Examples
Example 1.
The Observation time is 24. The total Number of items is 15.

The input file contains 10 triads:
9 1 3
9 0 1
11 1 1
12 0 1
13 1 1
13 0 1
15 0 1
17 1 1
21 1 1
22 0 1

5 items were suspended at different times. Totally 7 components failed, 3 of them at time 9. The total number of items in the input file is 12, which is less than input total number 15, therefore in this example 3 items were suspended in addition at the observation time 24.

Maximum likelihood estimator (MLE) is used to calculate underlying Weibull function parameters. Benard method is selected to calculate and show corresponding probabilities on the diagram. The confidence level is calculated as two-sided with level 0.9 using Fisher matrix method. In this case variance and covariance of underlying function parameters are calculated.

In the Table you can see the calculated Probability values (Benard method) for all event times, corresponding values of Weibull function (W), as well as Upper (UCL) and Lower (LCL) confidence levels. The result of calculation is also shown in the diagram.

Output:

Calculation #1. Tue Feb 09 09:21:29 EST 2016

Entered number of components: 15
Ranking type is: Benard
Distribution function is: Weibull with paramter beta=2.1968112 eta=23.642372
Method is: MLE
Mean=20.938183 Standard deviation=10.059827
Correlation r^2=0.74453294 Error=0.15344626
Confidence level is: 90.0%
Confidence calculation method is: Fisher matrix
Var(beta)=0.4724186; Covar(beta, eta)=-1.1018871; Var(eta)=19.138119
TimeProbabilityLCLWUCL
9.0 0.045454547 0.0044566886 0.11292514 0.22139359
9.0 0.11038961 0.0044566886 0.11292514 0.22139359
9.0 0.17532468 0.0044566886 0.11292514 0.22139359
11.0 0.24567099 0.045475923 0.16990082 0.2943257
13.0 0.32305196 0.10591945 0.23568217 0.3654449
17.0 0.42254174 0.26900032 0.3840157 0.4990311
21.0 0.52203155 0.4360428 0.5373445 0.63864625

Example 2.
The Observation time is 300. The total Number of items is 9.

Input file contains 9 triads:
40.4 1 1 46.7 1 1 63.3 1 1 78.5 1 1 84.0 1 1 109.3 1 1 134.3 1 1 160.1 1 1 297.9 1 1

All 9 items failed during the observation time.

Benard method is selected to calculate and show on the diagram corresponding probabilities. Maximum likelihood estimator (MLE) is used to calculate underlying Log-Normal function parameters. The confidence level is calculated as two sided with level 0.9 using Likelihood ratio method.

In the Table you can see the calculated Probability values (selected Benard method) for all event times, corresponding values of Log-Normal function (W), as well as Upper (UCL) and Lower (LCL) confidence levels. The result of calculation also is shown in the diagram.

Output:

Calculation #1. Tue Feb 09 09:21:29 EST 2016

Entered number of components: 9
Ranking type is: Benard
Distribution function is: LogNormal with parameter mu=4.5390115 sigma=0.59350705
Method is: MLE
Mean=111.624084 Standard deviation=72.53546
Correlation r^2=0.97581536 Error=0.11254475
Confidence level is: 90.0%
Confidence calculation method is: Likelihood ratio
TimeProbabilityLCLWUCL
40.4 0.07446808 0.00995 0.07844307 0.25495
46.7 0.18085106 0.02495 0.12070777 0.31495
63.3 0.28723404 0.09995 0.25494516 0.45995
78.5 0.39361703 0.19495 0.38346398 0.59495
84.0 0.5 0.22995 0.4276747 0.63995
109.3 0.60638297 0.38495 0.6030704 0.78995
134.3 0.71276593 0.51995 0.72852486 0.88495
160.1 0.81914896 0.60495 0.817117 0.93995
297.9 0.9255319 0.84995 0.97445285 0.99495