Skip to main content
Log in

Progressive censoring methodology: an appraisal

  • Invited Paper
  • Published:
TEST Aims and scope Submit manuscript

Abstract

Properties of progressively censored order statistics and inferential procedures based on progressively censored samples have recently attracted considerable attention in the literature. In this paper, I provide an overview of various developments that have taken place in this direction and also suggest some potential problems of interest for further research.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    MATH  MathSciNet  Google Scholar 

  • Aggarwala R (2001b) Progressive censoring: a review. In: Balakrishnan N, Rao CR (eds) Advances in reliability. Handbook of statistics, vol 20. North-Holland, Amsterdam, pp 373–429

    Google Scholar 

  • Aggarwala R, Balakrishnan N (1996) Recurrence relations for single and product moments of progressive Type-II right censored order statistics from exponential and truncated exponential distributions. Ann Inst Stat Math 48:757–771

    MATH  MathSciNet  Google Scholar 

  • Aggarwala R, Balakrishnan N (1998) Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. J Stat Plann Inference 70:35–49

    MATH  MathSciNet  Google Scholar 

  • Aggarwala R, Balakrishnan N (2002) Maximum likelihood estimation of the Laplace parameters based on progressive Type-II censored samples. In: Balakrishnan N (ed) Advances on methodological and applied aspects of probability and statistics. Taylor & Francis, Philadelphia, pp 159–167

    Google Scholar 

  • Alvarez-Andrade S, Bordes L (2004) Empirical quantile process under Type-II progressive censoring. Stat Probab Lett 68:111–123

    MATH  MathSciNet  Google Scholar 

  • Alvarez-Andrade S, Balakrishnan N, Bordes L (2007) Homogeneity tests based on several progressively Type-II censored samples. J Multivar Anal 98(6):1195–1213

    MathSciNet  MATH  Google Scholar 

  • Arnold BC (1983) Pareto distributions. International Co-operative Publishing House, Fairland

    MATH  Google Scholar 

  • Arnold BC, Balakrishnan N (1989) Relations, bounds and approximations for order statistics. Lecture notes in statistics, vol 53. Springer, New York

    MATH  Google Scholar 

  • Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York

    MATH  Google Scholar 

  • Bairamov I, Eryilmaz S (2006) Spacings, exceedances and concomitants in progressive type II censoring scheme. J Stat Plann Inference 136:527–536

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N (1983) Empirical power study of a multi-sample test of exponentiality based on spacings. J Stat Comput Simul 18:265–271

    Google Scholar 

  • Balakrishnan N (1990) Improving the Hartley–David–Gumbel bound for the mean of extreme order statistics. Stat Probab Lett 9:291–294

    MATH  Google Scholar 

  • Balakrishnan N (ed) (1992) Handbook of the logistic distribution. Dekker, New York

    MATH  Google Scholar 

  • Balakrishnan N (1993) A simple application of binomial-negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants. Stat Probab Lett 18:301–305

    MATH  Google Scholar 

  • Balakrishnan N (2007) Permanents, order statistics, outliers, and robustness. Rev Mat Complut 20:7–107

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Balakrishnan N, Asgharzadeh A (2005) Inference for the scaled half-logistic distribution based on progressively Type-II censored samples. Commun Stat Theory Methods 34:73–87

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Bordes L (2004) Non-parametric hazard rate estimation under progressive Type-II censoring. In: Balakrishnan N, Rao CR (eds) Advances in survival analysis. Handbook of statistics, vol 23. North-Holland, Amsterdam, pp 227–249

    Google Scholar 

  • Balakrishnan N, Brain C, Mi J (2002) Stochastic order and MLE of the mean of the exponential distribution. Methodol Comput Appl Probab 4:83–93

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Burkschat M, Cramer E, Hofmann G (2007) Can progressive censoring be better than right censoring? (submitted)

  • Balakrishnan N, Childs A, Chandrasekar B (2002) An efficient computational method for moments of order statistics under progressive censoring. Stat Probab Lett 60:359–365

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Cohen AC (1991) Order statistics and inference: estimation methods. Academic, Boston

