Moving Average control charts for Burr X and Inverse Gaussian distributions

• Authors: SHAFQAT Ambreen , ASLAM Muhammad , ALBASSAM Mohammed
• Languages of publication: EN

Abstracts

EN

The Burr X and inverse Gaussian (IG) distributions have been considered to design an attribute control chart for time truncated life test with the moving average (MA) scheme w. The presentation of the MA control chart has been estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is determined for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart has been compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than that of the existing control chart.

Keywords

EN

control chart; Burr X distribution; inverse Gaussian distribution; average run length

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2020
• Volume: 30
• Issue: 4
• Pages: 81-94

Contributors

author

SHAFQAT Ambreen

• Department of Statistics and Financial Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China

author

ASLAM Muhammad

• Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

author

ALBASSAM Mohammed

• Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

References

• BISSELL D., MONTGOMERY D.C., Introduction to statistical quality control, Stat., 2006, DOI: 10.2307 /2988304.
• DOUGLAS M.C., Introduction to Statistical Quality Control, Wiley, 2009.
• KRAMER H., SCHMID W., The influence of parameter estimation on the ARL of Shewhart type charts for time series, Stat. Pap., 2000, DOI: 10.1007/bf02926102.
• PRAJAPATI D.R., MAHAPATRA P.B., Control charts for variables to monitor the process mean and dispersion. A literature review, Int. J. Product. Qual. Manage., 2009, DOI: 10.1504/IJPQM.2009.024223.
• GADRE M.P., RATTIHALLI R.N., Some group inspection based multi-attribute control charts to identify process deterioration, Econ. Qual. Control., 2010, DOI: 10.1515/eqc.2005.191.
• HUANG S., YANG J., XIE M., A Study of control chart for monitoring exponentially distributed characteristics based on type-II censored samples, Qual. Reliab. Eng. Int., 2017, DOI: 10.1002/qre.2122.
• MONTGOMERY D.C., Introduction to statistical quality control, 6th Ed., 2009, DOI: 10.1017/CBO9781107415324.004.
• KHOO M.B.C., A moving average control chart for monitoring the fraction non-conforming, Qual. Rel. Eng. Int., 2004, DOI: 10.1002/qre.576.
• WONG H.B., GAN F.F., CHANG T.C., Designs of moving average control chart, J. Stat. Comput. Simul., 2004, DOI: 10.1080/0094965031000105890.
• PATIL S.H., RATTIHALLI R.N., Economic design of moving average control chart for continued and ceased production process, Econ. Qual. Control., 2010, DOI: 10.1515/eqc.2009.129.
• PATIL S.H., SHIRKE D.T., Economic design of moving average control chart for non-normal data using variable sampling intervals, J. Ind. Prod. Eng., 2015, DOI: 10.1080/21681015.2015.1023854.
• AZAM M., ASLAM M., JUN C.H., Designing of a hybrid exponentially weighted moving average control chart using repetitive sampling, Int. J. Adv. Manuf. Technol., 2015, DOI: 10.1007/s00170-014-6585-x.
• AHMAD L., ASLAM M., KHAN N., JUN C.H., Double moving average control chart for exponentially distributed life using EWMA, AIP Conf. Proc., 2017, DOI: 10.1063/1.5012222.
• ASLAM M., AHMAD L., JUN C.H., ARIF O.H., A control chart for COM-Poisson distribution using multiple dependent state sampling, Qual. Reliab. Eng. Int., 2016, DOI: 10.1002/qre.1965.
• AZAM M., AHMAD L., ASLAM M., Design of X-bar chart for Burr distribution under the repetitive sampling, Sci. Int., 2016, 28 (4), 3265–3271.
• SHAFQAT A., HUANG Z., ASLAM M., Design of X-bar control chart based on inverse Rayleigh distribution under repetitive group sampling, Ain Shams Eng. J., 2020, DOI: 10.1016/j.asej.2020.06.001.
• ALGHAMDI S.A.D., ASLAM M., KHAN K., JUN C.H., A time truncated moving average chart for the Weibull distribution, IEEE Access., 2017, DOI: 10.1109/ACCESS.2017.2697040.
• HAQ A., BROWN J., MOLTCHANOVA E., New exponentially weighted moving average control charts for monitoring process mean and process dispersion, Qual. Reliab. Eng. Int., 2015, DOI: 10.1002/qre.1646.
• KHOO M.B.C., YAP P.W., Joint monitoring of process mean and variability with a single moving average control chart, Qual. Eng., 2005, DOI: 10.1081/QEN-200028689.
• LI Z., ZOU C., GONG Z., WANG Z., The computation of average run length and average time to signal. An overview, J. Stat. Comput. Simul., 2014, DOI: 10.1080/00949655.2013.766737.
• MOLNAU W.E., RUNGER G.C., MONTGOMERY D.C., SKINNER K.R., LOREDO E.N., PRABHU S.S., A program for ARL calculation for multivariate EWMA charts, J. Qual. Technol., 2001, DOI: 10.1080/00224065.2001.11980109.
• CROWDER S.V., A simple method for studying run-length distributions of exponentially weighted moving average charts, Technometrics, 1987, DOI: 10.1080/00401706.1987.10488267.
• CHANANET C., SUKPARUNGSEE S., AREEPONG Y., The ARL of EWMA Chart for monitoring ZINB model using Markov chain approach, Int. J. Appl. Phys. Math., 2014, DOI: 10.7763/ijapm.2014.v4.290.
• SPARKS R.S., A group of moving averages control plan for signaling varying location shifts, Qual. Eng., 2003, DOI: 10.1081/QEN-120018385.
• SPARKS R., Weighted moving averages: An efficient plan for monitoring specific location shifts, Int. J. Prod. Res., 2004, DOI: 10.1080/0020754042000197720.
• WETHERILL G.B., BROWN D.W., Statistical process control for the process industries, Front. Stat. Qual. Control, 1992, DOI: 10.1007/978-3-662-11789-7_17.
• SHAFQAT A., HUSSAIN J., AL-NASSER A.D., ASLAM M., Attribute control chart for some popular distributions, Commun. Stat.-Theory Meth., 2018, DOI: 10.1080/03610926.2017.1335414.
• SCHAFFER J.R., KIM M.J., Number of replications required in control chart Monte Carlo simulation studies, Commun. Stat. Simul. Comput., 2007, DOI: 10.1080/03610910701539963.
• SHAFQAT A., HUANG Z., ASLAM M., NAWAZ M.S., A nonparametric repetitive sampling DEWMA control chart based on linear prediction, IEEE Access., 2020, DOI: 10.1109/ACCESS.2020.2989132.
• ASLAM M., BANTAN R.A.R., KHAN N., Design of SN2-NEWMA control chart for monitoring process having indeterminate production data, Processes, 2019, DOI: 10.3390/pr7100742.
• SULLIVAN J.H., WOODALL W.H., A comparison of multivariate control charts for individual observations, J. Qual. Technol., 1996, DOI: 10.1080/00224065.1996.11979698.
• FU J.C., SPIRING F.A., XIE H., On the average run lengths of quality control schemes using a Markov chain approach, Stat. Probab. Lett., 2002, DOI: 10.1016/S0167-7152(01)00183-3.

Identifiers

DOI

10.37190/ord200406