Economic statistical design for x-bar control chart

Abstract

At the present, the economic mathematical models are not widely used to find the optimal sample size and sampling frequency related to the implementation of the control chart because the models are quite complex, and difficult to evaluate and optimize. The objective of this thesis is to develop an understandable economic mathematic model that is easily solved by simple spreadsheet software. The developed model can be used to determine sample size and sampling frequency that minimize total quality cost related to the implementation of control chart while statistical quality constraints which are type 1 error (α) and type 2 error (β) are retained. Both quality and cost criteria under the real situation of the case study company are used in order to make the model realistic. Quality costs in the model consist of Appraisal costs and Failure costs. Prevention costs are excluded from the model because they are not dependent on sample size and sampling frequency. Costs related to the control chart are collected and analyzed about their relationship to the control chart. Then, the economic mathematical model is optimized under two designed scenarios to find the optimum sample size and sampling frequency that minimize the total cost. The first scenario is to find the optimum sampling plan under the current number of testing machines while the new additional testing machines are allowed in the second scenario. Also, a sensitivity analysis is developed to illustrate how sensitive of each variable and parameter over the costs. After all, the benefit from the model is that the cost will be reduced while statistical quality constraints is retained by appropriate sample size and sampling frequency.