RELIABILITY ANALYSIS CHARTS         Select Distribution
 
3 MIX3 OK
Units with Multiple Failure Modes           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.
Mixed: PDF, Reliability, Unreliability, Hazard Rate, Cumulative Hazard Rate
GROUP DATA
Average 3333.3333
Sample Standard Deviation 2793.1296
Optimal Number of Groups [Sturges' Rule] 7.4918531
Groups 17
Total Number of Observations 90
RESIDUAL LIFETIME
Residual Lifetime Percentile 50.0%
Median Residual Lifetime 2836.3636
Standard Error of Median Residual Lifetime 258.73181
GOOGNESS OF FIT
Probability Distribution Function MIX3
Weight w1 0.3402704 P
Weight w2 0.1374869 P
Weight w3 0.5222427 P
Number of Parameters Estimated m [m ≤ n] 2
Total Number of Parameters n 3
Chi-Square Σ(Oi-Ei)2/Ei 9.8215662
Degrees of Freedom df 8
Test χ2 15.507313
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
Copyright 2010 by Macroknow Inc. All Rights Reserved.
GOODNESS-OF-FIT TESTS: GROUP DATA   Confidence Level 95.0% Select Distribution
 
3 MIX3 OK
Units with Multiple Failure Modes         Significance Level 5.0%   Time-to-Failure Data for Units with Multiple Failure Modes from Dimitri Kececioglu, Reliability Engineering Handbook, Vol. 1 (Englewood Cliffs, NJ: Prentice Hall, Inc.), pp. 536-556.
GROUP DATA
  Average 3333.3333
  Sample Standard Deviation 2793.1296
      Optimal Number of Groups [Sturges' Rule] 7.4918531
  Groups 17
  Total Number of Observations 90
RESIDUAL LIFETIME
  Residual Lifetime Percentile 50.0%
  Median Residual Lifetime 2836.3636
  Standard Error of Median Residual Lifetime 258.73181
GOOGNESS OF FIT
  Probability Distribution Function MIX3 P
  Weight w1 0.3402704 P
  Weight w2 0.1374869 P
  Weight w3 0.5222427
  Number of Parameters Estimated m [m ≤ n] 2
  Total Number of Parameters n 3
  Chi-Square Σ(Oi-Ei)2/Ei 9.8215662
  Degrees of Freedom df 8
  Test χ2 15.507313
  Accept / Reject ACCEPT
  Chi-Square Rank 1
   
       
The marker P identifies the probability distribution's parameters.
Chi-Square Goodness-of-Fit Tests
MIX
w1
w2
w3
Legend
Copyright 2010 by Macroknow Inc. All Rights Reserved.