A likelihood control chart for monitoring bivariate lifetime processes

Document Type : Research Paper

Authors

1 Khorasan Razavi Agricultural and Natural research and Education center, Mashhad, Iran

2 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

In this survey, two new control charts CCLR and CCALR for bivariate exponential variables by dependence structure based on Farlie-Gumbel-Morgenstern copula model are introduced. Simulation study is done to make a comparison between two proposed control charts in terms of average run length (ARL). Results show that the CCALR performs better than CCLR. A
numerical example is provided to fortify the theoretical findings.

Keywords


[1] Abbasi Ganji Z, Sadeghpour Gildeh B, Amini M, and Babaei A (2022) Statistical inference for the non-conforming rate of FGM copula-based bivariate exponential lifetime. Journal of Mahani Mathematical Research Center, 11 (1): 1-27.
[2] Apley DW, & Shi J (1999) The GLRT for statistical process control of auto correlated processes. IIE Transactions, 31 (12): 1123-1134.
[3] Cadre B, Pelletier B, Pudlo P (2013) Estimation of density level sets with a given probability content. Journal of Nonparametric Statistics 25 (1): 261-272.
[4] Capizzi G, Masarotto G (2008) Practical design of generalized likelihood ratio control charts for autocorrelated data. Technometrics 50: 357-370.
[5] Liu SQ, Su Q, Li P (2014) Research on the quality stability evaluation and monitoring based on the pre-control chart. International Journal of Quality & Reliability Management 31 (9): 966-982.
[6] MacCarthy BL, Wasusri T (2002) A review of non-standard applications of statistical process control (SPC) charts. International Journal of Quality & Reliability Management 19 (3): 295-320.
[7] Qi D, Li Z, Zi X,Wang Z (2017)Weighted likelihood ratio chart for statistical monitoring of queuing systems. Quality and Reliability Engineering International 14 (1): 19-30.
[8] Qi D, Wang Z, Zi X, Li Z (2016) Phase II monitoring of generalized linear pro les using weighted likelihood ratio charts. Computers & Industrial Engineering 94: 178-187.
[9] Sklar AW (1959) Fonctions de repartition a n dimension et leurs marges. Publications de l'Institut de Statistique de l'Universite de Paris, 8: 229-231.
[10] Verdier G (2013) Application of copulas to multivariate control charts. Journal of Statistical Planning and Inference 143: 2151-2159.
[11] Wu C, Yu M, Zhuang F (2017) Properties and enhancements of robust likelihood CUSUM control chart. Computers & Industrial Engineering 114: 80-100.
[12] Xu L, Peng Y, Reynolds MR (2015) An individuals generalized likelihood ratio control chart for monitoring linear pro les. Quality and Reliability Engineering International 31 (4): 589-599.
[13] Xu L, Wang S, Reynolds MR (2013) A generalized likelihood ratio control chart for monitoring the process mean subject to linear drifts. Quality and Reliability Engineering International 29 (4): 545-553.
[14] Zhang J, Li Z, Wang Z (2009) Control chart based on likelihood ratio for monitoring linear pro les. Computational Statistics and Data Analysis 53 (4): 1440-1448.
[15] Zhang J, Zou C, Wang Z (2010) A control chart based on likelihood ratio test for monitoring process mean and variability. Quality and Reliability Engineering international 26: 63-73.
[16] Zhou Q, Luo Y,Wang Z (2010) A control chart based on likelihood ratio test for detecting patterned mean and variance shifts. Computational Statistics and Data Analysis 54:1634-1645.
[17] Zhou Q, Zou C, Wang Z, Jiang W (2012) Likelihood-based EWMA charts for monitoring poisson count data with time-varying sample sizes. Journal of American Statistical Association 107 (499): 1049-1062.
  • Receive Date: 28 February 2022
  • Revise Date: 06 April 2022
  • Accept Date: 17 April 2022
  • First Publish Date: 17 April 2022