Qual Quant (2015) 49:1185–1202
A new Shewhart control chart for monitoring process
mean based on partially ordered judgment subset
Abdul Haq · Amer Ibrahim Al-Omari
Published online: 3 June 2014
© Springer Science+Business Media Dordrecht 2014
Abstract In this paper, we propose a new improved Shewhart control chart for monitoring the
process mean based on partially ordered judgment subset sampling design. The performance
of the suggested control chart is compared with some of the existing control charts based on
simple random sampling and ranked set sampling methods. Average, standard deviation and
percentiles of the run lengths are used to evaluate the performances of the control charts. It
is observed that the proposed control chart is efﬁcient in detecting random shifts in process
mean as compared with the traditional quality control charts.
Keywords Partially ordered judgment subset sampling · Simple random sampling ·
Ranked set sampling · Control chart · Average run length · Monte Carlo simulations
A control chart is one of the commonly used tools for monitoring quality of the characteristic
of interest in a manufacturing process, i.e. to investigate whether a process is in control or not.
Statistical quality control charts was ﬁrst considered by Shewhart (1924). The assumption of
normality for the process characteristic is a main condition in most of these control charts.
The efﬁciency of the Shewhart control charts appear in determination the causes of variation
from the inherent causes of variation or uncontrollable. A good control chart must continue
sampling if the process is in-control, but if the process becomes out-of-control, the control
chart must give an out-of control signal to stop sampling as soon as possible.
The ranked set sampling (RSS) method was suggested by McIntyre (1952) for estimating
the population mean of pasture and forage yields. The RSS scheme is a more powerful
Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
A. I. Al-Omari (
Department of Mathematics, Faculty of Sciences, Alal-Bayt University, Mafraq 25113, Jordan