Assessing the Impact of Head Starts in the Performance of One- Sided Markov-type Control Schemes

ABSTRACT Head start values — that is, non-zero initial values for the summary statistics of Markovtype control schemes such as the well known CUSUM schemes — are throughly recommended in the literature and used by quality control practitioners. The rationale of it is as follows: if the process is operating in-control, the summary statistic of the control scheme is soon brought to zero, so that the expected effect of the head start is minimal; otherwise, the operator is alerted to the out-of-control situation much sooner, which may prevent start-up problems. This paper emphasizes on the assessment of the impact of the adoption of a head start on the run length, the indisputedly popular performance measure of control schemes. It also brings the issue of stochastically monotone matrices into focus in the statistical process control setting and investigates their influence on the alarm rate function, the ageing character and the equilibrium rate function of the run length of one-sided Markov-type control schemes.