Quality requirements of manufactured products or parts are given in the form of specification limits on the quality characteristics of individual units. If a product is to meet the customer’s fitness for use criteria, it should be produced by a process which is stable or repeatable. In other words, it must be capable of operating with little variability around the target value or nominal value of the product’s quality characteristic. In order to maintain and improve product quality, we need to apply statistical process control techniques such as histogram, check sheet, Pareto chart, cause and effect diagram, or control charts. Among those techniques, the most important one is control charting. The cumulative sum (CUSUM) control charts have been used in statistical process control (SPC) in industries for monitoring process shifts and supporting online measurement. The objective of this research is to apply Taguchi's quality loss function concept to cost based CUSUM control chart design. In this study, a modified quality loss function was developed to reflect quality loss situation where general quadratic loss curve is not appropriate. This research also provided a methodology for the design of CUSUM charts using Taguchi quality loss function concept based on the minimum cost per hour criterion. The new model differs from previous models in that the model assumes that quality loss is incurred even in the incontrol period. This model was compared with other cost based CUSUM models by Wu and Goel, According to numerical sensitivity analysis, the proposed model results in longer average run length in in-control period compared to the other two models.

1. Introduction
  1.1 CUSUM Background and Theory
  1.2 CUSUM Control Charts
 2. Proposed Model
  2.1 Symbol Description
  2.2 Definition of Cycle Time
  2.3 Cost Description
  2.4 Determination of Model Parameters
  2.5 ARL Calculation Algorithm
 3. Computer Program
  3.1 Application of Loss Function to other CUSUMCost Model
  3.2 Goel and Wu’s Model
  3.3 Application of Loss Function to the CostModel
 4. Numerical and Sensitivity Analysis
  4.1 Numerical Example Analysis
  4.2 Results
  4.3 Sensitivity Analysis
 5. Conclusions

• Jungdae Kim(Industry-Academy Cooperation Foundation, Korea Nazarene University) | 김정대 Corresponding Author