RELIABILITY ANALYSIS CHARTS

Select Distribution

3

RAY

OK

Time-to-Failure Data for Bearings

Time-to-Failure Data for Bearings from Charles Lipson and Narendra J. Sheth, Statistical Design and Analysis of Engineering Experiments (New York, NY: MacGraw-Hill, Inc.), 1973), pp. 403-406.

Rayleigh: PDF, Reliability, Unreliability, Hazard Rate, Cumulative Hazard Rate

GROUP DATA

Average

28.965385

Sample Standard Deviation

15.255264

Optimal Number of Groups [Sturges' Rule]

4.7004397

Groups

13

Total Number of Observations

13

RESIDUAL LIFETIME

Residual Lifetime Percentile

50.0%

Median Residual Lifetime

23.15

Standard Error of Median Residual Lifetime

5.9491596

GOOGNESS OF FIT

Probability Distribution Function

RAY

Scale Parameter η

24.67551

P

Number of Parameters Estimated m [m ≤ n]

0

Total Number of Parameters n

1

Chi-Square Σ(Oi-Ei)2/Ei

0.2445389

Degrees of Freedom df

12

Test χ2

21.02607

Accept / Reject

ACCEPT

Chi-Square Rank

1

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)

Failure [Hazard] Rate at Midpoint

Mi

Median Residual Lifetime

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