Document Type : Research Note

**Authors**

Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9414, Iran

**Abstract**

Various control charts have been proposed to monitor generalized linear profiles in Phase II. However, robustness of the proposed methods in detecting different types and especially different directions of changes is not well-studied in the literature. In real-world applications different kinds of changes such as drift and multiple change are likely to happen which can be isotonic (increasing) or antitonic (decreasing). This paper studies the robustness of Rao Score Test (RST) method, T2, and multivariate exponential weighted moving average (MEWMA) in different types, drift and multiple, and directions of changes. Rao Score Test method also benefits from a change-point detection approach whose performance is studied as well. According to the results, generally RST method shows a better performance in detecting different types of changes. Moreover, the performance of the RST method is robust to direction of the change, while T2 and MEWMA are not ARL-unbiased and show different performances under isotonic and antitonic changes. Therefore, to address this issue, we proposed a bias-reduced estimator to be used in T2. Our results demonstrate that the proposed control chart outperforms T2 and is less biased than T2. Finally, a real-world problem is presented in which aforementioned methods are applied to real data.

**Keywords**

**Main Subjects**

1. Kang, L. and Albin, S.L. On-line monitoring when

the process yields a linear prole", Journal of Quality

Technology, 32(4), pp. 418{426 (2000).

2. Noorossana, R., Saghaei, A., and Amiri, A., Statistical

Analysis of Prole Monitoring, 1st Edn., In Wiley

Series in Probability and Statistics (2011).

3. Niaki, S.T.A. and Khedmati, M. Identifying the

change time of multivariate binomial processes for step

changes and drifts", Journal of Industrial Engineering

International, 9(1), p. 3 (2013).

4. Kazemzadeh, R.B., Noorossana, R., and Ayoubi, M.

Change point estimation of multivariate linear pro-

les under linear drift", Communications in Statistics-

Simulation and Computation, 44(6), pp. 1570{1599

(2015).

5. Korkas, K.K. and PryzlewiczV, P. Multiple changepoint

detection for non-stationary time series using

wild binary segmentation", Statistica Sinica, pp. 287{

311 (2017).

6. Atashgar, K. Identication of the change point: an

overview", The International Journal of Advanced

Manufacturing Technology, 64(9{12), pp. 1663{1683

(2013).

7. Aminikhanghahi, S. and Cook, D.J. A survey of methods

for time series change point detection", Knowledge

and Information Systems, 51(2), pp. 339{367 (2017).

8. Woodall, W.H., Spitzner, D.J., Montgomery, D.C.,

and Gupta, S. Using control charts to monitor process

and product quality proles", Journal of Quality

Technology, 36(3), pp. 309{320 (2004).

9. Qiu, P. Distribution-free multivariate process control

based on log-linear modeling", IIE Transactions,

40(7), pp. 664{677 (2008).

570 S. Hajifar and H. Mahlooji/Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 557{571

10. Yeh, A.B., Huwang, L., and Li, Y.M. Prole monitoring

for a binary response", IIE Transactions, 41(11),

pp. 931{941 (2009).

11. Paynabar, K., Jin, J., and Yeh, A.B. Phase I riskadjusted

control charts for monitoring surgical performance

by considering categorical covariates", Journal

of Quality Technology, 44(1), pp. 39{53 (2012).

12. Soleymanian, M.E., Khedmati, M., and Mahlooji, H.

Phase II monitoring of binary response proles", Scientia

Iranica, Transaction E, Industrial Engineering,

20(6), p. 2238 (2013).

13. Koosha, M. and Amiri, A. Generalized linear mixed

model for monitoring autocorrelated logistic regression

proles", The International Journal of Advanced Manufacturing

Technology, 64(1{4), pp. 487{495 (2013).

14. Amiri, A., Koosha, M., and Azhdari, A. T2 based

methods for monitoring gamma proles", In International

Conference on Industrial Engineering and

Operations Management, pp. 580{585 (2012).

15. Noorossana, R., Aminnayeri, M., and Izadbakhsh, H.

Statistical monitoring of polytomous logistic proles

in phase II", Scientia Iranica, 20(3), pp. 958{966

(2013).

16. Amiri, A., Koosha, M., Azhdari, A., and Wang, G.

Phase I monitoring of generalized linear model-based

regression proles", Journal of Statistical Computation

and Simulation, 85(14), pp. 2839{2859 (2015).