    MATH  Google Scholar 

  • Balakrishnan N, Cramer E (2007) Progressive censoring from heterogeneous distributions with applications to robustness. Ann Inst Stat Math (to appear)

  • Balakrishnan N, Cramer E, Kamps U (2001) Bounds for means and variances of progressive Type II censored order statistics. Stat Probab Lett 54:301–315

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Cramer E, Kamps U (2005) Relation for joint densities of progressively censored order statistics. Statistics 39:529–536

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Cramer E, Kamps U, Schenk N (2001) Progressive Type II censored order statistics from exponential distributions. Statistics 35:537–556

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Dembińska A (2007a) Progressively Type-II right censored order statistics from discrete distributions. J Stat Plann Inference (to appear)

  • Balakrishnan N, Dembińska A (2007b) Ordered random variables from discontinuous distributions (submitted)

  • Balakrishnan N, Habibi Rad A, Arghami NR (2007) Testing exponentiality based on Kullback–Leibler information with progressively Type-II censored data. IEEE Trans Reliab 56:301–307

    Google Scholar 

  • Balakrishnan N, Han D (2007) Optimal progressive Type-II censoring schemes for non-parametric confidence intervals of quantiles. Commun Stat Simul Comput (to appear)

  • Balakrishnan N, Hossain A (2007) Inference for the Type-II generalized logistic distribution under progressive Type-II censoring. J Stat Comput Simul (to appear)

  • Balakrishnan N, Joshi PC (1981) Moments of order statistics from doubly truncated power function distribution. Aligarh J Statist 1:98–105

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Joshi PC (1982) Moments of order statistics from doubly truncated Pareto distribution. J Indian Stat Assoc 20:109–117

    MathSciNet  Google Scholar 

  • Balakrishnan N, Kannan N (2001) Point and interval estimation for parameters of the logistic distribution based on progressively Type-II censored samples. In: Balakrishnan N, Rao CR (eds) Advances in reliability. Handbook of statistics, vol 20. North-Holland, Amsterdam, pp 431–456

    Google Scholar 

  • Balakrishnan N, Kannan N (2007) Recursive algorithm for single and product moments of progressive Type-II right censored order statistics from logistic distribution (submitted)

  • Balakrishnan N, Kannan N, Lin C-T, Ng HKT (2003) Point and interval estimation for Gaussian distribution, based on progressively Type-II censored samples. IEEE Trans Reliab 52:90–95

    Google Scholar 

  • Balakrishnan N, Kannan N, Lin C-T, Wu SJS (2004) Inference for the extreme value distribution under progressive Type-II censoring. J Stat Comput Simul 74:25–45

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Kateri M (2007) On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data (submitted)

  • Balakrishnan N, Kim J-A (2004) EM algorithm and optimal censoring schemes for progressively Type-II censored bivariate normal data. In: Balakrishnan N, Kannan N, Nagaraja HN (eds) Advances in ranking and selection, multiple comparisons, and reliability: methodology and applications. Birkhäuser, Boston, pp 21–45

    Google Scholar 

  • Balakrishnan N, Kim J-A (2005) Point and interval estimation for bivariate normal distribution based on progressively Type-II censored data. Commun Stat Theory Methods 34:1297–1347

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Lin C-T (2002) Exact linear inference and prediction for exponential distributions based on general progressively Type-II censored samples. J Stat Comput Simul 72:677–686

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Lin C-T (2003) On the distribution of a test for exponentiality based on progressively Type-II right censored spacings. J Stat Comput Simul 73:277–283

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Malov SV (2005) Some characterizations of exponential distribution based on progressively censored order statistics. In: Balakrishnan N, Bairamov IG, Gebizlioglu OL (eds) Advances on models, characterizations and applications. Chapman & Hall, New York, pp 97–109

    Google Scholar 

  • Balakrishnan N, Mi J (2003) Existence and uniqueness of the MLEs for normal distribution based on general progressively Type-II censored samples. Stat Probab Lett 64:407–414

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Ng HKT (2006) Precedence-type tests and applications. Wiley, Hoboken

