A new approach to robust economic design of control charts

Control charts are widely used in industrial practice to maintain manufacturing processes in desired operating conditions. Design of control charts aims at finding the best parameters for the operation of chart. In the case of economic designs, the control chart parameters are chosen in such a fashion that the cost of controlling the process is minimum. For an [email protected]? control chart, the design involves the selection of three parameters namely, the sample size, the sampling interval and the control limit coefficient. The effectiveness of a design relies on the accuracy of estimation of input parameters used in the model. The input parameters are some cost parameters like 'cost of false alarms', and some process parameters like 'process failure rate'. Conventional control chart designs consider point estimates for the input parameters. The point estimates used in the design may not represent the true parameters and some times may be far from true values. This situation may lead to severe cost penalties for not knowing the true values of the parameters. In order to reduce such cost penalties, each cost and process parameter can be expressed in a range such that it covers the true parameter. This in turn, calls for a design procedure, which considers a range for each parameter, and selects the best control chart parameters. Present paper deals with the economic design of an [email protected]? control chart, in which the input parameters are expressed as ranges. A risk-based approach has been employed to find the optimum parameters of an [email protected]? control chart. Genetic algorithm (GA) has been used as a search tool to find the best design (input) parameters with which the control chart has to be designed. Performance of average based and risk-based designs are compared with respect to the risks they produce. Risk-based design methodology has been extended to incorporate statistical constraints also. The proposed method minimizes the risk of not knowing the true parameters to be used in the design, and is robust to the true parameter values.

[1]  J. Bert Keats,et al.  Economic Modeling for Statistical Process Control , 1997 .

[2]  T. McWilliams.  Economic Control Chart Designs and the In-Control Time Distribution: A Sensitivity Study , 1989 .

[3]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[4]  M. A. Rahim,et al.  Economic design of x -control charts under Weibull shock models , 1988 .

[5]  Kevin W Linderman,et al.  Robust economic control chart design , 2002 .

[6]  Joseph J. Pignatiello,et al.  Optimal Economic Design of X¯-Control Charts When Cost Model Parameters are Not Precisely Known , 1988 .

[7]  D. Montgomery,et al.  A Combined Adaptive Sample Size and Sampling Interval X Control Scheme , 1994 .

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

[9]  William H. Woodall,et al.  Weaknesses of The Economic Design of Control Charts , 1986 .

[10]  Sheldon M. Ross,et al.  Introduction to Probability Models, Eighth Edition , 1972 .

[11]  Shyama N Nandi.  Economic design of control charts , 1992 .

[12]  William H. Woodall,et al.  The Statistical Design of Quality Control Charts , 1985 .

[13]  Erwin M. Saniga,et al.  Economic Statistical Control-Chart Designs With an Application to and R Charts , 1989 .

[14]  J. Surtihadi,et al.  Exact economic design of X¯ charts for general time in-control distributions , 1994 .

[15]  A. Goel,et al.  An Algorithm for the Determination of the Economic Design of -Charts Based on Duncan's Model , 1968 .

[16]  Douglas C. Montgomery,et al.  Economic design of X control charts for two manufacturing process models , 1985 .

[17]  Lonnie C. Vance,et al.  The Economic Design of Control Charts: A Unified Approach , 1986 .

[18]  E. Saniga.  Economic Statistical Control-Chart Designs with an Application to X̄ and R Charts@@@Economic Statistical Control-Chart Designs with an Application to X and R Charts , 1989 .

[19]  Joseph G. Voelkel,et al.  Guide to Quality Control , 1982 .