Steady-State Behavior of Fraction Nonconforming Control Charts Using Sign Statistic

In the previous two Chapters, we proposed fraction nonconforming nonparametric control charts to monitor process location and process variability. It is also shown that performance of proposed control charts are superior to that of the Shewhart X and sign charts. If process is running in an in-control state for a long period, it will reach in steady-state mode. In order to characterize long-term properties of a control chart, it is an appropriate to investigate the steady-state ARL. Crosier (1986) suggested a technique for obtaining steady-state ARL of CUSUM chart using the Markov chain approach. Saccucci and Lucas (1990) have given a FORTRAN computer program for the computation of ARL of EWMA and combined ShewhartEWMA control schemes. The program calculates zero-state and steady-state ARL using the Markov chain approach. Champ (1992) has computed steadystate ARL of Shewhart control chart with supplementary runs rules. Davis and Woodall (2002) studied the steady-state properties of synthetic control chart to monitor shifts in process mean. Costa and Rahim (2006) proposed a synthetic control chart for process mean and variance based on non-central chi-square statistic. Lim and Cho (2009) developed a control charts with m-of-m runs rules to study the economical-statistical properties of control chart using steady-state ARL. In the present Chapter, we report steady-state behavior of synthetic and m-of-m control charts using sign statistics defined in equations (3.1) and (4.2). The rest of Chapter is organized as follows.