    MATH  Google Scholar 

  • Balakrishnan N, Ng HKT, Kannan N (2002) A test of exponentiality based on spacings for progressively Type-II censored data. In: Huber-Carol C, Balakrishnan N, Nikulin MS, Mesbah M (eds) Goodness-of-fit tests and model validity. Birkhäuser, Boston, pp 89–111

    Google Scholar 

  • Balakrishnan N, Ng HKT, Kannan N (2004) Goodness-of-fit tests based on spacings for progressively Type-II censored data from a general location-scale distribution. IEEE Trans Reliab 53:349–356

    Google Scholar 

  • Balakrishnan N, Rao CR (1997) Large-sample approximations to the best linear unbiased estimation and best linear unbiased prediction based on progressively censored samples and some applications. In: Panchapakesan S, Balakrishnan N (eds) Advances in statistical decision theory and applications. Birkhäuser, Boston, pp 431–444

    Google Scholar 

  • Balakrishnan N, Sandhu RA (1995) A simple simulational algorithm for generating progressive Type-II censored samples. Am Stat 49:229–230

    Google Scholar 

  • Balakrishnan N, Sandhu RA (1996) Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type-II censored samples. Sankhyā Ser B 58:1–9

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Sultan KS (1998) Recurrence relations and identities for moments of order statistics. In: Balakrishnan N, Rao CR (eds) Order statistics: theory and methods. Handbook of statistics, vol 16. North-Holland, Amsterdam, pp 149–228

    Google Scholar 

  • Balakrishnan N, Tripathi RC, Kannan N (2007) On the joint distribution of placement statistics under progressive censoring and applications to precedence test. J Stat Plann Inference (to appear)

  • Balasooriya U (2001) Progressively censored variables-sampling plans for life testing. In: Balakrishnan N, Rao CR (eds) Advances in reliability. Handbook of statistics, vol 20. North-Holland, Amsterdam, pp 457–467

    Google Scholar 

  • Balasooriya U, Balakrishnan N (2000) Reliability sampling plans for the lognormal distribution, based on progressively censored samples. IEEE Trans Reliab 49:199–203

    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

    MATH  Google Scholar 

  • Balasooriya U, Saw SLC, Gadag VG (2000) Progressively censored reliability sampling plans for the Weibull distribution. Technometrics 42:160–168

    Google Scholar 

  • Basak I, Balakrishnan N (2003) Robust estimation under progressive censoring. Comput Stat Data Anal 44:349–376

    MathSciNet  MATH  Google Scholar 

  • Basak I, Basak P, Balakrishnan N (2006) On some predictors of times to failure of censored items in progressively censored samples. Comput Stat Data Anal 50:1313–1337

    MathSciNet  Google Scholar 

  • Bhattacharya B (2007) Testing for ordered failure rates under general progressive censoring. J Stat Plann Inference 137:1775–1786

    MATH  Google Scholar 

  • Bordes L (2004) Non-parametric estimation under progressive censoring. J Stat Plann Inference 119:179–189

    MathSciNet  Google Scholar 

  • Brascamp HJ, Lieb EH (1975) Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma. In: Arthurs AM (ed) Functional integration and its applications. Clarendon Press, Oxford, pp 1–14

    Google Scholar 

  • Burkschat M, Cramer E, Kamps U (2006) On optimal schemes in progressive censoring. Stat Probab Lett 76:1032–1036

    MATH  MathSciNet  Google Scholar 

  • Cacciari M, Montanari GC (1987) A method to estimate the Weibull parameters for progressively censored tests. IEEE Trans Reliab 36:87–93

    MATH  Google Scholar 

  • Cacoullos T, Papathanasiou V (1985) On upper bounds for the variance of functions of random variables. Stat Probab Lett 3:175–184

    MATH  MathSciNet  Google Scholar 

  • Chandrasekar B, Balakrishnan N (2002) On a multiparameter version of Tukey’s linear sensitivity measure and its properties. Ann Inst Stat Math 54:796–805

