Abstract:
Shewhart, cumulative sum and exponentially weighted moving average control charts
were introduced for monitoring process mean. These charts were subsequently used
for monitoring process variance. Later, it was realized that process monitoring is a
bivariate problem and several joint monitoring scheme for process mean and variance
were introduced by many authors. The challenge in the advanced joint monitoring
scheme is that it should be sensitive for both small and larger changes either in
process mean, variance or both. In this thesis, a new advanced joint monitoring
scheme for process mean and variance called semi-elliptical exponentially weighted
moving average scheme is proposed for Gaussian processes with its design procedure
for the industry. The performance of this new scheme is compared with the joint
monitoring schemes suggested by other authors using a new comparison index
proposed in this thesis. Application of this new scheme is tested with real and
simulated data sets.
Most frequently, this new scheme detected various magnitudes ofshifts in mean and
variance quicker than any other schemes. In overall, the new scheme developed in this
study performs better than the existing schemes with some limitations when the shift
in mean, variance or both is large. A big advantage ofthis new scheme is, the design
parameters are independent ofsample size. As this scheme use the standardized mean
and variance, this scheme can be used to monitor several parameters at a time in a
single display. Unlike most ofthe joint monitoring scheme, this new scheme takes the
drop in variance as the desirable state when the mean is on target. Therefore this
scheme can be recommended for advanced joint monitoring of process mean and
variance. The new methodology is very useful for many industrial applications.
Furthermore improvements are suggested on this scheme to monitor multi quality
parameters simultaneously.
