Exponential cumulative sums chart for detecting shifts in time-between-events

Time-between-events (TBE) charts use the time interval T between events to monitor process shifts (or failure rates λ). This paper presents a two-sided TBE cumulative sums (CUSUM) chart called a weighted CUSUM(WCUSUM)chart for detecting either a deterioration (decrease in T) or an improvement (increase in T) in the condition of a process. A new kind of WCUSUM chart that has an additional charting power parameter w is proposed here. A WCUSUM chart’s efficiency can be improved by using the parameter w, based on an estimated value of the mean shift. In addition, a methodology and optimal design are presented for minimising the average loss. Construction of the WCUSUM chart is illustrated by considering a random shift δ in λ (including both increasing and decreasing shifts) in the design.

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

[2]  James M. Lucas,et al.  Counted Data CUSUM's , 1985 .

[3]  Min Xie,et al.  Design of exponential control charts based on average time to signal using a sequential sampling scheme , 2015 .

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

[5]  Fugee Tsung,et al.  A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison , 2006 .

[6]  Amitava Mukherjee,et al.  Distribution‐free Lepage Type Circular‐grid Charts for Joint Monitoring of Location and Scale Parameters of a Process , 2017, Qual. Reliab. Eng. Int..

[7]  Ryoji Tamura,et al.  On a Modification of Certain Rank Tests , 1963 .

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

[9]  Patrick D. Bourke,et al.  The RL2 chart versus the np chart for detecting upward shifts in fraction defective , 2006 .

[10]  Philippe Castagliola,et al.  A CUSUM scheme for event monitoring , 2013 .

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

[12]  Ingram Olkin,et al.  The Exponential Distribution , 2007 .

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

[14]  Michael B. C. Khoo,et al.  Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated , 2015 .

[15]  Fugee Tsung,et al.  A new multivariate EWMA scheme for monitoring covariance matrices , 2014 .

[16]  Chong Li.  An integrated approach to evaluating the production system in closed-loop supply chains , 2013 .

[17]  Yu Tian,et al.  Optimization design of the charts for monitoring process capability , 2002 .

[18]  Acheson J. Duncan,et al.  The Economic Design of X Charts Used to Maintain Current Control of a Process , 1956 .

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

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

[21]  R. N. Rattihalli,et al.  Unit and Group-Runs Chart to Identify Increases in Fraction Nonconforming , 2005 .

[22]  Ying Liu,et al.  A binomial CUSUM chart for detecting large shifts in fraction nonconforming , 2008 .

[23]  Amitava Mukherjee,et al.  Distribution-Free Exceedance CUSUM Control Charts for Location , 2013, Commun. Stat. Simul. Comput..

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

[25]  Yizhong Ma,et al.  Integration of SPC and performance maintenance for supply chain system , 2016 .

[26]  A. K. Mccracken,et al.  Control Charts for Simultaneous Monitoring of Parameters of a Shifted Exponential Distribution , 2015 .

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

[28]  Zhang Wu,et al.  Design of the sum-of-conforming-run-length control charts , 2001, Eur. J. Oper. Res..

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

[30]  Amitava Mukherjee,et al.  Design and implementation of CUSUM exceedance control charts for unknown location , 2014 .

[31]  Abdur Rahim,et al.  A balanced two-sided CUSUM chart for monitoring time between events , 2015 .

[32]  Douglas C. Montgomery,et al.  Research Issues and Ideas in Statistical Process Control , 1999 .

[33]  Thong Ngee Goh,et al.  Economic design of cumulative count of conforming charts under inspection by samples , 2008 .

[34]  Rickie J. Domangue,et al.  Some omnibus exponentially weighted moving average statistical process monitoring schemes , 1991 .

[35]  Marion R. Reynolds,et al.  Should Observations Be Grouped for Effective Process Monitoring? , 2004 .