    MATH  MathSciNet  Google Scholar 

  • Chandrasekar B, Leo Alexander T, Balakrishnan N (2002) Equivariant estimation for parameters of exponential distributions based on Type-II progressively censored samples. Commun Stat Theory Methods 31:1675–1686

    MATH  Google Scholar 

  • Chatterjee SK, Sen PK (1973) Nonparametric testing under progressive censoring. Calcutta Stat Assoc Bull 22:13–50

    MATH  MathSciNet  Google Scholar 

  • Childs A, Balakrishnan N (2000) Conditional inference procedures for the Laplace distribution when the observed samples are progressively censored. Metrika 52:253–265

    MATH  MathSciNet  Google Scholar 

  • Childs A, Chandrasekar B, Balakrishnan N (2007) Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkhäuser, Boston, pp 323–334

    Google Scholar 

  • Cohen AC (1963) Progressively censored samples in life testing. Technometrics 5:327–329

    MATH  MathSciNet  Google Scholar 

  • Cohen AC (1966) Life testing and early failure. Technometrics 8:539–549

    Google Scholar 

  • Cohen AC (1975) Multi-censored sampling in the three parameter Weibull distribution. Technometrics 17:347–351

    MATH  MathSciNet  Google Scholar 

  • Cohen AC (1976) Progressively censored sampling in the three parameter log-normal distribution. Technometrics 18:99–103

    MATH  MathSciNet  Google Scholar 

  • Cohen AC (1991) Truncated and censored samples: theory and applications. Dekker, New York

    MATH  Google Scholar 

  • Cohen AC, Norgaard NJ (1977) Progressively censored sampling in the three parameter gamma distribution. Technometrics 19:333–340

    MATH  MathSciNet  Google Scholar 

  • Cohen AC, Whitten BJ (1988) Parameter estimation in reliability and life span models. Dekker, New York

    MATH  Google Scholar 

  • Cramer E (2004) Logconcavity and unimodality of progressively censored order statistics. Stat Probab Lett 68:83–90

    MATH  MathSciNet  Google Scholar 

  • Cramer E, Kamps U, Rychlik T (2004) Unimodality of uniform generalized order statistics, with applications to mean bounds. Ann Inst Stat Math 56:183–192

    MATH  MathSciNet  Google Scholar 

  • D’Agostino RB, Stephens MA (eds) (1986) Goodness-of-fit techniques. Dekker, New York

    MATH  Google Scholar 

  • David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, Hoboken

    MATH  Google Scholar 

  • Dharmadhikari S, Joag-Dev K (1988) Unimodality, convexity, and applications. Academic, Boston

    MATH  Google Scholar 

  • Epstein B, Sobel M (1953) Life testing. J Amer Stat Assoc 48:486–502

    MATH  MathSciNet  Google Scholar 

  • Epstein B, Sobel M (1954) Some theorems relevant to life testing from an exponential distribution. Ann Math Stat 25:373–381

    MathSciNet  MATH  Google Scholar 

  • Fischer T, Balakrishnan N, Cramer E (2007) Mixture representation for order statistics from INID progressive censoring and its applications (submitted)

  • Fisher RA (1934) Two new properties of mathematical likelihood. Proc Roy Soc Ser A 144:285–307

    MATH  Google Scholar 

  • Gajjar AV, Khatri CG (1969) Progressively censored samples from log-normal and logistic distributions. Technometrics 11:793–803

    MATH  Google Scholar 

  • Gertsbakh I, Kagan AM (1999) Characterization of the Weibull distribution by properties of the Fisher information under Type-I censoring. Stat Probab Lett 42:99–105

    MATH  MathSciNet  Google Scholar 

  • Gibbons DI, Vance LC (1983) Estimators for the 2-parameter Weibull distribution with progressively censored samples. IEEE Trans Reliab 32:95–99

    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

    Google Scholar 

  • Guilbaud O (2001) Exact non-parametric confidence intervals for quantiles with progressive Type-II censoring. Scand J Statist 28:699–713

