Topic: The Hotelling T2 control chart Minimum 10 pages. Please study the chart, and apply to the data using Minitab. Data for Minitab can be created but the report should be explained clearly....

Executive Summary
Control chart is one of the most important tools which is often used for the purpose of
statistical quality control for various processes. Control chart is a graphical representation of
the dimensions or other aspects of the products which is being studies during any process
changes. Amongst the various graphical control charts, one of the most important and widely
used is Hotelling T
2
control chart which is a multivariate control and hence is based on
squared standardized (generalized) multivariate distances from the general mean. In this
paper a discussion has been carried out on the importance of this control chart and the way
the same can be used with an example of Hotelling T
2
control chart vis. a vis. other types of
control charts.
Introduction
For the topic of statistical quality control, amongst the most important tools which are used
are control charts. A control chart can be defined as a graph which is used for studying the
way a process changes over a period of time. For creation of the control chart plotting of data
in time order is carried out. Usually a control chart consists of
 a central line that depicts the average value of the variable that is being studied for the
control chart,
 A line depicting the upper limit for the control chart and
 A line depicting the lower limit for the control chart.
All of these lines are calculated and plotted basis the historical data or the specifications for
the processes which are being run and being tracked by the control chart. These process
behaviour charts are usually used as the tools for statically process control which tracks if the
specific business process of manufacturing process is running within the desired control
limits or not.
There are various control charts which have been developed over the period of time all of
which help in effective as well as effective tracking of the business process of manufacturing
process.
If 99.73% of all the values which are generated by the business process of manufacturing
process fall between the upper and lower limits for control, it can be said that the process
statistic is normal and hence the process is under control. If there are observations which
belong to the region excluding the control region, or there is any type of systematic
patternthat can be identified within the plotted variable, an inference can be made that some
new and unexpectedsource of variation has become part of the process. This is termed as a
special-cause variation.
In view of the fact that a high degree of variation leads to higher costs for quality, a control
chart which can detect and indicate the presence of a special-cause calls for
urgentexamination.
Amongst the various control charts which have high degree of application for the statistical
quality control within the business or manufacturing processes, one of the significantly used
control chart is Hotelling Control Chart. This control chart is prepared basis the Hotelling T
2

distance.

Body
The Hotelling T
2
distance can be defined as the measure which accounts for the covariance
structure of a multivariate normal distribution. Harold Hotelling had proposed this statistic in
the year 1947 and the same has been termed as Hotelling T
2
.
Hotelling T
2
can be seen as the Student's-t statistic’s multivariate counterpart. The statistic is...