Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2699–2716 | Cite as

An Efficient Phase I Analysis of Linear Profiles with Application in Photo-Voltaic System

  • Tahir MahmoodEmail author
  • Saddam Akber Abbasi
  • Muhammad Riaz
  • Nasir Abbas
Research Article - Systems Engineering


In many manufacturing industries, quality of an item depends on different characteristics and their relationship may be modeled by profiles. For instance, in photo-voltaic (PV) system, output voltage is dependent on the capacitance level of capacitors, used in the Z-source inverter. Control chart is a dynamic tool that works under two different phases namely Phase I and Phase II. The unknown parameters are estimated in Phase I, while Phase II focuses on monitoring of the process using estimated control limits from Phase I. In this study, we have investigated Phase I monitoring of linear profile parameters under several sampling approaches including ranked set sampling (RSS), double RSS, median RSS (MRSS), double MRSS, extreme RSS (ERSS) and double ERSS. A comparative analysis on the performance of existing and proposed schemes is performed in terms of probability to signal. The results advocate that the proposed methods under different ranked set schemes offer superior detection abilities as compared to the existing schemes for varying shifts in profile parameters (intercept, slope and error variance). Moreover, a real application related to PV system is included to show the practical demonstration of the profile monitoring (for the output voltage in relation to capacitance level) under proposed schemes.


Control chart Statistical process control Linear profile parameters Probability to signal Ranked set sampling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



Funding was provided by King Fahd University of Petroleum and Minerals (Grant No. IN171016).