    MATH  MathSciNet  Google Scholar 

  • Guilbaud O (2004) Exact non-parametric confidence, prediction and tolerance intervals with progressive Type-II censoring. Scand J Statist 31:265–281

    MATH  MathSciNet  Google Scholar 

  • Han D, Balakrishnan N, Sen A, Gouno E (2006) Corrections on “Optimal step-stress test under progressive Type-I censoring”. IEEE Trans Reliab 55:613–614

    Google Scholar 

  • Herd RG (1956) Estimation of the parameters of a population from a multi-censored sample. Ph.D. Thesis, Iowa State College, Ames, Iowa

  • Hofmann G, Balakrishnan N, Ahmadi J (2005) Characterization of hazard function by Fisher information in minima and upper record values. Stat Probab Lett 72:51–57

    MATH  MathSciNet  Google Scholar 

  • Hofmann G, Cramer E, Balakrishnan N, Kunert G (2005) An asymptotic approach to progressive censoring. J Stat Plann Inference 130:207–227

    MATH  MathSciNet  Google Scholar 

  • Ibragimov IA (1956) On the composition of unimodal distributions. Teor Veroyatnost Primenen 1:283–288

    MATH  Google Scholar 

  • Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, 2nd edn, vol 1. Wiley, New York

  • Joshi PC (1978) Recurrence relations between moments of order statistics from exponential and truncated exponential distributions. Sankhyā Ser B 39:362–371

    MATH  Google Scholar 

  • Joshi PC (1979) A note on the moments of order statistics from doubly truncated exponential distribution. Ann Inst Stat Math 31:321–324

    MATH  Google Scholar 

  • Joshi PC (1982) A note on the mixed moments of order statistics from exponential and truncated exponential distributions. J Stat Plann Inference 6:13–16

    MATH  Google Scholar 

  • Kamps U (1995a) A concept of generalized order statistics. J Stat Plann Inference 48:1–23

    MATH  MathSciNet  Google Scholar 

  • Kamps U (1995b) A concept of generalized order statistics. Teubner, Stuttgart

    MATH  Google Scholar 

  • Kamps U, Cramer E (2001) On distributions of generalized order statistics. Statistics 35:269–280

    MATH  MathSciNet  Google Scholar 

  • Keseling C (1999) Characterizations of probability distributions by generalized order statistics (in German). Ph.D. Thesis, Aachen University of Technology, Aachen, Germany

  • Keseling C, Kamps U (2003) A theorem of Rossberg for generalized order statistics. Sankhyā 65:259–270

    MathSciNet  Google Scholar 

  • Kundu D, Joarder A (2006) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528

    MathSciNet  MATH  Google Scholar 

  • Kundu D, Kannan N, Balakrishnan N (2004) Analysis of progressively censored competing risks data. In: Balakrishnan N, Rao CR (eds) Advances in survival analysis. Handbook of statistics, vol 23. North-Holland, Amsterdam, pp 331–348

    Google Scholar 

  • Lin C-T, Wu SJS, Balakrishnan N (2004) Interval estimation of parameters of log-gamma distribution based on progressively censored data. Commun Stat Theory Methods 33:2595–2626

    MATH  MathSciNet  Google Scholar 

  • Lin C-T, Wu SJS, Balakrishnan N (2006a) Monte Carlo methods for Bayesian inference on the linear hazard rate distribution. Commun Stat Theory Methods 35:575–590

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  • London D (1988) Survival models. Actex Publications, Connecticut

    Google Scholar 

  • Louis TA (1982) Finding the observed information matrix when using the EM algorithm. J Roy Stat Soc Ser B 44:226–233

    MATH  MathSciNet  Google Scholar 

  • Majumdar H, Sen PK (1978) Nonparametric tests for multiple regression under progressive censoring. J Multivar Anal 8:73–95

    MATH  MathSciNet  Google Scholar 

  • Malmquist S (1950) On a property of order statistics from a rectangular distribution. Skand Aktuarietidskr 33:214–222

    MathSciNet  Google Scholar 

  • Mann NR (1969) Exact three-order-statistic confidence bounds on reliable life for a Weibull model with progressive censoring. J Am Stat Assoc 64:306–315

