An integrated economic model for inventory and quality control problems

This paper develops an integrated economic model for inventory and quality control problems. The joint X¯ and R charts are used to control the production process, and this is combined with the determination of the economic production quantity in production processes. The production process is subject to an assignable cause which shifts the process from an in-control state to an out-of-control state. Shifts in both the process mean and the process variance are considered. When a signal for an assignable cause is triggered, a search is initiated and is terminated upon finding the cause within a pre-specified target time. The process is then brought back to an in-control state by repair. However, if the assignable cause is not discovered within the pre-specified time, production is allowed to continue until the next sampling or warning, whichever occurs first. In this case, either the alarm is considered to be false with a probability of Type I error or the assignable cause has not been eliminated with a probability of Type II error. In the latter case, the process produces products in an out-of-control state until the next sampling or warning, whichever occurs first. However, this state does not indicate any severe damage to the system. Joint X¯ and R charts are used for monitoring both the process mean and the process variance. Under these conditions, a generalized economic model for the joint determination of production quantity, an inspection schedule, and the design of the X¯ and R control charts are developed. A direct search optimization method is used to determine the optimal decision variables of the economic model.

[1]  George Tagaras.  A Survey of Recent Developments in the Design of Adaptive Control Charts , 1998 .

[2]  M. A. Rahim.  Determination of Optimal Design Parameters of Joint X̄ and R Charts , 1989 .

[3]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[4]  Douglas C. Montgomery,et al.  The Economic Design of Control Charts: A Review and Literature Survey , 1980 .

[5]  Meir J. Rosenblatt,et al.  Simultaneous determination of production cycle and inspection schedules in a production system , 1987 .

[6]  M. A. Rahim,et al.  AN INTEGRATED ECONOMIC DESIGN MODEL FOR QUALITY CONTROL, REPLACEMENT, AND MAINTENANCE , 2001 .

[7]  Antonio Fernando Branco Costa,et al.  Joint economic design of x and R charts under Weibull shock models , 2000 .

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

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

[11]  Smiley W. Cheng,et al.  Monitoring Process Mean and Variability with One EWMA Chart , 2001 .

[12]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .

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

[14]  Lonnie C. Vance.  Bibliography of Statistical Quality Control Chart Techniques, 1970-1980 , 1983 .

[15]  P. K. Banerjee,et al.  THE ECONOMIC DESIGN OF CONTROL CHARTS: A RENEWAL THEORY APPROACH , 1987 .

[16]  Antonio Fernando Branco Costa,et al.  JOINT ECONOMIC DESIGN OF X¯ AND R CONTROL CHARTS FOR PROCESSES SUBJECT TO TWO INDEPENDENT ASSIGNABLE CAUSES , 1993 .

[17]  Abdur Rahim,et al.  An economic model for \font\twelveit=cmti10 scaled 1600$\overline{\kern‐0.85ex\hbox{\twelveit X}}$\nopagenumbers\end and R charts with time‐varying parameters , 2002 .

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

[19]  M. A. Rahim.  JOINT DETERMINATION OF PRODUCTION QUANTITY, INSPECTION SCHEDULE, AND CONTROL CHART DESIGN , 1994 .

[20]  Antonio Fernando Branco Costa.  Joint X̄ and R charts with variable parameters , 1998 .

[21]  P. D. T. O'Connor.  Introduction to Statistical Quality Control (2nd edition), D. C. Montgomery, Wiley, 1991. Number of pages: 702. £49.35, Paperback £17.50 , 1991 .

[22]  Kenneth E. Case,et al.  Economic Design of a Joint X- and R -Control Chart , 1981 .

[23]  P. K. Banerjee,et al.  Optimal production run for a process with random linear drift , 1988 .

[24]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

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

[26]  Mohamed Ben-Daya,et al.  A generalized economic model for joint determination of production run, inspection schedule and control chart design , 1998 .

[27]  W. K. Chiu,et al.  Economic Design of Attribute Control Charts , 1975 .