www.iiec2013.ir Monitoring Autocorrelated Reliability Data in Multistage Processes Shervin Asadzadeh 1* , Abdollah Aghaie 2* , Seyed Taghi Akhavan Niaki 3** 1 Corresponding Author, PhD Student, sh_asadzadeh@dena.kntu.ac.ir 2 Professor, aaghaie@kntu.ac.ir 3 Professor, niaki@sharif.edu * Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran ** Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran Abstract— In this paper, multistage process monitoring with the purpose of improving the product reliability is addressed. To this end, the process output is usually inspected under specific load conditions and the tensile strength of reliability-related quality characteristic is measured. However, in some cases, the observations from the process output are autocorrelated. This makes the use of existing monitoring procedures futile. Therefore, the proportional hazards (PH) models have been modified to effectively justify the effect of cascade property in line with the autocorrelation issue and three monitoring schemes are devised. The problem of unobserved heterogeneity is discussed as well. The simulation-based study is conducted to investigate the performance of the proposed control charts. The results reveal that the cumulative sum control chart is superior in that it can detect shifts much faster. Finally, the impact of ignoring autocorrelation has been studied which confirms the significant effect of autocorrelation on the performance of the process control. Keywords- multistage processes; autocorrelated observations; proportional hazards model, CUSUM control chart, EWMA control chart I. INTRODUCTION Multistage process monitoring has become an important issue because almost all products go through several different steps before they are finally made [1]. This implies that a change in an upcoming quality characteristic may affect some or all outgoing quality variables in successive stages of a process. The mentioned property is best known as cascade property which is the main feature of multistage processes. Cause-selecting chart (CSC) [2] is the most effective procedure to monitor and diagnose dependent process steps with normally distributed quality characteristics. To relax the normality assumption, monitoring schemes based on the generalized linear models were proposed and extended [3-6]. The underlying idea is to adjust the values of the quality characteristic of interest for the effect of all influential covariates. The importance of monitoring such cascade processes turns this area as an attractive avenue for future research and both manufacturing and service operations have been addressed and studied by a lot of researchers [7]. However, in some industrial or service processes, the main intention of using a control scheme is to improve the product reliability by monitoring specific quality characteristics. For instance, the skein strength of spun cotton, the tensile strength of adhesive bond between a vinyl fabric and foam backing in the interior of a car and the tensile strength of a weld are among the most well-known reliability-based quality variables in industrial processes, while the survival times of patients after performing the surgery operation can be referred to as the quality characteristic of interest in service processes. Such reliability data are typically censored since it suffices for them to reach a pre-determined bound chosen to ensure the reliability of products. Moreover, these reliability data often come from parametric distributions, namely Location-Scale and Log- Location-Scale [8]. Extreme value, Weibull and Lognormal are among the most widely used distributions for modeling reliability data. There exist a large number of researches in which the monitoring procedures were proposed to address Location-Scale and Log-Location-Scale distributions; see [9- 14]. Moreover, the problem of monitoring reliability data whose values are censored due to the presence of a censoring mechanism has been fully explored by Steiner and Mackay [15-17]. In fact, the so-far proposed monitoring procedures have been concentrated on a single stage process. But, the two mentioned features make the monitoring of such quality variables difficult specifically when their relationship with preceding covariates must be taken into account as in multistage processes. The more complicated picture arises in