A Two-Plan Sampling System for Life Testing Under Weibull Distribution

  • Aslam, Muhammad (Department of Statistics, Forman Christian College University) ;
  • Balamurali, Saminathan (Department of Mathematics, Kalasalingam University) ;
  • Jun, Chi-Hyuck (Department of Industrial and Management Engineering, Pohang University of Science and Technology) ;
  • Ahmad, Munir (Department of Statistics, National College of Business Administration & Economics)
  • Received : 2009.07.27
  • Accepted : 2010.01.20
  • Published : 2010.03.01


A two-plan sampling system is proposed for a failure-censored life testing when the lifetime follows a Weibull distribution with known shape parameter. The proposed sampling system is based on a switching rule, for switching between the tightened and the normal inspection levels when lots are submitted for inspection in the order of production or in some other systematic way. The design parameters of the proposed sampling system are determined by the two-point approach considering the producer's risks and the consumer's at the specified acceptable reliability level and the lot tolerance reliability level, respectively. It has been observed that the proposed system requires only a single failure for the observation.


Acceptable Reliability Level;Consumer's Risk;Lot Tolerance Reliability Level;OC Curve;Producer's Risk;Sampling by Variables


Supported by : National Research Foundation of Korea


  1. Balamurali, S. and Jun, C-H. (2009), Designing of a variables two plan system by minimizing the average sample number, Journal of Applied Statistics, 36, 1159-1172.
  2. Calvin, T. W. (1977), TNT zero acceptance number sampling, American Society for Quality Control Annual Technical Conference Transactions, Philadelphia, PA, 35-39.
  3. Dodge, H. F. (1965), Evaluation of a sampling system having rules for switching between normal and tightened inspection, Technical Report No.14, Statistics Center, Rutgers University, Piscataway, NJ.
  4. Fertig, K. W. and Mann, N. R. (1980), Life-test sampling plans for two-parameter Weibull populations, Technometrics, 22, 165-177.
  5. Hald, A. and Thyregod, P. (1965), The composite operating characteristic under normal and tightened sampling inspection by attributes, Bulletin of the International Statistical Institute, 41, 517-529.
  6. Jun, C-H., Balamurali, S., and Lee, S-H. (2006), Variables sampling plans for Weibull distributed lifetimes under sudden death testing, IEEE Transactions on Reliability, 55(1), 53-58.
  7. Muthuraj, D. and Senthilkumar, D. (2006), Designing and construction of tightened-normal-tightened variables sampling scheme, Journal of Applied Statistics, 33, 101-111.
  8. Schneider, H. (1989), Failure-censored variables-sampling plans for lognormal and Weibull distributions, Technometrics, 31, 199-206.
  9. Soundararajan, V. and Vijayaraghavan, R. (1990), Construction and Selection of Tightened-Normal-Tightened (TNT) Plans, Journal of Quality Technology, 22, 146-153.
  10. Stephens, K. S. and Larson, K. E. (1967), An evaluation of the MIL-STD 105D system of sampling plans, Industrial Quality Control, 23, 310-319.
  11. Vijayaraghavan, R. and Soundararajan, V. (1996), Procedures and tables for the selection of tightenednormal- tightened (TNT(n; $c_1$, $c_2$)) sampling schemes, Journal of Applied Statistics, 23, 69-79.

Cited by

  1. Attribute Control Charts for the Weibull Distribution under Truncated Life Tests vol.27, pp.3, 2015,
  2. Design of a Quick Switching Sampling System Based on the Coefficient of Variation vol.6, pp.4, 2018,