A control chart based on likelihood ratio test for monitoring process mean and variability

Quality and Reliability Engineering International

Volumn 26, Issue 1, 2010, Pages 63-73

  Zhang, Jiujun ^a,b   Zoub, Changliang ^b   Wang, Zhaojun ^b  

^a LIAONING UNIVERSITY   (China)

^b NANKAI UNIVERSITY   (China)

Author keywords

EWMA; Likelihood ratio test; Process mean; Process variance; Statistical process control

Indexed keywords

AVERAGE RUN LENGTHS; CHEMICAL PROCESS CONTROL; CONTROL CHARTS; DATA EXAMPLES; GENERALIZED LIKELIHOOD RATIO TEST; LIKELIHOOD RATIO TEST; LIKELIHOOD RATIO TESTS; MARKOV CHAIN MODELS; MONITORING PROCESS; PROCESS MEAN; PROCESS VARIANCE; SAMPLING POINTS;

MARKOV PROCESSES; MAXIMUM LIKELIHOOD ESTIMATION; QUALITY CONTROL; STATISTICAL TESTS; SURFACE TREATMENT;

STATISTICAL PROCESS CONTROL;

EID: 76949094946     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.1036     Document Type: Article

References (19)

1. Saniga EM. Econometric statistical control chart design with an application to x̄ and R control charts. Technometrics 1989; 31:313-320.
2. Rahim MA. Determination of optimal design parameters of joint x̄ and R charts. Journal of Quality Technology 1989; 21:65-70.
3. Costa AFB. Joint econometric design of x̄ and R control charts for processes subject to two independent assignable causes. IIE Transactions 1993; 25:27-33.
4. Rahim MA, Costa AFB. Joint economic design of x̄ and R charts under Weibull shock models. International Journal of Production Research 2000; 28:2871-2889.
5. Gan FF. Joint monitoring of process mean and variance using exponentially weighted moving average control charts. Technometrics 1995; 37:446-453.
6. Reynolds MR, Stumbos ZG. Monitoring the process mean and variance using individual observations and variable sampling intervals. Journal of Quality Technology 2001; 33:181-205.
7. Domangun R, Patch SC. Some omnibus exponentially weighted moving average statistical process monitoring schemes. Technometrics 1991; 33:299-314.
8. Chen G, Cheng SW, Xie H. Monitoring process mean and variability with one EWMA chart. Journal of Quality Technology 2001; 33:223-233.
9. Costa AFB, Rahim MA. Monitoring process mean and variability with one non-central chi-square chart. Journal of Applied Statistics 2004; 31: 1171-1183.
10. Wu Z, Tian Y. Weighted-loss-function CUSUM chart for monitoring mean and variance of a production process. International Journal of Production Research 2005; 43:3027-3044.
11. Calzada ME, Scariano SM, Chen G. Computing average run lengths for the MaxEWMA chart. Communications in Statistics: Simulation and Computation 2004; 33:489-503.
12. Lowry CA, Woodall WH, Champ CW, Rigdon WE. A multivariate exponentially weighted moving average control chart. Technometrics 1992; 34:46-53.
13. Lucas JM, Saccucci MS. Exponentially weighted moving average control schemes: Properties and enhancements (with Discussion). Technometrics 1990; 32:1-29.
14. Huang L, Yeh AB, Wu CW. Monitoringmultivariate process variability for individual observations. Journal of Quality Technology 2007; 39:258-278.
15. Zou C, Tsung F, Wang Z. Monitoring general linear profiles using multivariate EWMA schemes. Technometrics 2007; 49:395-408.
16. Han D, Tsung F. A reference-free cuscore chart for dynamicmean change detection and a unified framework for charting performance comparison. Journal of the American Statistical Association 2006; 101:368-386.
17. Brook D, Evans DA. An approach to the probability distribution of cusum run length. Biometrika 1972; 59:539-549.
18. Runger GC, Prabhu SS. A Markov chain model for the multivariate exponentially weighted moving average control chart. Journal of American Statistical Association 1996; 91:1701-1706.
19. Molnau WE, Runger GC, Montgomery DC, Skinner KR, Loredo EN, Prabhu SS. A program for ARL calculation for multivariate EWMA Charts. Journal of Quality Technology 2001; 33:515-521.