Proceedings of the 4 th World Congress on Mechanical, Chemical, and Material Engineering (MCM'18) Madrid, Spain – August 16 – 18, 2018 Paper No. ICMIE 130 DOI: 10.11159/icmie18.130 ICMIE 130-1 A Cost Comparison of the Synthetic and Shewhart X Charts Wai Chung Yeong 1 , Sok Li Lim 2 , Zhi Lin Chong 3 , Peh Sang Ng 3 1 Department of Operations and Management Information Systems, Faculty of Business and Accountancy Universiti Malaya, 50603 Kuala Lumpur, Malaysia yeongwc@um.edu.my 2 Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya 50603 Kuala Lumpur, Malaysia sokli@um.edu.my 3 Department of Physical and Mathematical Sciences, Faculty of Science, Universiti Tunku Abdul Rahman 31900 Kampar, Malaysia chongzl@utar.edu.my, psng@utar.edu.my Abstract – Although control charts are useful tools for quality monitoring, the cost of implementing the chart may prohibit practitioners from implementing it. The cost of sampling, cost of repairs, cost of defective products due to a failure in detecting out-of-control conditions, cost of false alarms etc can be prohibitively high. Hence, this paper compares the cost between the synthetic X and Shewhart X charts, so that practitioners could identify which chart is more economical to implement. The synthetic X chart was initially proposed to improve the ability in detecting changes in the process mean. This paper has shown that not only does the synthetic X chart has better detection ability than the Shewhart X chart, it is also more economical to implement. Thus, practitioners are recommended to adopt the synthetic X chart. Keywords: Optimal Chart Parameters, Optimal Cost, Quality Control, Shewhart X Chart, Synthetic X Chart. 1. Introduction Control charts are frequently adopted to monitor various processes to detect the presence of assignable causes which results in an out-of-control condition, especially in various engineering applications and manufacturing environments. However, the cost of implementing control charts can be high, which makes it less attractive for practitioners to adopt it. In the literature, control charts are mostly designed to optimize its’ performance in detecting an out-of-control condition, but the cost of implementing the chart is not given much attention, even though cost is very important for industries. Hence, this paper would like to compare the cost of two charts in the literature, i.e. the Shewhart X chart and the synthetic X chart. The Shewhart X chart is the first chart proposed in the literature. This chart works by producing an out- of-control signal when the sample mean is outside the upper or lower control limits, i.e. when X UCL  or X LCL  . Due to its’ simplicity, it is frequently implemented in industries. However, it shows weak performance in detecting small and moderate shifts. Since then, a number of new charts are proposed which improves the performance of the Shewhart X chart, one of which is the synthetic X chart. The synthetic X chart is proposed by [1]. The synthetic chart consists of a / X S sub-chart and a CRL/S sub-chart. It operates by defining an X sample as non-conforming if the sample mean, X is smaller than the lower control limit of the / X S sub-chart or larger than the upper control limit of the / X S sub-chart. An out-of-control signal is generated when the number of X samples between the current and the last non-conforming samples, i.e. the conforming run length, is smaller than or equal to L, the lower control limit of the CRL/S sub-chart. Note that the conforming run length follows a geometric distribution. [1] has shown that the synthetic chart shows significantly better performance than the Shewhart chart, in terms of fewer samples required to detect an out-of-control condition. Several extensions are done on the synthetic chart. [2] proposed a synthetic chart to jointly monitor the mean and variance, [3, 4] proposed a