Abstract
Sequential estimation problems for the mean parameter of an exponential distribution has received much attention over the years. Purely sequential and accelerated sequential estimators and their asymptotic second-order characteristics have been laid out in the existing literature, both for minimum risk point as well as bounded length confidence interval estimation of the mean parameter. Having obtained a data set from such sequentially designed experiments, the paper investigates estimation problems for the associatedreliability function. Second-order approximations are provided for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup. An ad hoc bias-corrected version is also introduced. Then, the proposed estimator is investigated further under some specific sequential sampling strategies, already available in the literature. In the end, simulation results are presented for comparing the proposed estimators of the reliability function for moderate sample sizes and various sequential sampling strategies.
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References
Anscombe FJ (1952) Large sample theory of sequential estimation. Proc Camb Phil Soc 48:600–607
Basu AP (1991) Sequential methods in reliability and life testing. In: Ghosh BK, Sen PK (Eds) Handbook of Sequential Analysis. Marcel Dekker Inc, New York 581–592
Chow YS, Hsiung C, Lai T (1979) Extended renewal theory and moment convergence in Anscombe’s Theorem. Ann Prob 7:304–318
Chow YS, Robbins H (1965) On the asymptotic theory of fixed width sequential confidence intervals for the mean. Ann Math Statist 36:457–462
Mukhopadhyay N (1988) Sequential estimation problems for negative exponential populations. Commun Statist (Reviews Section), Theory & Methods 17:2471–2506
Mukhopadhyay N (1993) An alternative formulation of accelerated sequential procedures with applications. Dept Statist Tech Rep #93-27, Univ of Connecticut Storrs
Mukhopadhyay N, Chattopadhyay S (1991) Sequential methodologies for comparing exponential mean survival times. Sequential Analysis 10:139–148
Mukhopadhyay N, Datta S (1995) On fine-tuned bounded risk sequential point estimation of the mean of an exponential distribution. S Afr Statist J 29:9–27
Mukhopadhyay N, Datta S (1996) On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities. Ann Inst Statist Math 48:497–507
Starr N, Woodroofe M (1972) Further remarks on sequential estimation: The exponential case. Ann Math Statist 43:1147–1154
Woodroofe M (1977) Second order approximations for sequential point and interval estimation. Ann Statist 5:984–995
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Mukhopadhyay, N., Padmanabhan, A.R. & Solanky, T.K.S. On estimating the reliability after sequentially estimating the mean: The exponential case. Metrika 45, 235–252 (1997). https://doi.org/10.1007/BF02717106
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DOI: https://doi.org/10.1007/BF02717106