and the shape = 2.22947.

Now we can go into Maple and substitute these values into the equation.

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Exercise 3 Refer to Excel file HW1_E3.xls for Monte Carlo simulation results.

150100500

0.012

0.008

0.004

0.000

t

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0.01

t

Percent

150100500

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50

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t

Percent

150100500

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t

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C orrelation 0.999

Shape 2.21863

Scale 81.0299

Mean 71.7645

StDev 34.1753

Median 68.6911

IQ R 47.6695

Failure 1000

C ensor 0

AD* 0.456

Table of StatisticsProbability Density F unction

Surv iv al F unction Hazard F unction

Distribution Overview Plot for tLSXY Estimates-Complete Data

Weibull



When we compare the results obtained from the Excel spread sheet versus the results

obtained from Minitab, it can be seen that the MEAN value is very similar.

Exercise 4

See Maple file HW1_E4.mw for results.

Exercise 5

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hw_1.pdf

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