Skip to main content
Log in

Optimal progressive group-censoring plans for exponential distribution in presence of cost constraint

  • Note
  • Published:
Statistical Papers Aims and scope Submit manuscript


This article discusses a life test under progressive type-I group-censoring. We use maximum likelihood method to obtain the point and interval estimators of the parameter of lifetime distribution. In order to obtain a precise estimate of mean life, one needs to design an optimal life test. Thus, this article proposes an approach to determine the number of test units, number of inspections, and length of inspection interval of a life test under a pre-determined budget of experiment such that the asymptotic variance of estimator of mean life is minimum. The method will be applied to two numerical examples and the sensitivity analysis will be investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Aggarwala R (2001) Progressive interval censoring: some mathematical results with applications to inference. Commun Stat Theory Methods 30: 1921–1935

    Article  MATH  MathSciNet  Google Scholar 

  • Ali Mousa MAM, Jaheen ZF (2002) Bayesian prediction for progressively censored data from the Burr model. Stat Papers 43: 587–593

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Aggarwala R (2000) Progressive censoring—theory, methods, and applications. Birkhäuser, Boston

    Google Scholar 

  • Balasooriya U, Saw SLC (1998) Reliability sampling plans for the two-parameter exponential distribution under progressive censoring. J Appl Stat 25: 707–714

    Article  MATH  Google Scholar 

  • Casella G, Berger RL (2002) Statistical inference, 2nd edn. Duxbury, Pacific Grove, CA

    Google Scholar 

  • Chen Z, Mi J (1996) Confidence interval for the mean of the exponential distribution, based on grouped data. IEEE Trans Reliab 45: 671–677

    Article  Google Scholar 

  • Dakin RJ (1965) A tree search algorithm for mixed integer programming problems. Comput J 8: 250–255

    Article  MATH  MathSciNet  Google Scholar 

  • Fernández AJ (2004) On estimating exponential parameters with general type II progressive censoring. J Stat Plan Inference 121: 135–147

    Article  MATH  Google Scholar 

  • Gouno E, Sen A, Balakrishnan N (2004) Optimal step-stress test under progressive type-I censoring. IEEE Trans Reliab 53: 388–393

    Article  Google Scholar 

  • Grossmann IE (2002) Review of nonlinear mixed-integer and disjunctive programming techniques. Optim Eng 3: 227–252

    Article  MATH  MathSciNet  Google Scholar 

  • Iyer SK, Jammalamadaka SR, Kundu D (2008) Analysis of middle-censored data with exponential lifetime distributions. J Stat Plan Inference 138: 3550–3560

    Article  MATH  MathSciNet  Google Scholar 

  • Kamat MP, Mesquita L (1994) Nonlinear mixed integer programming. In: Adeli H (eds) Advanced in design optimization. Chapman & Hall, London, pp 174–193

    Google Scholar 

  • Kundu D, Basu S (2000) Analysis of incomplete data in presence of competing risks. J Stat Plan Inference 87: 221–239

    Article  MATH  MathSciNet  Google Scholar 

  • Lawless JF (2003) Statistical models and methods for lifetime data, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Li X, Shia Y, Weia J, Chai J (2007) Empirical Bayes estimators of reliability performances using LINEX loss under progressively type-II censored sample. Math Comput Simul 73: 320–326

    Article  MATH  Google Scholar 

  • Lin C-T, Wu SJS, Balakrishnan N (2006) Inference for log-gamma distribution based on progressively type-II censored data. Commun Stat Theory Methods 35: 1271–1292

    Article  MATH  MathSciNet  Google Scholar 

  • Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New York

    MATH  Google Scholar 

  • Pal N, Jin C, Lim WK (2006) Handbook of exponential and related distributions for engineers and scientists. Chapman & Hall/CRC, Boca Raton, FL

    MATH  Google Scholar 

  • Pérez-González C, Fernández AJ (2008) Accuracy of approximate progressively censored reliability sampling plans for exponential models. Stat Papers. doi:10.1007/s00362-007-0048-5 (in press)

  • Soliman AA (2005) Estimation of parameters of life from progressively censored data using Burr-XII model. IEEE Trans Reliab 54: 34–42

    Article  Google Scholar 

  • Taha HA (1992) Operations research: an introduction, 5th edn. Macmillan, New York

    Google Scholar 

  • Tse S-K, Yuen H-K, Yang C (2002) Statistical analysis of exponential lifetimes under an integrated type-II interval censoring scheme. J Stat Comput Simul 72: 461–471

    Article  MATH  MathSciNet  Google Scholar 

  • Wu S-J (2003) Estimation for the two-parameter Pareto distribution under progressive censoring with uniform removals. J Stat Comput Simul 73: 125–134

    Article  MATH  MathSciNet  Google Scholar 

  • Wu S-J, Lin Y-P, Chen S-T (2008) Optimal step-stress test under type I progressive group-censoring with random removals. J Stat Plan Inference 138: 817–826

    Article  MATH  MathSciNet  Google Scholar 

  • Xiang L, Tse S-K (2005) Maximum likelihood estimation in survival studies under progressive interval censoring with random removals. J Biopharm Stat 15: 981–991

    Article  MathSciNet  Google Scholar 

  • Xiong C, Ming J (2004) Analysis of grouped and censored data from step-stress life test. IEEE Trans Reliab 53: 22–28

    Article  Google Scholar 

  • Yang C, Tse S-K (2005) Planning accelerated life tests under progressive type I interval censoring with random removals. Commun Stat Simul Comput 34: 1001–1025

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Shuo-Jye Wu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, SJ., Huang, SR. Optimal progressive group-censoring plans for exponential distribution in presence of cost constraint. Stat Papers 51, 431–443 (2010).

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: