Authors: Shabbir Ahmad; Muhammad Riaz; Saddam Akber Abbasi; Zhengyan Lin
Addresses: Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou, 310027, China; Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, 47040, Pakistan ' Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan; Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia ' Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia; Department of Statistics, University of Auckland, Auckland 1142, New Zealand ' Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou, 310027, China
Abstract: Standard Shewhart control charts are often based on the assumption that the observations follow a specific parametric distribution, such as the normal, and outlier-free samples are initially selected to construct control limits for future monitoring of process parameters, e.g., location, dispersion, etc. The median is a popular measure of location which is more robust than mean for heavily skewed distributions. In ideal circumstances (where all the underlying assumptions such as normality and independence are met), the median chart is shown to be less efficient that the mean chart. To overcome the efficiency loss of the median chart, this study presents a set of auxiliary information-based median type Shewhart charts based on parent normal, t and gamma distributed process environments under double sampling scheme. The performance of these charts is evaluated in terms of run length (RL) characteristics such as: average run length (ARL), median run length (MDRL), standard deviation of the run length distribution (SDRL), extra quadratic loss (EQL) and relative ARL (RARL). Moreover, the effects of Step 1 sample size and contaminated environments are examined on the ARL performance of different median-based charting structures, under double sampling scheme. Illustrative examples are also provided to explain the working of the said charts. [Received 24 March 2012; Revised 21 October 2012; Revised 27 January 2013; Accepted 12 February 2013]
Keywords: auxiliary information; average run length; ARL; contamination; double sampling; extra quadratic loss; EQL; median control charts; median run length; MDRL; normality; non-normality; relative ARL; RARL; standard deviation of run length distribution; SDRL; statistical process control; SPC.
European Journal of Industrial Engineering, 2014 Vol.8 No.4, pp.478 - 512
Received: 08 May 2021
Accepted: 12 May 2021
Published online: 14 Sep 2014 *