Monitoring schedule time using exponentially modified Gaussian distribution

ABSTRACT Control charts are efficient process monitoring tools used to distinguish between assignable and natural variations. This article presents a new time-between-events chart to monitor the scheduled time. In particular, exponentially modified Gaussian distribution is considered in the construction of the control chart. The performance of the chart is evaluated in terms of average run length and coefficient of variation of the run length. To show the significance of the proposed chart, the data on time in hours between the detection of cancer cells using 3 um erlotinib and schedule time in minutes of an employ are considered.

[1]  E. Grushka.  Characterization of exponentially modified Gaussian peaks in chromatography. , 1972, Analytical chemistry.

[2]  Philippe Castagliola,et al.  Exponential cumulative sums chart for detecting shifts in time-between-events , 2018, Int. J. Prod. Res..

[3]  V. McGuffin,et al.  Additivity of statistical moments in the exponentially modified Gaussian model of chromatography , 2003 .

[4]  Sajid Ali.  Time-between-events control charts for an exponentiated class of distributions of the renewal process , 2017, Qual. Reliab. Eng. Int..

[5]  Thong Ngee Goh,et al.  Cumulative probability control charts for geometric and exponential process characteristics , 2002 .

[6]  R. Delley.  Series for the exponentially modified Gaussian peak shape , 1985 .

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

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

[9]  E. Sager,et al.  The EMG Distribution and Aggregate Trade Elasticities , 2016 .

[10]  G. Takaoka,et al.  Multiparameter characterization of cluster ion beams , 2006 .

[11]  Yuri Kalambet,et al.  Reconstruction of chromatographic peaks using the exponentially modified Gaussian function , 2011 .

[12]  Christos Koukouvinos,et al.  Monitoring of time between events with a double generally weighted moving average control chart , 2018, Qual. Reliab. Eng. Int..

[13]  Pierre Gabriel,et al.  The contribution of age structure to cell population responses to targeted therapeutics. , 2011, Journal of theoretical biology.

[14]  C D Lai,et al.  Reduction of control-chart signal variablity for high-quality processes , 2008 .

[15]  Jung-Tai Chen,et al.  A Shewhart‐type Control Scheme to Monitor Weibull Data without Subgrouping , 2014, Qual. Reliab. Eng. Int..

[16]  Min Xie,et al.  Monitoring of Time-Between-Events with a Generalized Group Runs Control Chart , 2016, Qual. Reliab. Eng. Int..

[17]  Philippe Castagliola,et al.  Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions , 2019, Quality Engineering.

[18]  Rainer Göb,et al.  An Overview of Control Charts for High‐quality Processes , 2016, Qual. Reliab. Eng. Int..

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

[20]  Abdur Rahim,et al.  Time-Between-Event Control Charts for Sampling Inspection , 2014, Technometrics.

[21]  A. Golubev,et al.  Exponentially Modified Peak Functions in Biomedical Sciences and Related Disciplines , 2017, Comput. Math. Methods Medicine.

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

[23]  G. Smyth,et al.  Microarray background correction: maximum likelihood estimation for the normal–exponential convolution , 2008, Biostatistics.

[24]  Sajid Ali,et al.  High quality process monitoring using a class of inter-arrival time distributions of the renewal process , 2016, Comput. Ind. Eng..

[25]  Fang Yen Yen,et al.  Synthetic-Type Control Charts for Time-Between-Events Monitoring , 2013, PloS one.

[26]  A. Golubev,et al.  Exponentially modified Gaussian (EMG) relevance to distributions related to cell proliferation and differentiation. , 2010, Journal of theoretical biology.

[27]  Min Xie,et al.  Design of Gamma Charts Based on Average Time to Signal , 2016, Qual. Reliab. Eng. Int..

[28]  E. Navarro‐Pardo,et al.  ExGUtils: A Python Package for Statistical Analysis With the ex-Gaussian Probability Density , 2017, Front. Psychol..

[29]  N. Kumar.  Conditional analysis of Phase II exponential chart for monitoring times to an event , 2020, Quality Technology & Quantitative Management.