Synthetic-Type Control Charts for Time-Between-Events Monitoring

This paper proposes three synthetic-type control charts to monitor the mean time-between-events of a homogenous Poisson process. The first proposed chart combines an Erlang (cumulative time between events, Tr) chart and a conforming run length (CRL) chart, denoted as Synth-Tr chart. The second proposed chart combines an exponential (or T) chart and a group conforming run length (GCRL) chart, denoted as GR-T chart. The third proposed chart combines an Erlang chart and a GCRL chart, denoted as GR-Tr chart. By using a Markov chain approach, the zero- and steady-state average number of observations to signal (ANOS) of the proposed charts are obtained, in order to evaluate the performance of the three charts. The optimal design of the proposed charts is shown in this paper. The proposed charts are superior to the existing T chart, Tr chart, and Synth-T chart. As compared to the EWMA-T chart, the GR-T chart performs better in detecting large shifts, in terms of the zero- and steady-state performances. The zero-state Synth-T4 and GR-Tr (r = 3 or 4) charts outperform the EWMA-T chart for all shifts, whereas the Synth-Tr (r = 2 or 3) and GR-T 2 charts perform better for moderate to large shifts. For the steady-state process, the Synth-Tr and GR-Tr charts are more efficient than the EWMA-T chart in detecting small to moderate shifts.

[1]  Maria E. Calzada,et al.  The Generalized Synthetic Chart , 2009 .

[2]  Fah Fatt Gan,et al.  Designs of One- and Two-Sided Exponential EWMA Charts , 1998 .

[3]  T. N. Goh,et al.  SOME ADVANCED CONTROL CHARTS FOR MONITORING WEIBULL-DISTRIBUTED TIME BETWEEN EVENTS , 2006 .

[4]  M. Xie,et al.  Monitoring time-between-events for health management , 2010, 2010 Prognostics and System Health Management Conference.

[5]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Fraction Nonconforming Increases , 2001 .

[6]  Zhang Wu,et al.  A control scheme integrating the T chart and TCUSUM chart , 2011, Qual. Reliab. Eng. Int..

[7]  William H. Woodall,et al.  The Use of Control Charts in Health-Care and Public-Health Surveillance , 2006 .

[8]  Min Xie,et al.  Statistical Models and Control Charts for High-Quality Processes , 2002 .

[9]  Thong Ngee Goh,et al.  Cumulative quantity control charts for monitoring production processes , 2000 .

[10]  Min Xie,et al.  A study of time-between-events control chart for the monitoring of regularly maintained systems , 2009, Qual. Reliab. Eng. Int..

[11]  Julia L Sharp,et al.  CUSUM Analyses of Time-Interval Data for Online Radiation Monitoring , 2012, Health physics.

[12]  M. Xie,et al.  Time-between-events charts for on-line process monitoring , 2004, 2004 IEEE International Engineering Management Conference (IEEE Cat. No.04CH37574).

[13]  Murat Caner Testik,et al.  Impact of model misspecification on the exponential EWMA charts: a robustness study when the time-between-events are not exponential , 2010, Qual. Reliab. Eng. Int..

[14]  H.Y. Zhang,et al.  Economic design of integrated time-between-events chart system with independent quality characteristics , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

[15]  R. N. Rattihalli,et al.  A Group Runs Control Chart for Detecting Shifts in the Process Mean , 2004 .

[16]  T. N. Goh,et al.  A Comparative Study of Exponential Time between Events Charts , 2006 .

[17]  Patrick D. Bourke,et al.  The geometric CUSUM chart with sampling inspection for monitoring fraction defective , 2001 .

[18]  Thong Ngee Goh,et al.  The use of probability limits for process control based on geometric distribution , 1997 .

[19]  Abdur Rahim,et al.  A CCC‐r chart for high‐yield processes , 2001 .

[20]  Thong Ngee Goh,et al.  Economic design of time-between-events control chart system , 2011, Comput. Ind. Eng..

