Monitoring process mean using a second-order filter: Signal and system approach

In statistical process control one objective is to control the stability of a process. A process is stable when its mean is in control and variance bounded. Different control charts were introduced for monitoring the mean and variance of a process by plotting suitable test statistics on the chart. In this research design of a system which converts the sample mean to a test statistics was proposed. The second order filter, a special class of the Linear Time Invariant (LTI) systems, was used to design the converting system. It was shown that design of a low pass filter was better for detecting a level (mean) change in the process. Markov chain approach was also followed to construct appropriate control chart and to estimate its control limits. Simulated data under normality assumption for different scenarios were used to compare the proposed control chart with Shewhart and Exponentially Weighted Moving Average charts by means of ARL and PFS criteria. Existing data from the Central Bank of Iran was also applied to evaluate the suggested method. The signal to noise ratio was used to assess the performance of this method at different stages. Results indicate that the proposed method detects shifts more rapidly.