Life Cycle Reliability and Safety Engineering

, Volume 8, Issue 4, pp 329–335 | Cite as

Attribute control charts for the Dagum distribution under truncated life tests

  • Srinivasa Rao GaddeEmail author
  • A. K. Fulment
  • P. K. Josephat
Original Research


In this paper, an attribute control chart for lifetime of the product follows Dagum distribution under number of failures before a specified time period is proposed. The sensitivity of the proposed chart is studied using the average run length (ARL). The tables are presented for all shift sizes, different sample sizes, various values of shape parameters and specified ARL and shift constants. An application of the proposed control chart in industry for monitoring of non-conforming items is illustrated with simulation data.


Dagum distribution Attribute control chart Life test Average run length Simulation 

Mathematics Subject Classification

62N05 90B25 62P30 62H10 



  1. Al-Oraini HA, Rahim MA (2003) Economic statistical design of control charts for systems with gamma (λ, 2) in-control times. J Appl Stat 30:397–409MathSciNetzbMATHGoogle Scholar
  2. Amin R, Reynolds MR Jr, Bakir ST (1995) Non-parametric quality control charts based on the sign statistic. Commun Stat Theory Methods 24:1597–1623CrossRefGoogle Scholar
  3. Arif OH, Aslam M, Butt KA (2018) Attribute control chart for a lognormal distribution under accelerated time-censoring. J Comput Theor Nanosci 15(3):919–923CrossRefGoogle Scholar
  4. Aslam M, Jun C-H (2015) Attribute control charts for the Weibull distribution under truncated life tests. Qual Eng 27:283–288CrossRefGoogle Scholar
  5. Aslam M, Khan N, Jun C-H (2016) A control chart for time truncated life tests using pareto distribution of second kind. J Stat Comput Simul 86:2113–2122MathSciNetCrossRefGoogle Scholar
  6. Azam M, Aslam M, Jun C-H (2015) Designing of a hybrid exponentially weighted moving average control chart using repetitive sampling. Int J Adv Manuf Technol 77:1927–1933CrossRefGoogle Scholar
  7. Chen G, Cheng SW, Xie H (2001) Monitoring process mean and variability with one EWMA chart. J Qual Tech 33:223–233CrossRefGoogle Scholar
  8. Cheng SW, Thaga K (2006) Single variables control charts: an overview. Qual Reliab Eng Int 22:811–820CrossRefGoogle Scholar
  9. Cohen AC, Whitten BJ (1988) Parameter estimation in reliability and life span models. Marcel Dekker, New YorkzbMATHGoogle Scholar
  10. Dagum C (1977) A new model of personal income distribution: specification and estimation. Econ Appl XXX:413–436Google Scholar
  11. Dagum C (1980) The generation and distribution of income, the Lorenz curve and the Gini ratio. Econ Appl XXXIII:327–367Google Scholar
  12. Domma F, Giordano S, Zenga M (2009) The Fisher information matrix in doubly censored data from the Dagum distribution, Working Paper No 8, Department of Economics and Statistics, University of Calabria, ItalyGoogle Scholar
  13. Domma F, Giordano S, Zenga M (2011) The Fisher information matrix in right censored samples from the Dagum distribution, Working Paper No. 4, Department of Economics and Statistics, University of Calabria, ItalyGoogle Scholar
  14. Haq A (2014) An improved mean deviation exponentially weighted moving average control chart to monitor process dispersion under ranked set sampling. J Stat Simul Comput 84:2011–2024MathSciNetCrossRefGoogle Scholar
  15. He D, Grigoryan A, Sigh M (2001) Design of double-and triple-sampling X-bar control charts using genetic algorithms. Int J Prod Res 40:1387–1404CrossRefGoogle Scholar
  16. Joekes S, Barbosa EP (2013) An improved attribute control chart for monitoring non-conforming proportion in high quality processes. Control Eng Pract 21:407–412CrossRefGoogle Scholar
  17. Kleiber C (2008) A guide to the Dagum distribution. In: Duangkamon C (ed) Modeling income distributions and lorenz curves series: economic studies in inequality, social exclusion and well-being, vol 5. Springer, New York, NYGoogle Scholar
  18. Kleiber C, Kotz S (2003) Statistical size distribution in economics and actuarial sciences. Wiley, Hoboken, NJCrossRefGoogle Scholar
  19. Lee SH, Park JH, Jun C-H (2014) An exponentially weighted moving average chart controlling false discovery rate. J Stat Simul Comput 84:1830–1840MathSciNetCrossRefGoogle Scholar
  20. Lin YC, Chou CY (2007) Non-normality and the variable parameters ×× bar control charts. Eur J Oper Res Soc 176:361–373CrossRefGoogle Scholar
  21. McCracken AK, Chakraborti S (2013) Control charts for joint monitoring of mean and variance: an overview. Qual Tech Quant Manag 10:17–36CrossRefGoogle Scholar
  22. Montgomery DC (2009) Introduction to statistical quality control, 6th edn. Wiley, AmsterdamzbMATHGoogle Scholar
  23. Nichols MD, Padgett WJ (2006) A bootstrap control chart for Weibull percentiles. Qual Reliab Eng Int 22:141–151CrossRefGoogle Scholar
  24. Ou Y, Wu Z, Khoo MB, Chen N (2015) A rational sequential probability ratio test control chart for monitoring process shifts in mean and variance. J Stat Simul Comput 85:1765–1781MathSciNetCrossRefGoogle Scholar
  25. Quintano C, D’Agostino A (2006) Studying inequality in income distribution of single-person households in four developed countries. Rev Income Wealth 52(4):525–546CrossRefGoogle Scholar
  26. Rao GS (2018) A control chart for time truncated life tests using exponentiated half logistic distribution. Appl Math Inf Sci Int J 12(1):125–131MathSciNetCrossRefGoogle Scholar
  27. Shafqat A, Hussain J, Al-Nasser AD, Aslam M (2018) Attribute control chart for some popular distributions. Commun Stat Theory Methods 47(8):1978–1988MathSciNetCrossRefGoogle Scholar
  28. Wu Z, Wang Q (2007) An np control chart using double inspections. J Appl Stat 34:843–855MathSciNetCrossRefGoogle Scholar
  29. Wu Z, Luo H, Zhang X (2006) Optimal np control chart with curtailment. Eur J Oper Res 174:1723–1741CrossRefGoogle Scholar
  30. Zandi F, Niaki STA, Nayeri MA, Fathi M (2011) Change-point estimation of the process fraction non-conforming with a linear trend in statistical process control. Int J Comput Integr Manuf 24:939–947CrossRefGoogle Scholar

Copyright information

© Society for Reliability and Safety (SRESA) 2019

Authors and Affiliations

  1. 1.Department of StatisticsThe University of DodomaDodomaTanzania

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