[21]  T. Calvin,et al.  Quality Control Techniques for "Zero Defects" , 1983 .

[22]  Gyo-Young Cho,et al.  CUSUM charts with variable sampling intervals , 2009 .

[23]  T. N. Goh,et al.  Monitoring Inter-Arrival Times with Statistical Control Charts , 2006 .

[24]  Stephen B. Vardeman,et al.  Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed , 1985 .

[25]  Douglas C. Montgomery,et al.  Statistical quality control : a modern introduction , 2009 .

[26]  Thong Ngee Goh,et al.  Some effective control chart procedures for reliability monitoring , 2002, Reliab. Eng. Syst. Saf..

[27]  Farrokh Alemi,et al.  Time-between control charts for monitoring asthma attacks. , 2004, Joint Commission journal on quality and safety.

[28]  Charles W. Champ,et al.  Phase I control charts for times between events , 2002 .

[29]  Philippe Castagliola,et al.  On t and EWMA t charts for monitoring changes in the process mean , 2009, Qual. Reliab. Eng. Int..

[30]  Philippe Castagliola,et al.  A multivariate synthetic double sampling T2 control chart , 2013, Comput. Ind. Eng..

[31]  Thong Ngee Goh,et al.  A COMPARATIVE STUDY OF CCC AND CUSUM CHARTS , 1998 .

[32]  Jing Sun,et al.  Control charts based on the number of consecutive conforming items between two successive nonconforming items for the near zero-nonconformity processes , 2000 .

[33]  D. A. Evans,et al.  An approach to the probability distribution of cusum run length , 1972 .

[34]  Mats Brommels,et al.  Application of statistical process control in healthcare improvement: systematic review , 2007, Quality and Safety in Health Care.

[35]  Thong Ngee Goh,et al.  A control chart for the Gamma distribution as a model of time between events , 2007 .

[36]  Eralp Doğu.  MONITORING TIME BETWEEN MEDICAL ERRORS TO IMPROVE HEALTH-CARE QUALITY , 2012 .

[37]  Fah Fatt Gan.  Design of optimal exponential CUSUM control charts , 1994 .

[38]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Small Shifts in the Process Mean , 2000 .

[39]  R. R. L. Kantham,et al.  Assessing Software Reliability using Inter Failures Time Data , 2011 .

[40]  Connie M. Borror,et al.  Robustness of the time between events CUSUM , 2003 .

[41]  Patrick D. Bourke,et al.  Detecting a shift in fraction nonconforming using runlength control charts with 100% inspection , 1991 .

[42]  Giovanni Radaelli.  Planning time-between-events Shewhart control charts , 1998 .

[43]  Philippe Castagliola,et al.  Economically Optimum Design of a Synthetic X¯ Chart , 2012, Qual. Reliab. Eng. Int..

[44]  Christian H. Weiß,et al.  Properties of the exponential EWMA chart with parameter estimation , 2010, Qual. Reliab. Eng. Int..

[45]  D. T. Shirke,et al.  Nonparametric Synthetic Control Charts for Process Variation , 2012, Qual. Reliab. Eng. Int..

[46]  Thong Ngee Goh,et al.  Economic design of exponential charts for time between events monitoring , 2005 .

[47]  D. T. Shirke,et al.  A Multivariate Synthetic Control Chart for Monitoring Process Mean Vector , 2008 .

[48]  R. Jarrett.  A note on the intervals between coal-mining disasters , 1979 .

[49]  William H. Woodall,et al.  Evaluating and Improving the Synthetic Control Chart , 2002 .

[50]  Thong Ngee Goh,et al.  A shewhart‐like charting technique for high yield processes , 1995 .

[51]  Willem Albers.  The optimal choice of negative binomial charts for monitoring high-quality processes , 2008 .

[52]  Maria E. Calzada,et al.  A Note on the Lower-Sided Synthetic Chart for Exponentials , 2003 .

[53]  Philippe Castagliola,et al.  Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length , 2011, Qual. Reliab. Eng. Int..