Abstract
In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson (J Am Stat Assoc 70:145–150, 1975). In this article, we develop joint BLUPs of two future failure times based on early failure times by minimizing the determinant of the variance–covariance matrix of the predictors. The advantage of applying joint prediction is demonstrated by using two real data sets. The non-existence of joint BLUPs in certain setups is also discussed.
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References
Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic Press, Boston
Balakrishnan N, Rao CR (1997) A note on the best linear unbiased estimation based on order statistics. Am Stat 51:181–185
Balasooriya U (1989) Detection of outliers in the exponential distribution based on prediction. Commun Stat Theory Methods 18:711–720
Bhaumik DK, Gibbons RD (2004) An upper prediction limit for the arithmetic mean of a lognormal random variable. Technometrics 46:239–248
Doganaksoy N, Balakrishnan N (1997) A useful property of best linear unbiased predictors with applications to life-testing. Am Stat 51:22–28
Goldberger AS (1962) Best linear unbiased prediction in the generalized linear regression model. J Am Stat Assoc 57:369–375
Kaminsky KS, Nelson PI (1975) Best linear unbiased prediction of order statistics in location and scale families. J Am Stat Assoc 70:145–150
Kaminsky KS, Nelson PI (1998) Prediction of order statistics. In: Balakrishnan N, Rao CR (eds) Handbook of statistics, vol 17-order statistics: applications. North-Holland, Amsterdam, pp 431–450
Krishnamoorthy K, Hasan MS (2018) Prediction limits for the mean of a sample from a lognormal distribution: uncensored and censored cases. J Environ Stat 8:1–14
Nelson W (2003) Applied life data analysis. Wiley, Hoboken
Patel JK (1989) Prediction intervals—a review. Commun Stat Theory Methods 18:2393–2465
Schmee J, Nelson W (1979) Predicting from early failures the last failure time of a (log) normal sample. IEEE Transections Reliab R–28:22–28
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The authors express their sincere thanks to the anonymous reviewers and the Editor for their valuable comments and suggestions on an earlier version of this manuscript which led to this improved version.
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Balakrishnan, N., Bhattacharya, R. D-optimal joint best linear unbiased prediction of order statistics. Metrika 85, 253–267 (2022). https://doi.org/10.1007/s00184-021-00835-0
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DOI: https://doi.org/10.1007/s00184-021-00835-0