The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-1835-y ORIGINAL ARTICLE On efficient estimation strategies in monitoring of linear profiles Abdaljbbar B. A. Dawod 1 · Marwan Al-Momani 1 · Saddam Akber Abbasi 2 Received: 12 August 2017 / Accepted: 25 February 2018 © Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract A fundamental strategy to diminish variations in manufacturing process urged the practitioners to characterize the quality of a process by a relationship between the response variable and one or more explanatory variables instead of a single quality characteristic; this state is known as a profile or a function. Profile monitoring mainly aims to test the stability of this relationship. Many researches have been carried out to study the different sampling techniques in the performance of linear profile under the maximum likely hood (MLE) estimation strategy, whereas using different estimation strategy has not been discussed so far. This paper is dedicated to introduce Bayesian estimation strategies with a proposal of novel control charts for jointly monitoring the linear profile. We considered restricted and pretest estimators, besides the estimation of distrust probability under the null hypothesis. Analytical and numerical results showed that the proposed estimators outperformed the MLE method. The proposed control charts have been used to monitor the two-phase flow in the oil industry to control the relationship between the flow rate and the pressure difference between two points. Keywords Intercept · Slope · Error variance · EWMA · Linear profiles · Restricted estimator · Pretest estimator · Average run length 1 Introduction Statistical process control (SPC) is a bunch of techniques used to monitor and manage the special causes of variation in a manufacturing or service processes. SPC has been adopted widely in variant new applications such as medicine, business, engineering, and social sciences (cf. [1, 2]). Control charts is the most widely used SPC toolkit; it can be used for monitoring location, dispersion, coefficient of variation, intercept, slope, etc (cf. [3, 4]). Mainly control charts are classified into memory less and memory control charts. [5] introduced Shewhart chart as a memory less chart by using the current sample information which makes it effective to detect large shifts. In contrast, [6, 7] proposed cumulative sum (CUSUM) and exponentially  Marwan Al-Momani almomani@kfupm.edu.sa 1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia 2 Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar weighted moving average (EWMA) charts, respectively, both charts utilize past and present information of the process which makes them effective to detect small and moderate shifts. From the practical perspective, control charts consists of two parts: retrospective phase (phase I) and monitoring phase (phase II). In phase I, a dataset is collected from the targeted process under stable conditions that represents the in-control state of the process, construct the control limits, and investigate their reliability. Phase II utilizes the control limits from phase I to monitor the process in the future (cf. [8–10]). Many studies have been carried out to improve control charts for linear profiling, for example, [3] introduced two control chart structures to monitor a semiconductor manufacturing that was formulated as a simple linear regression with known coefficients. They used multivariate T 2 chart and EWMA/Range(R) chart (i.e., EWMA chart in conjunction with R chart to monitor the mean and the variation respectively). Their charts based on the bivariate normality assumptions of the least square estimators. [11] proposed a control chart as combination of three univariate EWMA charts to monitor the intercept, slope, and the standard deviation in phase II simultaneously.