  1. 1.
    Lior, N.: Energy resources and use: the present situation and possible paths to the future. Energy 33(6), 842–857 (2008)CrossRefGoogle Scholar
  2. 2.
    Remya, V.; Parthiban, P.; Ansal, V.; Nandakumar, A.: Single-phase DVR with semi-Z-source inverter for power distribution network. Arab. J. Sci. Eng. (2017). Google Scholar
  3. 3.
    Abido, M.; Khalid, M.S.; Worku, M.Y.: An efficient ANFIS-based PI controller for maximum power point tracking of PV systems. Arab. J. Sci. Eng. 40(9), 2641–2651 (2015)CrossRefGoogle Scholar
  4. 4.
    Al-Shohani, W.A.: Performance of photovoltaic module for different sites in Iraq. Arab. J. Sci. Eng. 38(2), 277–283 (2013)CrossRefGoogle Scholar
  5. 5.
    Vincheh, M.R.; Kargar, A.; Markadeh, G.A.: A hybrid control method for maximum power point tracking (MPPT) in photovoltaic systems. Arab. J. Sci. Eng. 39(6), 4715–4725 (2014)CrossRefGoogle Scholar
  6. 6.
    Azam, M.; Arshad, A.; Aslam, M.; Jun, C.-H.: A control chart for monitoring the process mean using successive sampling over two occasions. Arab. J. Sci. Eng. 42(7), 2915–2926 (2017)CrossRefGoogle Scholar
  7. 7.
    Chen, Y.-K.; Chen, C.-Y.: Economic design of cumulative conformance count charts with variable sampling intervals. Arab. J. Sci. Eng. 37(7), 2079–2088 (2012)CrossRefGoogle Scholar
  8. 8.
    Seif, A.; Moghadam, M.B.; Faraz, A.; Heuchenne, C.: Statistical merits and economic evaluation of T\(^{2}\) control charts with the VSSC scheme. Arab. J. Sci. Eng. 36(7), 1461–1470 (2011)CrossRefGoogle Scholar
  9. 9.
    Shewhart, W.A.: Economic Control of Quality of Manufactured Product. ASQ Quality Press, Milwaukee (1931)Google Scholar
  10. 10.
    Mehmood, R.; Riaz, M.; Does, R.J.: Quality quandaries: on the application of different ranked set sampling schemes. Qual. Eng. 26(3), 370–378 (2014)CrossRefGoogle Scholar
  11. 11.
    Nazir, H.Z.; Schoonhoven, M.; Riaz, M.; Does, R.J.: Quality quandaries: How to set up a robust Shewhart control chart for dispersion? Qual. Eng. 26(1), 130–136 (2014)CrossRefGoogle Scholar
  12. 12.
    Nazir, H.Z.; Schoonhoven, M.; Riaz, M.; Does, R.J.: Quality quandaries: a stepwise approach for setting up a robust Shewhart location control chart. Qual. Eng. 26(2), 246–252 (2014)CrossRefGoogle Scholar
  13. 13.
    Riaz, M.; Does, R.J.: An alternative to the bivariate control chart for process dispersion. Qual. Eng. 21(1), 63–71 (2008)CrossRefGoogle Scholar
  14. 14.
    Riaz, M.; Mehmood, R.; Does, R.J.: On the performance of different control charting rules. Qual. Reliab. Eng. Int. 27(8), 1059–1067 (2011)CrossRefGoogle Scholar
  15. 15.
    Sindhu, T.N.; Riaz, M.; Aslam, M.; Ahmed, Z.: Bayes estimation of Gumbel mixture models with industrial applications. Trans. Inst. Meas. Control 38(2), 201–214 (2016)CrossRefGoogle Scholar
  16. 16.
    Mahmood, T.; Nazir, H.Z.; Abbas, N.; Riaz, M.; Ali, A.: Performance evaluation of joint monitoring control charts. Sci. Iran. 24(4), 2152–2163 (2017)Google Scholar
  17. 17.
    Abbasi, S.A.; Riaz, M.; Miller, A.; Ahmad, S.: On the performance of phase I dispersion control charts for process monitoring. Qual. Reliab. Eng. Int. 31(8), 1705–1716 (2015)CrossRefGoogle Scholar
  18. 18.
    Jensen, W.A.; Jones-Farmer, L.A.; Champ, C.W.; Woodall, W.H.: Effects of parameter estimation on control chart properties: a literature review. J. Qual. Technol. 38(4), 349–364 (2006)CrossRefGoogle Scholar
  19. 19.
    Mehmood, R.; Riaz, M.; Mahmood, T.; Abbasi, S.A.; Abbas, N.: On the extended use of auxiliary information under skewness correction for process monitoring. Trans. Inst. Meas. Control 39(6), 883–897 (2017)CrossRefGoogle Scholar
  20. 20.
    Vining, G.: Technical advice: phase I and phase II control charts. Qual. Eng. 21(4), 478–479 (2009)CrossRefGoogle Scholar
  21. 21.
    Kang, L.; Albin, S.L.: On-line monitoring when the process yields a linear profile. J. Qual. Technol. 32(4), 418–426 (2000)CrossRefGoogle Scholar
  22. 22.
    Kim, K.; Mahmoud, M.A.; Woodall, W.H.: On the monitoring of linear profiles. J. Qual. Technol. 35(3), 317–328 (2003)CrossRefGoogle Scholar
  23. 23.
    Noorossana, R., Amiri, A., Vaghefi, A., Roghanian, E.: Monitoring quality characteristics using linear profile. In: Proceedings of the 3rd International Industrial Engineering Conference 2004, pp. 246–255Google Scholar
  24. 24.
    Noorossana, R., Vaghefi, S., Amiri, A.: The effect of non-normality on monitoring linear profiles. In: Proceedings of the 2nd International Industrial Engineering Conference, Riyadh, Saudi Arabia, 2004Google Scholar
  25. 25.
    Zou, C.; Zhang, Y.; Wang, Z.: A control chart based on a change-point model for monitoring linear profiles. IIE Trans. 38(12), 1093–1103 (2006)CrossRefGoogle Scholar
  26. 26.
    Croarkin, M.; Varner, R.N.: Measurement assurance for dimensional measurements on integrated-circuit photomasks. Final Report National Bureau of Standards, Washington, DC. Statistical Engineering Division (1982)Google Scholar
  27. 27.
    Gupta, S.; Montgomery, D.; Woodall, W.: Performance evaluation of two methods for online monitoring of linear calibration profiles. Int. J. Prod. Res. 44(10), 1927–1942 (2006)CrossRefGoogle Scholar
  28. 28.
    Noorossana, A.; Amiri, A.: Enhancement of linear profiles monitoring in phase II. Amirkabir J. Sci. Technol. 18(66–B), 19–27 (2007)Google Scholar
  29. 29.
    Woodall, W.H.: Current research on profile monitoring. Production 17(3), 420–425 (2007)CrossRefGoogle Scholar
  30. 30.
