Reliability Function Estimation Using Jackknife Resampling and Transformations
Abstract
For the reliability of systems, one of the main objectives is to estimate the reliability function, using the Kaplan-Meier and Nelson-Aalen estimators, under the non-parametric approach. When computational techniques are used, the Jackknife delete-I strategy offers advantages due to its consistency properties for variance estimation. However, there is uncertainty regarding the possibility of improving the estimates when the number (d) of observations that are deleted in the Jackknife delete-d sequential procedure is increased. On the other hand, due to their asymptotic variance stabilization properties, the log and log(-log) transformations are used to find confidence intervals (CI) for the reliability function. This work proposes to simultaneously combine the two strategies to find the CI for the reliability function, proposing a new procedure that does not require parametric adjustment during the time of occurrence of the event of interest, in addition to improving the estimation of the reliability function when the censoring percentages are high and the sample sizes are small, the main objective of the study. A comparison is made In the investigation via simulation with sample sizes (10,25,50) and percentages of censored data (0%,15%,50%) to calculate the error rates (T.E) and quality indices (I ) thus improving the estimates, with high censoring percentages (50%). The results of this work show that interval estimation can be improved in complex scenarios of censoring and sample sizes to the literature on reliability data analysis.
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References
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