Apr-Jun.12 - the Nitie

Performance of traditional
chart with correlated data
Sukhraj Singh*
Dr. D. R. Prajapati**
Shewhart charts are the prominent charts used to detect the
larger shifts in the mean of the process. They are widely used in
the all type of the processes as well as in the service industries.
It is usually assumed that the observations from the process
output are independent and identically distributed (i.i.d.). But
in actual practice, for many processes the observations are
effect on the performance of the Shewhart (standard) chart.
The performance of the traditional (Shewhart) chart is studied
for the i.i.d. data and for the positively correlated data. The
Average Run Lengths (ARLs) at various sets of parameters of
the chart are computed by simulation, using the MATLAB
software. The behavior of the chart at the various shifts in
the process mean is studied and analyzed. It is concluded that
when the level of correlation increases, both the false alarm
rate and out of control ARL increase. In this paper, optimal
schemes of the chart for each level of the correlation are
suggested.
Key Words: Traditional charts, Average run length,
independent and identically distributed data, Autocorrelation,
MATLAB
INTRODUCTION
Control charts are one of the powerful tools of the
Statistical Process Control (SPC) techniques, which are
widely used in industry for process improvement and
for estimating parameters or monitoring the variability
of a given process. Shewhart charts were originally
developed by Walter F. Shewhart (1931). The limits of
the chart are known as upper control limit (UCL) and
LCL = +
deviation.
Figure 1 shows the sample
lower control limits.
chart with upper and
* Research Scholar in the department of
Mechanical Engineering,
PEC University of Technology, Chandigarh-160012
(India). E-mail: sukhraj7in@yahoo.co.in
** Assistant Professor in the department of
Mechanical Engineering,
PEC University of Technology
(formerly Punjab Engineering College),
Chandigarh-160012 (India).
E-mail: praja_3000@yahoo.com
(Corresponding Author)
Figure 1 Sample
chart
The process is assumed to be out of control when the
sample average falls beyond these limits. The Shewhart
in processes. It is assumed that the process observations
are i.i.d but usually there is some correlation among the
data and when this correlation is build up automatically
in the entire process, this phenomenon is called
Autocorrelation.
Vol. 36, No. 2, April-June, 2012
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