A Novel Differential Evolution Algorithm with Q- Learning for Economical and Statistical Design of X- Bar Control Charts Ahmad Abdulla Al-Buenain Mechanical and Industrial Engineering Department Qatar University Doha, Qatar laa1304017@student.qu.edu.qa Damla Kizilay Industrial Engineering Department Izmir Democracy University Izmir, Turkey damla.kizilay@idu.edu.tr Ozge Buyukdagli The International University of Sarajevo, Department of Computer Science Sarajevo, Bosnia Herzegovina obuyukdagli@ius.edu.ba M. Fatih Tasgetiren Logistics Management Department, Yasar University Izmir, Turkey fatih.tasgetiren@yasar.edu.tr Abstract—This paper presents a novel differential evolution algorithm with Q-Learning (DE_QL) for the economical and statistical design of X-Bar control charts, which has been commonly used in industry to control manufacturing processes. In X-Bar charts, samples are taken from the production process at regular intervals for measurements of a quality characteristic and the sample means are plotted on this chart. When designing a control chart, three parameters should be selected, namely, the sample size (n), the sampling interval (h), and the width of control limits (k). On the other hand, when designing an economical and statistical design, these three control chart parameters should be selected in such a way that the total cost of controlling the process should be minimized by finding optimal values of these three parameters. In this paper, we develop a DE_QL algorithm for the global minimization of a loss cost function expressed as a function of three variables , , and  in an economic model of the X-bar chart. A problem instance that is commonly used in the literature has been solved and better results are found than the earlier published results. Keywords—Differential evolution, Q-learning, X-Bar control charts, Economical design of control charts. I. INTRODUCTION Statistical control charts are generally used to control manufacturing processes. The main objective of a control chart design is to detect the process shift by distinguishing between two different sources of variation in a process. These variations are called as assignable and common causes of variability [1]. In general, there are two types of control charts, i.e., charts for variables and charts for attributes. X-bar is a type of variable control chart, which is most widely employed in the industry because of its simplicity. The purpose of these charts is to determine the assignable causes leading to nonconforming products in manufacturing. When these assignable causes are determined, corrective actions can be taken before a large number of nonconforming products are manufactured. In addition, these methods also provide effective tools for determining the process parameters and making an analysis of process capability. As mentioned before, in the design of a control chart, three parameters should be determined. These are sample size , sampling interval ℎ, and width of control limits  for the chart. Selecting these three parameters is also known as the design of a control chart. In general, control charts have been designed to minimize the two statistical errors, namely Type-I error () and Type-II error (). However, in practice, the design of a control chart has some economical activities like sampling and testing, determining out-of-control signals, correcting and revising the out-of-control process, the loss of the company’s goodwill on the delivering nonconforming products to customers and so on. For these reasons, the economical design of a control chart has been attracting more attention over recent years [2]. The economical design is a mathematical model where parameters of a control chart should be found by minimizing an expected cost function, which includes costs of sampling and testing, costs related to determining out-of-control signals and possibly correcting the assignable cause(s), and costs of allowing nonconforming units to customers. Duncan [3] first proposed an economic model for the design of the X-bar chart where they assumed that a random shift in the process means due to single assignable cause and the moving from in-control to the out-of-control state have an exponential distribution. Panagos et al. [4] defined two distinct situations in economic design (i) the process continues in operation while searches for the assignable cause are made and (ii) the process must be shut down during the search. Detailed literature reviews can be found in Montgomery [2], Svoboda [5] and Ho and Case [6] on the economic design of control charts where it is observed that the majority of the researchers have considered X-bar chart and Duncan’s [3] single assignable cause model where the loss cost is expressed as a function of three variables  , ℎ and  . Choosing these parameters on economic criteria is called economical design, and it is getting more and more popular due to its ability and capability of having the process under statistical control at lower cost [7–13]. The effectiveness of economic design depends on how accurately this loss cost function is minimized to determine the values of the three design variables. Several optimization techniques have been proposed to minimize these design variables [4–6,14]. However, very recently, some global optimization methods such as Genetic Algorithm [15], Particle Swarm Optimization [16,17], Simulated Annealing [18] have been developed to solve the problem on hand. tried for the same purpose. Some other global optimization algorithms have been also proposed for the economic design of charts other than the X-bar chart [19,12]. In addition to the above, teaching–learning-based optimization (TLBO) has been proposed for the minimization of the loss cost 978-1-7281-6929-3/20/$31.00 ©2020 IEEE