An Economic-Statistical Design of x Control Charts with Multiple Assignable Causes

Duncan first proposed the economic design of x control charts in 1956 to control normal process means and ensure that an economic design control chart actually lowers the cost, compared with a Shewhart control chart. Many authors have studied the control charts from economic viewpoint from then on. An economic design does not consider the statistical properties, such as type I or type II error and average time to signal (ATS). To improve these issues, an economicstatistical design of control charts has been developed under the consideration of one assignable cause. However, there are multiple assignable causes in the real practice such as machine problem, material deviation, human errors, etc. In order to have a real application, this research will extend the original research from single to multiple assignable causes to establish an economic-statistical model of x control chart. A numerical example is used to illustrate the performance of the proposed model and to compare the lost cost between the pure economic and economic-statistical control chart design. A sensitivity analysis is also conducted in this numerical example.

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

[2]  A. Duncan.  The Economic Design of -Charts When There is a Multiplicity of Assignable Causes , 1971 .

[3]  Douglas C. Montgomery,et al.  Process failure mechanisms and optimal design of fraction defective control charts , 1976 .

[4]  Erwin M. Saniga,et al.  Joint Economically Optimal Design of X and R Control Charts , 1977 .

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

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

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

[8]  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 .

[9]  Thomas P. McWilliams,et al.  Economic, Statistical, and Economic-Statistical X̄ Chart Designs , 1994 .

[10]  Kenneth E. Case,et al.  Economic Design of Control Charts: A Literature Review for 1981–1991 , 1994 .

[11]  Zhang Wu,et al.  Asymmetric control limits of the x‐bar chart for skewed process distributions , 1996 .

[12]  Su-Fen Yang,et al.  Economic statistical design of S control charts using Taguchi loss function , 1998 .

[13]  Hsin-Hung Wu,et al.  An economic design for variable sampling interval MA control charts , 2003 .

[14]  Yee-Ming Chen,et al.  An Economic design for a variable-sampling-interval ${\bar{x}}$ control chart for a continuous-flow process , 2005 .

[15]  Fong-jung Yu,et al.  Optimization of design parameters for control charts with multiple assignable causes , 2006 .

[16]  Zhang Wu,et al.  The cost minimization and manpower deployment to SPC in a multistage manufacturing system , 2007 .

[17]  John Francis Kros,et al.  Economic design of Xbar control charts with continuously variable sampling intervals , 2010, Qual. Reliab. Eng. Int..

[18]  A. Baki Engin,et al.  Using economic X control chart design methodology to estimate and optimize machine efficiency in the case of multimachine assignments , 2010 .