Qual Quant (2009) 43:865–874
Asymmetric control limits for small samples
Berna Yazici · Betül Kan
Published online: 7 September 2008
© Springer Science+Business Media B.V. 2008
Abstract When designing control charts, it is usually assumed that the measurement in
the subgroups are normally distributed. The assumption of normality implies that the control
limits for a chart for sample averages will be symmetrical about the centerline of the chart.
However, the assumption of an underlying normal distribution of the data may not hold in
some processes. If the measurements are asymmetrically distributed then the decision maker
may choose different actions. One thing that can be done is to consider the degree of skew-
ness. If the nature of the underlying distribution is skewed, then the traditional Shewhart
individuals chart may not be valid. This paper presents a technique for constructing appro-
priate asymmetric control limits when the distribution of data cannot be assumed to be a
normal distribution. Meanwhile, it proposes a skewness correction method for the generated
Burr, lognormal and exponential distributions. Some numerical calculations are generated
for n= 2, 3, 4 by using MATLAB.
Keywords Control charts · Non-normality · Skewness correction (SC) ·
Individuals control charts (I Chart) · Skewed distributions
Control charts are widely used in industry and powerful tools in statistical process control.
But the conventional control charts proposed by Shewart (1924) assumes that the distribution
of the quality characteristic is normal or approximately normal. There are numerous studies
present solutions in case of violation of this assumption.
Cowden (1957) proposed a split distribution method which provides asymmetric control
limits when the underlying population is skewed. Ferrell (1958) assumed a log-normal
B. Yazici (
) · B. Kan
Department of Statistics, Anadolu University, 26470 Eskisehir, Turkey
e-mail: email@example.com; firstname.lastname@example.org