The VSI synthetic chart for the mean is still not in existent in the literature. To the best of the authors’ knowledge the adaptive synthetic charts that exist in the literature are mainly those mentioned above. Another adaptive synthetic control chart with the VSI feature is the synthetic Max chart proposed by Chen and Huang, for jointly monitoring the process mean and standard deviation. Huang and Chen and Chen and Huang developed adaptive synthetic S and synthetic R charts, respectively, by incorporating the VSI feature, for a quick detection of the process standard deviation. The concept of varying at least one of the control chart’s parameters has been extended to adaptive type synthetic control charts. Furthermore, numerous findings of the VSI control charts showed that these charts are substantially more efficient than the traditional FSI control charts. The results showed that the variable parameters chart is more powerful than the Cumulative Sum (CUSUM) chart for detecting shifts in the process mean. Costa extended the study of the Shewhart chart by incorporating variable parameters (VP), where the sample size, sampling interval and factor controlling the width of the action limits, are all varied. The variable sample size and sampling interval (VSSI) procedure incorporating ideas of the variable sampling interval (VSI) and variable sample size (VSS) approaches presented by Costa, is substantially more effective for detecting moderate process mean shifts compared with the VSI and VSS charts. Costa proposed taking variable sample sizes (VSS) from a process at FSI so that the chart outperforms the Shewhart chart for detecting moderate process mean shifts. Varying the sampling interval between samples is an alternative method adopted for a quicker detection of an out-of-control process as compared with the conventional fixed sampling interval (FSI) Shewhart chart. The economic statistical design is different from the economic design as the former includes statistical constraints in its design.Īn adaptive control chart involves varying at least one of the chart's parameters, such as the sampling interval, sample size or the width constant of control limits. studied the economic design and the economic statistical design of the synthetic chart using loss functions. provided an optimal design of the synthetic chart using the median run length ( MRL) criterion while Yeong et al. studied the run-length performance of the synthetic chart with unknown process parameters as the actual parameters are rarely known in practice. substantially reduces the out-of-control average run length ( ARL 1) and average number of observations to signal ( ANOS) by nearly half, as compared with the synthetic and double sampling charts. The synthetic double sampling chart proposed by Khoo et al. presented the combined synthetic and chart, where this chart produces an out-of-control signal when a sample mean falls beyond the limits of the chart or when the synthetic chart signals. Numerous studies on synthetic control charts have been made by researchers in recent years. Wu and Spedding introduced the combined Shewhart and conforming run length ( CRL) charts, which is called the synthetic control chart. Hence, numerous researches were made to improve the performance of the Shewhart chart by enhancing the chart's sensitivity to detect small and moderate mean shifts.Ĭombining charts is not a new procedure in the literature of control charts, see for example. However, this chart only gives a quick detection of large shifts but responds slowly to small and moderate shifts. The traditional Shewhart chart is commonly used to detect large mean shifts in manufacturing and service processes. Recently, many researchers have contributed to the area of control charts, such as, to name a few. As a consequence of variability, no two products coming from the same process are the same. Variability exists in all processes and it is the tendency of a change occurring in a process. A control chart is probably the most technically sophisticated tool among the basic Statistical Process Control (SPC) problem-solving tools to achieve process stability by reducing variability in the process.
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