Abstract

This study is to propose and design a new X-bar control chart utilizing previous subgroup information called a multiple dependent state control chart based on double control limits. The in-control Average Run Length (ARL) and the out-of-control ARLs according to mean shifts are derived. The performance of the proposed control chart is compared with the traditional X-bar chart in terms of ARLs, which shows the outperformance of the proposed control chart. This idea can be easily extended to other types of control charts.

Keywords:

Average run length, double control limits, multiple dependent state plan,

References

1. Aslam, M., M. Azam and C.H. Jun, 2013. Multiple dependent states sampling plan based on process capability index. J. Test. Eval., 41(2): 340-346.
   CrossRef    
2. Balamurali, S. and C.H. Jun, 2007. Multiple dependent state sampling plans for lot acceptance based on measurement data. Eur. J. Oper. Res., 180: 1221-1230.
   CrossRef    
3. Ben-Daya, M. and M.A. Rahim, 2000. Effect of maintenance on the economic design of X-bar control chart. Eur. J. Oper. Res., 120: 131-143.
   CrossRef    
4. Caballero Morales, S.O., 2013. Economic statistical design of integrated x-bar-s control chart with preventive maintenance and general failure distribution. PLoS ONE, 8(3): e59039.
   CrossRef    PMid:23527082 PMCid:PMC3601122    
5. Chen, W.S., F.J. Yu, R.S. Guh and Y.H. Lin, 2011. Economic design of x-bar control charts under preventive maintenance and Taguchi loss functions. J. Appl. Res., 3: 103-109.
   
6. Chiu, H.N., 1995. The economic design of X-bar and S2 control charts with preventive maintenance and increasing hazard rate. J. Qual. Maint. Eng., 1: 17-40.
   CrossRef    
7. Fallah Nezhad, M.S. and S.T.A. Niaki, 2010. A new monitoring design for uni-varite statistical control charts. Inform. Sci., 180: 1051-1059.
   CrossRef    
8. He, D., A. Grigoryan and M. Sigh, 2002. Design of double- and triple-sampling X-bar control charts using genetic algorithms. Int. J. Prod. Res., 40(6): 1387-1404.
   CrossRef    
9. Mehrafrooz, Z. and R. Noorossana, 2011. An integrated model based on statistical process control and maintenance. Comput. Ind. Eng., 61: 1245-1255./> CrossRef    
10. Rahim, M.A., 1989. Determination of optimal design parameters of joint X bar and R charts. J. Qual. Technol., 21: 65-70.
    
11. Saniga, E., 1989. Economical statistical control-chart designs with an application to X-bar and R charts. Technometrics, 31: 313-320.
    CrossRef    
12. Saniga, E. and D.J. Davis, 2001. Economic-statistical design of X-bar and R or X-bar and S charts. J. Qual. Technol., 33: 234-241.
    
13. Wortham, A.W. and R.C. Baker, 1976. Multiple deferred state sampling inspection. Int. J. Prod. Res., 14: 719-731.
    CrossRef    
14. Zhang, Y., P. Castagliola, Z. Wu and M. Khoo, 2011. The variable sampling interval X-bar chart with estimated parameters. Qual. Reliab. Eng. Int., 28: 19-34.
    CrossRef    

Competing interests

The authors have no competing interests.

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The authors have no competing interests.