Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

An attribute inspection control chart for process mean monitoring

  • 187 Accesses

  • 11 Citations

Abstract

This paper proposes a new control chart, denoted by \( {\overset{-}{X}}^{att} \), for evaluating the stability of a process mean. This chart is based on attribute inspection rather than physical measurements (taken with an instrument such as a caliper or precise balance) of the quality characteristics of interest of the sampled items. Based on a go–no-go gauge device (which generates five categorizations), the average of a quality characteristic of interest is controlled. In equally spaced times, samples of n items are collected, and the averages are estimated by means of \( {\overset{-}{X}}^{att} \) based solely on the obtained categorization to decide whether the process is in control. Once the distribution of \( {\overset{-}{X}}^{att} \) is calculated, the decision problem is defined in terms of a mathematical programming formulation to find the dimensions to be used in the go–no-go gauge and to find the control limits that minimize the average run length (ARL) for the out-of-control situation and that are constrained to a prefixed ARL for the under-control situation. As shown by extensive computational experiments, the newly introduced \( {\overset{-}{X}}^{att} \) control chart outperforms the conventional \( \overset{-}{X} \) control chart for small shifts in the means and is still competitive otherwise. Because the new \( {\overset{-}{X}}^{att} \) control chart uses attributes, it can be considered a viable alternative to the conventional \( \overset{-}{X} \) control chart.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Abujiya MR, Riaz M, Lee MH (2016) A new combined Shewhart-cumulative sum S chart for monitoring process standard deviation. Qual Reliab Eng Int 32(3):1149–1165

  2. 2.

    Aparisi F, de Luna MA (2009) Synthetic X¯ control charts optimized for in-control and out-of-control regions. Comput Oper Res 36(12):3204–3214

  3. 3.

    Aslam M, Azam M, Khan N, Jun CH (2015a) A mixed control chart to monitor the process. Int J Prod Res 53(15):4684–4693

  4. 4.

    Aslam M, Nazir A, Jun CH (2015b) A new attribute control chart using multiple dependent state sampling. Trans Inst Meas Control 37(4):569–576

  5. 5.

    Chung KJ (1993) An economic study of X-charts with warning limits. Comput Ind Eng 24(1):1–7

  6. 6.

    Haridy S, Wu Z, Lee KM, Rahim MA (2014) An attribute chart for monitoring the process mean and variance. Int J Prod Res 52(11):3366–3380

  7. 7.

    Ho LL, Quinino RC (2016) Combining attribute and variable data to monitor process variability: MIX S2 control chart. Int J Adv Manuf Technol:1–8. DOI: 10.1007/s00170-016-8702-5. (Available on line 14th April 2016)

  8. 8.

    Kennedy CW, Hoffman EG, Bond SD (1987) Inspection and gaging, 6th edn. Industrial Press Inc., NewYork

  9. 9.

    Knoth S (2015) Run length quantiles of EWMA control charts monitoring normal mean or/and variance. Int J Prod Res 53(15):4629–4647

  10. 10.

    Leoni RC, Costa AFB, Machado MAG (2015) The effect of the autocorrelation on the performance of the T2 chart. Eur J Oper Res 247(1):155–165

  11. 11.

    Liu Y, Xue L (2015) The optimization design of EWMA charts for monitoring environmental performance. Ann Oper Res 228(1):113–124

  12. 12.

    Makis V (2008) Multivariate Bayesian control chart. Oper Res 56(2):487–496

  13. 13.

    Montgomery DC (2008) Introduction to statistical quality control, 6th edn. John Wiley & Sons, New York

  14. 14.

    Nenes G, Panagiotidou S (2013) An adaptive Bayesian scheme for joint monitoring of process mean and variance. Comput Oper Res 40(11):2801–2815

  15. 15.

    Niaki STA, Abbasi B (2007) Bootstrap method approach in designing multi-attribute control charts. Int J Adv Manuf Technol 35(5–6):434–442

  16. 16.

    Ou Y, Wu Z, Yu FJ, Shamsuzzaman M (2011) An SPRT control chart with variable sampling intervals. Int J Adv Manuf Technol 56(9–12):1149–1158

  17. 17.

    Prajapati DR, Singh S (2016) Autocorrelated process monitoring using simple and effective X¯ chart. Int J Adv Manuf Technol 85(1):929–939

  18. 18.

    Quinino RC, Ho LL, Trindade ALG (2015) Monitoring the process mean based on attribute inspection when a small sample is available. J Oper Res Soc 66(11):1860–1867

  19. 19.

    Riaz M & Does RJMM (2009) A process variability control chart. Computational statistics 24.(2): 345–368.

  20. 20.

    Wu Z, Jiao J (2008) A control chart for monitoring process mean based on attribute inspection. Int J Prod Res 46(15):4331–4347

  21. 21.

    Wu Z, Khoo MB, Shu L, Jiang W (2009) An np control chart for monitoring the mean of a variable based on an attribute inspection. Int J Prod Econ 121(1):141–147

  22. 22.

    Yang M, Wu Z, Lee KM, Khoo MB (2012) The X control chart for monitoring process shifts in mean and variance. Int J Prod Res 50(3):893–907

  23. 23.

    Yang SF, Arnold BC (2016) A new approach for monitoring process variance. J Stat Comput Simul 86:2749–2765

  24. 24.

    Yang SF, Arnold BC (2016) Monitoring process variance using an ARL-unbiased EWMA-p control chart. Qual Reliab Eng Int 32(3):1227–1235

  25. 25.

    Zhang J, Zou C & Wang Z (2011) A new chart for detecting the process mean and variability. Commun Stat-Simul C 40(5): 728–743.

Download references

Author information

Correspondence to Frederico R. B. Cruz.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Quinino, R.C., Bessegato, L.F. & Cruz, F.R.B. An attribute inspection control chart for process mean monitoring. Int J Adv Manuf Technol 90, 2991–2999 (2017). https://doi.org/10.1007/s00170-016-9627-8

Download citation

Keywords

  • Quality
  • Control chart
  • Optimization
  • Attribute and variable control charts
  • Average run length