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A New Decision Theoretic Sampling Plan for Type-I and Type-I Hybrid Censored Samples from the Exponential Distribution

Author

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  • Deepak Prajapati

    (Indian Institute of Technology Kanpur)

  • Sharmistha Mitra

    (Indian Institute of Technology Kanpur)

  • Debasis Kundu

    (Indian Institute of Technology Kanpur)

Abstract

The study proposes a new decision theoretic sampling plan (DSP) for Type-I and Type-I hybrid censored samples when the lifetimes of individual items are exponentially distributed with a scale parameter. The DSP is based on an estimator of the scale parameter which always exists, unlike the MLE which may not always exist. Using a quadratic loss function and a decision function based on the proposed estimator, a DSP is derived. To obtain the optimum DSP, a finite algorithm is used. Numerical results demonstrate that in terms of the Bayes risk, the optimum DSP is as good as the Bayesian sampling plan (BSP) proposed by Lin et al. (2002) and Liang and Yang (2013). The proposed DSP performs better than the sampling plan of Lam (1994) and Lin et al. (2008a) in terms of Bayes risks. The main advantage of the proposed DSP is that for higher degree polynomial and non-polynomial loss functions, it can be easily obtained as compared to the BSP.

Suggested Citation

  • Deepak Prajapati & Sharmistha Mitra & Debasis Kundu, 2019. "A New Decision Theoretic Sampling Plan for Type-I and Type-I Hybrid Censored Samples from the Exponential Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 251-288, December.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:2:d:10.1007_s13571-018-0167-0
    DOI: 10.1007/s13571-018-0167-0
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    References listed on IDEAS

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    1. Huang, Wen-Tao & Lin, Yu-Pin, 2004. "Bayesian sampling plans for exponential distribution based on uniform random censored data," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 669-691, January.
    2. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    3. Yu-Pin Lin & TaChen Liang & Wen-Tao Huang, 2002. "Bayesian Sampling Plans for Exponential Distribution Based on Type I Censoring Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 100-113, March.
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    Cited by:

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    2. Yunhan Liu & Changchun Gao & Xiaofeng Liu & Ping Luo & Jianguo Ren, 2024. "A Comparison of MLE for Some Index Distributions Based on Censored Samples," Mathematics, MDPI, vol. 12(20), pages 1-15, October.

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