    Google Scholar 

  • Mann NR (1971) Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics 13:521–533

    MATH  MathSciNet  Google Scholar 

  • Marohn F (2002) A characterization of generalized Pareto distributions by progressive censoring schemes and goodness-of-fit tests. Commun Stat Theory Methods 31:1055–1065

    MATH  MathSciNet  Google Scholar 

  • Montanari GC, Cacciari M (1988) Progressively-censored aging tests on XLPE-insulated cable models. IEEE Trans Electr Insulation 23:365–372

    Google Scholar 

  • Moriguti S (1953) A modification of Schwarz’s inequality with applications to distributions. Ann Math Stat 24:107–113

    MathSciNet  MATH  Google Scholar 

  • Nagaraja HN (1982) On the non-Markovian structure of discrete order statistics. J Stat Plann Inference 7:29–33

    MATH  MathSciNet  Google Scholar 

  • Nagaraja HN (1986) A note on conditional Markov property of discrete order statistics. J Stat Plann Inference 13:37–43

    MATH  MathSciNet  Google Scholar 

  • Nagaraja HN (1992) Order statistics from discrete distributions (with discussion). Statistics 23:189–216

    MATH  MathSciNet  Google Scholar 

  • Nagaraja HN (1994) Tukey’s linear sensitivity and order statistics. Ann Inst Stat Math 46:757–768

    MATH  MathSciNet  Google Scholar 

  • Nelson W (1982) Applied life data analysis. Wiley, New York

    MATH  Google Scholar 

  • Nevzorov VB (2001) Records: mathematical theory. Translations of mathematical monographs, vol 194. American Mathematical Society, Providence

    Google Scholar 

  • Ng HKT, Balakrishnan N (2005) Weighted precedence and maximal precedence tests and an extension to progressive censoring. J Stat Plann Inference 135:197–221

    MATH  MathSciNet  Google Scholar 

  • Ng HKT, Chan PS, Balakrishnan N (2002) Estimation of parameters from progressively censored data using the EM algorithm. Comput Stat Data Anal 39:371–386

    MATH  MathSciNet  Google Scholar 

  • Ng HKT, Chan PS, Balakrishnan N (2004) Optimal progressive censoring plans for the Weibull distribution. Technometrics 46:470–481

    MathSciNet  Google Scholar 

  • Rényi A (1953) On the theory of order statistics. Acta Math Acad Sci Hung 4:191–231

    MATH  Google Scholar 

  • Rezaei M (2007) Analysis of competing risks data for lognormal model under progressive Type-II censoring. Commun Stat Theory Methods (to appear)

  • Ringer LJ, Sprinkle EE (1972) Estimation of the parameters of the Weibull distribution from multicensored samples. IEEE Trans Reliab 21:6–51

    Article  Google Scholar 

  • Robinson JA (1983) Bootstrap confidence intervals in location-scale models with progressive censoring. Technometrics 25:179–187

    Google Scholar 

  • Rüschendorf L (1985) Two remarks on order statistics. J Stat Plann Inference 11:71–74

    MATH  Google Scholar 

  • Sampford MR (1952) The estimation of response-time distributions, Part II. Biometrics 9:307–369

    MathSciNet  Google Scholar 

  • Sanjel D, Balakrishnan N (2007) A Laguerre polynomial approximation for a goodness-of-fit test for exponential distribution based on progressively censored data. J Stat Comput Simul (to appear)

  • Schilling EG (1982) Acceptance sampling in quality control. Dekker, New York

    MATH  Google Scholar 

  • Shah BK (1966) On the bivariate moments of order statistics from a logistic distribution. Ann Math Stat 37:1002–1010

    MATH  Google Scholar 

  • Shah BK (1970) Note on moments of a logistic order statistics. Ann Math Stat 41:2151–2152

    Google Scholar 

  • Sherif A, Tan P (1978) On structural predictive distribution with Type-II progressively censored Weibull data. Stat Hefte 19:247–255

