General information |
Description |
The Kaplan-Meier product limit estimator The following equation of the estimator for non-parametric Reliability for data sets with multiple failures and suspensions is used in the calculation: |
where m is the total number of failure groups (points on the diagram) with k_{j} number of failures in each j-th data group, |
Here n is the total number of items under observation, s_{j} is number of suspensions in j-th data group. The reliability estimate is calculated for times t_{i} at which one or more failures occurred. If at the same time both failures and suspensions occurred, it is assumed that the suspensions occur slightly after the failures.
Rank method |
Parameter a=0.3 yields Benard’s formula, a=0.5 corresponds to Hazen’s approximation. The case a=0 corresponds to the mean ranking. We also use the rank adjustment method for right censored (suspension) data which is based on the Mean Order Number (MON) and is used in the above formula instead of i. It is given by recurrent formula |
Increment I_{i} is calculated as |
where r_{i} is the total number of items beyond the current suspended set. Confidence bounds are calculated using Greenwood’s formula for variance |
The confidence bounds for reliability are calculated as |
where α is the desired confidence level. For exponential Greenwood’s formula we have the following bounds |
More detailed description of the applied techniques can be found in [1]. [1] O’Connor, Patrick D T. and Kleyner, Andre. Practical Reliability Engineering, 5th Edition. Chichester: Wiley, 2012, 512pp. |