    Zou, C.; Zhou, C.; Wang, Z.; Tsung, F.: A self-starting control chart for linear profiles. J. Qual. Technol. 39(4), 364–375 (2007)CrossRefGoogle Scholar
  31. 31.
    Zhang, J.; Li, Z.; Wang, Z.: Control chart based on likelihood ratio for monitoring linear profiles. Comput. Stat. Data Anal. 53(4), 1440–1448 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Saghaei, A.; Mehrjoo, M.; Amiri, A.: A CUSUM-based method for monitoring simple linear profiles. Int. J. Adv. Manuf. Technol. 45(11), 1252–1260 (2009)CrossRefGoogle Scholar
  33. 33.
    Mahmoud, M.A.; Morgan, J.; Woodall, W.H.: The monitoring of simple linear regression profiles with two observations per sample. J. Appl. Stat. 37(8), 1249–1263 (2010)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Noorossana, R.; Fatemi, S.; Zerehsaz, Y.: Phase II monitoring of simple linear profiles with random explanatory variables. Int. J. Adv. Manuf. Technol. 76(5–8), 779–787 (2015)CrossRefGoogle Scholar
  35. 35.
    Dawod, A.B.; Al-Momani, M.; Abbasi, S.A.: On efficient estimation strategies in monitoring of linear profiles. Int. J. Adv. Manuf. Technol. (2018). Google Scholar
  36. 36.
    Riaz, M.; Mahmood, T.; Abbasi, S.A.; Abbas, N.; Ahmad, S.: Linear profile monitoring using EWMA structure under ranked set schemes. Int. J. Adv. Manuf. Technol. 91(5–8), 2751–2775 (2017)CrossRefGoogle Scholar
  37. 37.
    Mahmood, T.; Riaz, M.; Omar, M.H.; Xie, M.: Alternative methods for the simultaneous monitoring of simple linear profile parameters. Int. J. Adv. Manuf. Technol. 97(5–8), 2851–2871 (2018). CrossRefGoogle Scholar
  38. 38.
    Wang, F.K.; Tamirat, Y.; Lo, S.C.; Aslam, M.: Dependent mixed and mixed repetitive sampling plans for linear profiles. Qual. Reliab. Eng. Int. 33(8), 1669–1683 (2017)CrossRefGoogle Scholar
  39. 39.
    Tamirat, Y.: Implementing EWMA yield index for product acceptance determination in autocorrelation between linear profiles. In: Calisir F., Camgoz Akdag H. (eds.) Industrial Engineering in the Industry 4.0 Era. Lecture Notes in Management and Industrial Engineering. Springer, Cham (2018).
  40. 40.
    Mestek, O.; Pavlík, J.; Suchánek, M.: Multivariate control charts: control charts for calibration curves. Fresenius’ J. Anal. Chem. 350(6), 344–351 (1994)CrossRefGoogle Scholar
  41. 41.
    Stover, F.S.; Brill, R.V.: Statistical quality control applied to ion chromatography calibrations. J. Chromatogr. A 804(1), 37–43 (1998)CrossRefGoogle Scholar
  42. 42.
    Mahmoud, M.A.; Woodall, W.H.: Phase I analysis of linear profiles with calibration applications. Technometrics 46(4), 380–391 (2004)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Mahmoud, M.A.; Parker, P.A.; Woodall, W.H.; Hawkins, D.M.: A change point method for linear profile data. Qual. Reliab. Eng. Int. 23(2), 247–268 (2007)CrossRefGoogle Scholar
  44. 44.
    Yeh, A.; Zerehsaz, Y.: Phase I control of simple linear profiles with individual observations. Qual. Reliab. Eng. Int. 29(6), 829–840 (2013)CrossRefGoogle Scholar
  45. 45.
    Jensen, W.A.; Birch, J.B.; Woodall, W.H.: Monitoring correlation within linear profiles using mixed models. J. Qual. Technol. 40(2), 167–183 (2008)CrossRefGoogle Scholar
  46. 46.
    Noorossana, R.; Aminmadani, M.; Saghaei, A.: Effect of phase I estimation error on the monitoring of simple linear profiles in phase II. Int. J. Adv. Manuf. Technol. 84(5–8), 873–884 (2016)Google Scholar
  47. 47.
    Maleki, M.; Amiri, A.; Taheriyoun, A.; Castagliola, P.: Phase I monitoring and change point estimation of autocorrelated Poisson regression profiles. Commun. Stat. Theory Methods (2017). Google Scholar
  48. 48.
    Kalaei, M.; Atashgar, K.; Niaki, S.T.A.; Soleimani, P.: Phase I monitoring of simple linear profiles in multistage processes with cascade property. Int. J. Adv. Manuf. Technol. 94(5–8), 1745–1757 (2018)CrossRefGoogle Scholar
  49. 49.
    McIntyre, G.: A method for unbiased selective sampling, using ranked sets. Aust. J. Agric. Res. 3(4), 385–390 (1952)CrossRefGoogle Scholar
  50. 50.
    Muttlak, H.: Median ranked set sampling. J. Appl. Stat. Sci. 6(4), 245–255 (1997)zbMATHGoogle Scholar
  51. 51.
    Samawi, H.M.; Ahmed, M.S.; Abu-Dayyeh, W.: Estimating the population mean using extreme ranked set sampling. Biom. J. 38(5), 577–586 (1996)CrossRefzbMATHGoogle Scholar
  52. 52.
    Al-Saleh, M.F.; Al-Kadiri, M.A.: Double-ranked set sampling. Stat. Probab. Lett. 48(2), 205–212 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Samawi, H.M.; Tawalbeh, E.M.: Double median ranked set sample: comparing to other double ranked samples for mean and ratio estimators. J. Mod. Appl. Stat. Methods 1(2), 428–442 (2002)CrossRefGoogle Scholar
  54. 54.
    Alodat, M.; Al-Rawwash, M.; Nawajah, I.: Inference about the regression parameters using median-ranked set sampling. Commun. Stat. Theory Methods 39(14), 2604–2616 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Samawi, H.; Ababneh, F.: On regression analysis using ranked set sample. J. Stat. Res. 35(2), 93–105 (2001)MathSciNetGoogle Scholar
  56. 56.
    Mukhtar, U.: Maximum power point tracking controllers for grid-connected PV systems. Master Thesis. King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia (2015)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  2. 2.Department of System Engineering and Engineering ManagementCity University of Hong KongKowloonHong Kong
  3. 3.Department of Mathematics, Statistics and PhysicsQatar UniversityDohaQatar

Personalised recommendations