Main Article Content


In this study, a multivariate gamma distribution is first introduced. Then, by defining a new statistic, three control charts called the MG charts, are proposed for this distribution. The first control chart is based on the exact distribution of this statistic, the second control chart is based on the Satterthwaite approximation, and the last is based on the normal approximation. Efficiency of the proposed control charts is evaluated by average run length (ARL) criterion.


Multivariate gamma distribution chi-square distribution average run length Satterthwaite approximation

Article Details

How to Cite
Torabi, H., Enami, S., & Niaki, S. (2021). New Control Charts for a Multivariate Gamma Distribution. Pakistan Journal of Statistics and Operation Research, 17(3), 607-614.


  1. Aslam, M., Srinivasa Rao, G., Ahmad, L. & Jun, C.H. (2017). A control chart for multivariate Poisson distribution using repetitive sampling. Journal of Applied Statistics, 44(1), 123–136. DOI:
  2. Ali Raza, M. & Aslam, M. (2018). Design of control charts for multivariate Poisson distribution using generalized multiple dependent state sampling. Quality Technology & Quantitative Management, 16(6),629-650. DOI:
  3. Aksoy, H. (2000). Use of gamma distribution in hydrological analysis. Turkish Journal of Engineering and Environmental Sciences, 24(6), 419-428.
  4. Agarwal, S.K. & Kalla, S.L. (1996). A generalized gamma distribution and its application in reliability. Communications in Statistics - Theory and Methods, 25(1), 201 – 210. DOI:
  5. Cozzucoli, P. C. & Marozzi, M. (2018). Monitoring multivariate Poisson processes: A review and some new results. Quality Technology & Quantitative Management, 15(1), 53–68. DOI:
  6. Casella, G. & Berger, R.L. (2002). Statistical Inference (Vol.2). Pacific Grove, CA: Duxbury.
  7. Chiu, J. E. & Kuo, T.I. (2007). Attribute control chart for multivariate Poisson distribution. Communications in Statistics-Theory and Methods, 37(1), 146–158. DOI:
  8. Derya, K. & Canan, H. (2012). Control Charts for Skewed Distributions: Weibull, Gamma, and Lognormal. Advances in Methodology & Statistics. Metodoloskizvezki, 9(2), 95-106.
  9. Khan, N., Aslam, M., Ahma, L. & Jun, C.H. (2017). A control chart for gamma distributed variables using repetitive sampling scheme. Pakistan Journal of Statistics and Operation Research, 13(1), 47–61. DOI:
  10. Mori, S., Nakata, D. & Kaneda, T. (2015). An Application of Gamma Distribution to the Income Distribution and the Estimation of Potential Food Demand Functions. Modern Economy, 6(9), 1001-1017. DOI:
  11. Montgomery, D.C. (2013). Design & Analysis of Experiments. John Wiley & Sons.
  12. Tan, C.M., Raghavan, N. & Roy, A. (2007). Application of gamma distribution in electro migration for submicron interconnects. Journal of Applied Physics, 102, 103703. DOI:
  13. Wilson, E.B. & Hilferty, M.M. (1931). The Distribution of Chi-Squares. Proceedings of the National Academy of Sciences of the United States of America, 17(12), 684–688. DOI:
  14. Zhang, C.W., Xie, M., Liu, J.Y. & Goh, T.N. (2007). A control chart for the Gamma distribution as a model of time between events. International Journal of Production Research, 45(23), 5649-5666. DOI:

Most read articles by the same author(s)