ORIGINAL ARTICLE A CUSUM-based method for monitoring simple linear profiles Abbas Saghaei & Marzieh Mehrjoo & Amirhossein Amiri Received: 13 November 2008 / Accepted: 15 April 2009 / Published online: 13 May 2009 # Springer-Verlag London Limited 2009 Abstract In most statistical process control applications, the quality of a process or product is characterized by univariate or multivariate quality characteristics and mon- itored by the corresponding univariate and multivariate control charts, respectively. However, sometimes, the quality of a process or a product is better characterized by a relationship between a response variable and one or more explanatory variables. This relationship, which can be linear, nonlinear, or even a complicated model, is referred to as a profile. So far, several methods have been proposed for monitoring simple linear profiles. In this paper, a new method based on cumulative sum statistics is proposed to enhance monitoring of linear profiles in phase II. The performance of the proposed method is evaluated by average run length criterion. A comprehensive comparison is also conducted between the performance of the proposed method and the existing methods for monitoring simple linear profiles. The results show that the proposed method performs satisfactorily. In addition, the effects of reference value, sample size, and corrected sum of squares of explanatory variables on the performance of the proposed method are investigated. Keywords Average run length (ARL) . Cumulative sum (CUSUM) control chart . Exponentially weighted moving average (EWMA) control chart . Profile . Statistical process control 1 Introduction The importance of statistical process control (SPC) techniques in quality improvement is well recognized in industry. Currently, most competitive manufacturing companies are implementing SPC in various applications. The process state is determined by using the distribution function of a single or multiple quality characteristics and then establishing a control chart. On the one hand, some of these control charts are univariate, such as Shewhart, cumulative sum (CUSUM), and exponentially weighted moving average (EWMA). On the other hand, there are charts like T 2 , multivariate CUSUM (MCU- SUM) and multivariate EWMA (MEWMA), which are classified as multivariate control charts. Sometimes, the quality of a process or product is characterized by a relationship between a response variable and one or more explanatory variables, which is referred to as profile. Stover and Brill [15], Mahmoud and Woodall [10], Woodall et al. [20], Wang and Tsung [17], Woodall [19], and Zou et al. [21] introduced practical applications of profiles. Kang and Albin [5] presented an example of a situation for which the linear profile of a process is of interest. In this case, there is a linear relationship between the measured pressure for a mass flow controller and the set point for flow. Figure 1 provides the illustration of this profile. Walker and Wright [16] used a nonlinear regression model to represent the vertical density of a particleboard as a function of depth (see Fig. 2). Montgomery [12] also Int J Adv Manuf Technol (2009) 45:1252–1260 DOI 10.1007/s00170-009-2063-2 A. Saghaei (*) : M. Mehrjoo Science and Research Branch, Islamic Azad University, Tehran, Iran e-mail: a.saghaei@srbiau.ac.ir M. Mehrjoo e-mail: m.mehrjoo@srbiau.ac.ir A. Amiri North Tehran Branch, Islamic Azad University, Tehran, Iran e-mail: amirhossein.amiri@gmail.com