    MathSciNet  MATH  Google Scholar 

  • Sinha AN, Sen PK (1982) Tests based on empirical processes for progressive censoring schemes with staggered entry and random withdrawal. Sankhyā Ser B 44:1–18

    MATH  MathSciNet  Google Scholar 

  • Sukhatme PV (1937) Tests of significance for samples of the χ 2 population with two degrees of freedom. Ann Eugen 8:52–56

    Google Scholar 

  • Tanner MA (1993) Tools for statistical inference: observed data and data augmentation methods, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Thomas DR, Wilson WM (1972) Linear order statistic estimation for the two-parameter Weibull and extreme value distributions from Type-II progressively censored samples. Technometrics 14:679–691

    MATH  Google Scholar 

  • Tiku ML (1980) Goodness of fit statistics based on the spacings of complete or censored samples. Aust J Stat 22:260–275

    Article  MATH  MathSciNet  Google Scholar 

  • Tran TTH (2006) Discrete generalized order statistics. Ph.D. Thesis, University of Oldenburg, Oldenburg, Germany

  • Tse S-K, Xiang L (2003) Interval estimation for Weibull-distributed life data under Type II progressive censoring with random removals. J Biopharm Stat 13:1–16

    MATH  Google Scholar 

  • Tse S-K, Yang C (2003) Reliability sampling plans for the Weibull distribution under Type II progressive censoring with binomial removals. J Appl Stat 30:709–718

    MathSciNet  MATH  Google Scholar 

  • Viveros R, Balakrishnan N (1994) Interval estimation of parameters of life from progressively censored data. Technometrics 36:84–91

    MATH  MathSciNet  Google Scholar 

  • Wingo DR (1973) Solution of the three-parameter Weibull equations by constrained modified quasilinearization (progressively censored samples). IEEE Trans Reliab 22:96–102

    Google Scholar 

  • Wingo DR (1993) Maximum likelihood methods for fitting the Burr Type XII distribution to multiply (progressively) censored life test data. Metrika 40:203–210

    MATH  MathSciNet  Google Scholar 

  • Wong JY (1993) Simultaneously estimating the three Weibull parameters from progressively censored samples. Microelectron Reliab 3:2217–2224

    Google Scholar 

  • Xie Q, Balakrishnan N, Han D (2007) Exact inference and optimal censoring scheme for a simple step-stress model under progressive Type-II censoring (submitted)

  • Yuen H-K, Tse S-K (1996) Parameters estimation for Weibull distributed lifetimes under progressive censoring with random removals. J Stat Comput Simul 55:57–71

    MATH  MathSciNet  Google Scholar 

  • Zheng G (2001) A characterization of the factorization of hazard function by the Fisher information under Type-II censoring with application to the Weibull family. Stat Probab Lett 52:249–253

    MATH  Google Scholar 

  • Zheng G, Gastwirth JL (2003) Fisher information in ordered randomly censored data with applications to characterization problems. Stat Sin 13:507–517

    MATH  MathSciNet  Google Scholar 

  • Zheng G, Park S (2004) On the Fisher information in multiply censored and progressively censored data. Commun Stat Theory Methods 33:1821–1835

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Balakrishnan.

Additional information

This invited paper is discussed in the comments available at: http://dx.doi.org/10.1007/s11749-007-0062-x, http://dx.doi.org/10.1007/s11749-007-0063-9, http://dx.doi.org/10.1007/s11749-007-0064-8, http://dx.doi.org/10.1007/s11749-007-0065-7, http://dx.doi.org/10.1007/s11749-007-0066-6, http://dx.doi.org/10.1007/s11749-007-0067-5, http://dx.doi.org/10.1007/s11749-007-0068-4, http://dx.doi.org/10.1007/s11749-007-0069-3, http://dx.doi.org/10.1007/s11749-007-0070-x, http://dx.doi.org/10.1007/s11749-007-0071-9.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Balakrishnan, N. Progressive censoring methodology: an appraisal. TEST 16, 211–259 (2007). https://doi.org/10.1007/s11749-007-0061-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11749-007-0061-y

Keywords

Mathematics Subject Classification (2000)

Navigation