PROBABILITY DISTRIBUTION CHARTS

Select Distribution

3

LN

REJECT

Lognormal

PDF, Reliability, Unreliability, Hazard Rate, Cumulative Hazard Rate

GROUP DATA

Average

3.7197

Sample Standard Deviation

2.1078337

Optimal Number of Groups [Sturges' Rule]

7.6438562

Number of Groups

8

Total Number of Observations

100

RESIDUAL LIFETIME

Residual Lifetime Percentile

50.0%

Median Residual Lifetime

3.4230769

Standard Error of Median Residual Lifetime

0.1923077

GOOGNESS OF FIT

Probability Distribution Function

LN

P

Mean μ

1.1953169

P

Standard Deviation σ

0.6696591

Number of Parameters Estimated m [m ≤ n]

2

Total Number of Parameters n

2

Chi-Square Σ(Oi-Ei)2/Ei

11.267153

Degrees of Freedom df

5

Test χ2

11.070498

Accept / Reject

REJECT

Chi-Square Rank

7

The marker P identifies the probability distribution's parameters.

Legend

SYMBOL

VARIABLE

T1=T

Start of Interval [Age at Start of Mission]

T2=T+t

End of Interval

t=T2-T1

Duration of Interval [Mission Time]

τ=(T1+T2)/2

Interval Midpoint

i

Group

H

Histogram

f(τ)

Probability Density Function at Midpoint

R(T)

Reliability [Survival or Cumulative Proportion Surviving] at T

R(T+t)

Reliability [Survival or Cumulative Proportion Surviving] at T+t

Q(T)

Unreliability [Failure or Cumulative Proportion Terminating] at T

Q(T+t)

Unreliability [Failure or Cumulative Proportion Terminating] at T+t

λ(τ)

Hazard Rate at Midpoint

Mi

Median Residual Lifetime

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