17. Qi, D., Wang, Z., Zi, X., and Li, Z. Phase II

monitoring of generalized linear proles using weighted

likelihood ratio charts", Computers & Industrial Engineering,

94, pp. 178{187 (2016).

18. Sogandi, F. and Amiri, A. Monotonic change point

estimation of generalized linear model-based regression

proles", Communications in Statistics-Simulation

and Computation, 46(3), pp. 2207{2227 (2017).

19. Khedmati, M. and Niaki, S.T.A. Phase II monitoring

of general linear proles in the presence of betweenpro

le autocorrelation", Quality and Reliability Engineering

International, 32(2), pp. 443{452 (2016).

20. Noorossana, R., Saghaei, A., Paynabar, K., and Abdi,

S. Identifying the period of a step change in highyield

processes", Quality and Reliability Engineering

International, 25(7), pp. 875{883 (2009).

21. Perry, M.B., Pignatiello Jr, J.J., and Simpson, J.R.

Estimating the change point of a Poisson rate parameter

with a linear trend disturbance", Quality and

Reliability Engineering International, 22(4), pp. 371{

384 (2006).

22. Noorossana, R. and Shadman, A. Estimating the

change point of a normal process mean with a monotonic

change", Quality and Reliability Engineering

International, 25(1), pp. 79{90 (2009).

23. Alaeddini, A., Ghazanfari, M., and Nayeri, M.A. A

hybrid fuzzy-statistical clustering approach for estimating

the time of changes in xed and variable sampling

control charts", Information Sciences, 179(11),

pp. 1769{1784 (2009).

24. Atashgar, K. and Noorossana, R. An integrating approach

to root cause analysis of a bivariate mean vector

with a linear trend disturbance", The International

Journal of Advanced Manufacturing Technology, 52(1{

4), pp. 407{420 (2011).

25. Ahmadzadeh, F. Change point detection with multivariate

control charts by articial neural network",

The International Journal of Advanced Manufacturing

Technology, 97(9{12), pp. 3179{3190 (2018).

26. Zou, C., Zhou, C., Wang, Z., and Tsung, F. A selfstarting

control chart for linear proles", Journal of

Quality Technology, 39(4), pp. 364{375 (2007).

27. Paynabar, K., Zou, C., and Qiu, P. A change-point

approach for phase-I analysis in multivariate prole

monitoring and diagnosis", Technometrics, 58(2), pp.

191{204 (2016).

28. Maleki, M.R., Amiri, A., and Taheriyoun, A.R. Identifying

the time of step change and drift in phase

II monitoring of autocorrelated logistic regression

proles", Scientia Iranica, Transactions E, Industrial

Engineering, 25(6), pp. 3654{3666 (2018).

29. Firth, D. Bias reduction of maximum likelihood

estimates", Biometrika, 80(1), pp. 27{38 (1993).

30. Shadman, A., Zou, C., Mahlooji, H., and Yeh, A.B.

A change point method for Phase II monitoring

of generalized linear proles", Communications in

Statistics-Simulation and Computation, 46(1), pp.

559{578 (2017).

31. Margavio, T.M., Conerly, M.D., Woodall, W.H., and

Drake, L.G. Alarm rates for quality control charts",

Statistics & Probability Letters, 24(3), pp. 219{224

(1995).

32. Hawkins, D.M., Qiu, P., and Kang, C.W. The change

point model for statistical process control", Journal of

Quality Technology, 35(4), pp. 355{366 (2003).

33. Heinze, G. and Schemper, M. A solution to the

problem of separation in logistic regression", Statistics

in Medicine, 21(16), pp. 2409{2419 (2002).

34. Kosmidis, I. and Firth, D. A generic algorithm for

reducing bias in parametric estimation", Electronic

Journal of Statistics, 4, pp. 1097{1112 (2010).

35. Heinze, G. and Schemper, M. A solution to the

problem of separation in logistic regression", Statistics

in Medicine, 21(16), pp. 2409{2419 (2002).

36. Shadman, A., Mahlooji, H., Yeh, A.B., and Zou, C. A

change point method for monitoring generalized linear

proles in phase I", Quality and Reliability Engineering

International, 31(8), pp. 1367{1381 (2015).

S. Hajifar and H. Mahlooji/Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 557{571 571

37. Ver Hoef, J.M. and Boveng, P.L. Quasi-Poisson vs.

negative binomial regression: how should we model

overdispersed count data?", Ecology, 88(11), pp. 2766{

2772 (2007).

Transactions on Industrial Engineering (E)

January and February 2021Pages 557-571