Page 209 - Special Topic Session (STS) - Volume 3

STS540 J.-C. Malela-Majika et al.

Shewhart monitoring schemes with
supplementary side-sensitive runs-rules for the
Burr-type XII distribution
J.-C. Malela-Majika, S.K. Malandala, M.A. Graham
University of Pretoria, South Africa

Abstract
Nonparametric or distribution-free control charts are highly desirable since a
minimal set of modeling assumptions are necessary for their implementation.
The traditional Shewhart monitoring scheme has been improved upon using
several techniques which include, amongst other, adding side-sensitive (SS)
and non-side-sensitive (NSS) runs-rules to them. It has been shown, in the
literature, that SS runs-rules outperform NSS schemes. Accordingly, here a SS
Shewhart-type monitoring scheme, supplemented with the 2-of-(ℎ + 1)
̅
standard and improved runs-rules (where h is a non-zero positive integer) for
non-normal data is proposed. A Markov chain approach is used to investigate
the zero-and steady-state performances. It is found that the proposed
schemes outperform many existing schemes. A summary and some
concluding remarks are given.

Keywords
Markov chain approach; side-sensitive schemes; steady-state performance;
zero-state performance

1. Introduction
In this paper it is assumed that the reader is familiar with the basics of
control charting, e.g. the construction of the basic Shewhart control chart, the
choice of which statistic to be plotted on the control chart (i.e. the choice of
charting or plotting statistic), the size of the shift to be detected, the sample
size, the frequency of sampling, the monitoring of location and/or spread,
metrics used to evaluate control chart performance, an in-control process vs.
and out-of-control process etc. All these issues are important as they need to
be addressed before a control chart can be implemented. In the statistical
process control and monitoring (SPCM) literature it is well-known that the
basic 1-of-1 scheme (denoted RR1-of-1 for our purposes) has control limits
/ = ± where is the distance between the centerline
0
0
(= ) and the control limits in standard deviation units, and are
0
the lower and upper control limits, respectively, and and are some
0
0
known in-control (IC) process mean and standard deviation, respectively. This
scheme signals when one plotting statistic (sample mean, ) plots on or
̅

198 |I S I W S C 2 0 1 9