An attribute control chart using discriminant limits for monitoring process under the Weibull distribution

A new efficient process monitoring scheme has been developed for a process under which the quality characteristic follows the Weibull distribution. Recently control charts using discriminant limits for process monitoring for a normal distribution have been developed. But, there are many situations in which the distribution of underlying data is not normal. So, the application of such chart to a skewed distribution like the Weibull distribution may lead to erroneous conclusions. In this paper, an attribute chart using discriminant limits for the Weibull distribution has been developed. The parameters of the proposed chart have been determined by considering the in-control average run lengths. An example using the simulation data has been included for the practical use of the proposed scheme. It has been observed that the proposed chart is efficient for the quick detection of an out-of-control process. A real example from a healthcare area is also added to show the application of the proposed control chart.

[1]  William H. Woodall,et al.  The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables , 1983 .

[2]  K. Fertig,et al.  Life-Test Sampling Plans for Two-Parameter Weibull Populations , 1980 .

[3]  Chi-Hyuck Jun,et al.  A Control Chart for Gamma Distributed Variables Using Repetitive Sampling Scheme , 2017 .

[4]  Chi-Hyuck Jun,et al.  Repetitive group sampling procedure for variables inspection , 2006 .

[5]  S. Crowder.  A simple method for studying run-length distribution of exponentially weighted moving average charts , 1987 .

[6]  Anastasia Ivanova,et al.  Two-stage designs for Phase 2 dose-finding trials. , 2012, Statistics in medicine.

[7]  Saowanit Sukparungsee,et al.  The ARL of EWMA Chart for Monitoring ZINB Model Using Markov Chain Approach , 2014 .

[8]  Norman L. Johnson,et al.  Cumulative Sum Control Charts and the Weibull Distribution , 1966 .

[9]  Roberto da Costa Quinino,et al.  An attribute control chart for monitoring the variability of a process , 2013 .

[10]  Ziren Wang,et al.  Discuss on Applying SPC to Quality Management in University Education , 2008, 2008 The 9th International Conference for Young Computer Scientists.

[11]  W. J. Padgett,et al.  A Bootstrap Control Chart for Weibull Percentiles , 2006, Qual. Reliab. Eng. Int..

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

[13]  A. S. Qureishi,et al.  The Discximination Between Two Weibull Processes , 1964 .

[14]  Chi-Hyuck Jun,et al.  A control chart for multivariate Poisson distribution using repetitive sampling , 2017 .

[15]  P. Masson,et al.  Quality control techniques for routine analysis with liquid chromatography in laboratories. , 2007, Journal of chromatography. A.

[16]  Chi-Hyuck Jun,et al.  The design of a new repetitive sampling control chart based on process capability index , 2016 .

[17]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[18]  Joel Smith,et al.  Control Charts Based on the Exponential Distribution: Adapting Runs Rules for the t Chart , 2013 .

[19]  Sven Knoth,et al.  Accurate ARL Calculation for EWMA Control Charts Monitoring Normal Mean and Variance Simultaneously , 2007 .

[20]  Muhammad Azam,et al.  Acceptance sampling plans for multi-stage process based on time-truncated test for Weibull distribution , 2015 .

[21]  Myoung-Jin Kim,et al.  Number of Replications Required in Control Chart Monte Carlo Simulation Studies , 2007, Commun. Stat. Simul. Comput..

[22]  Sang-Ho Lee,et al.  Variables sampling plans for Weibull distributed lifetimes under sudden death testing , 2006, IEEE Transactions on Reliability.

[23]  C. Jun,et al.  A group acceptance sampling plan for truncated life test having Weibull distribution , 2009 .

[24]  Veeresh Gadag,et al.  Progressively Censored Reliability Sampling Plans for the Weibull Distribution , 2000, Technometrics.

[25]  Henrik Madsen,et al.  Application of CUSUM charts to detect lameness in a milking robot , 2008, Expert Syst. Appl..

[26]  Sheue-Ling Hwang,et al.  Application control chart concepts of designing a pre-alarm system in the nuclear power plant control room , 2008 .

[27]  Chi-Hyuck Jun,et al.  Dispersion chart for some popular distributions under repetitive sampling , 2016 .

[28]  Elvira N. Loredo,et al.  A Program for ARL Calculation for Multivariate EWMA Charts , 2001 .

[29]  Chi-Hyuck Jun,et al.  Designing of X-bar control charts based on process capability index using repetitive sampling , 2014 .

[30]  Muhammad Azam,et al.  Designing of a new monitoring t-chart using repetitive sampling , 2014, Inf. Sci..