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Classical control charts were developed with the assumption that the quality characteristics being monitored are independent. However, observations from several time‐dependent processes, such as industrial or manufacturing, are bound to be autocorrelated such that their autocorrelations decay gradually (long memory) rather than exponentially (short memory). Runs rules monitoring schemes have been proposed in Statistical Process Control literature to monitor processes in the presence of autocorrelation by incorporating the autoregressive integrated moving average (ARIMA) class of models which can only handle autocorrelation with a short memory. This paper therefore incorporates the autoregressive fractionally integrated moving average (ARFIMA (1,d,1)) model into four one‐sided runs rules schemes to monitor the mean of an autocorrelated process with long memory. The performance of these four one‐sided schemes was assessed using average run length (ARL) and expected ARL (EARL) metrics. Based on the ARL and EARL of the improved runs rules (IRR) schemes, the IRR5‐of‐5 and IRR2‐of‐7 were found to issue an out‐of‐control signal faster than the corresponding standard runs rules (RR) schemes, RR5‐of‐5 and RR2‐of‐7, respectively. Also, the four one‐sided schemes IRR5‐of‐5, IRR2‐of‐7, RR5‐of‐5, and RR2‐of‐7 in their steady state condition perform better than their corresponding zero state condition. We further observed that as the fractional parameter d increases, the detection ability of the monitoring schemes reduces. The application of the four one‐sided schemes was demonstrated on the diameter of cable production. [ABSTRACT FROM AUTHOR]

A two‐sided nonparametric sequential probability ratio test (SPRT) control chart for process location is proposed. The mechanism of this chart is based on the SPRT for location based on the signs of the sequential observations that is extended for a two‐sided alternative hypothesis. Approximate expressions that relate the statistical performance measures of this chart with that of its corresponding one‐sided charts are obtained through a simulation study and are shown to be quite accurate. Furthermore, an approach to design the proposed chart is provided. The statistical performance of the proposed chart is numerically compared to that of the two‐sided Shewhart, cumulative sum, and exponentially weighted moving average sign charts for location and it is observed that in general the proposed chart significantly outperforms these charts for detecting a location shift of any size. An example is provided to illustrate the mechanism of the proposed chart. Also, the chart is extended for monitoring process dispersion. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study nonparametric exponentially weighted moving average (EWMA) control charts based on the sign statistic, which are suitable for detecting changes in process dispersion. The sign statistic is defined by using appropriate deciles of the in‐control process distribution. The statistical performances of the proposed charts are determined through Monte Carlo simulation. Practical guidelines are provided for the statistical designs of these charts. We evaluate the statistical performances of the proposed charts by comparing them with that of the deciles‐based CUSUM sign chart and the EWMA lnS2 chart. The comparisons show that the proposed charts are viable nonparametric methods for monitoring the process dispersion. Finally, we provide an illustrative example to demonstrate the implementation of the proposed charts in practice. [ABSTRACT FROM AUTHOR]

Maxwell distribution has several applications in modeling physical and chemical processes, as well as in reliability and lifetime data analysis. In this paper, we propose the one‐ and two‐sided SPRT control charts for monitoring the scale parameter of a Maxwell distributed process. Using a Markov chain approach, we obtain the measures of statistical performance for the one‐sided charts. Reasonably accurate relationships between the performance measures of a two‐sided SPRT chart and that of its corresponding one‐sided charts are derived through Monte‐Carlo simulations. Approaches for designing the one‐ and two‐sided SPRT charts having the specified in‐control and the optimal out‐of‐control performances are provided. The results of the numerical study reveal that the proposed charts significantly outperform the Shewhart and cumulative sum (CUSUM) charts for detecting a shift of any size in the scale parameter. The mechanisms of the one‐ and two‐sided SPRT charts are illustrated via two real‐data examples: the first in the monitoring of the urinary glycosaminoglycan concentration and the second in the monitoring of the bearing life. [ABSTRACT FROM AUTHOR]

The Shewhart control chart is a prominent tool for identifying the changes in process parameters that are of large magnitude, however, it has reduced ability to identify the process changes of small magnitudes. On the other hand, an exponentially weighted moving average (EWMA) control chart is superior to the Shewhart chart in identifying process changes of small magnitudes but it is less proficient than the later chart in identifying changes of large magnitudes. This paper suggests nonparametric combined Shewhart‐EWMA (CSE) charts based on the sign statistic for the process location and process dispersion. The statistical performance measures of these charts are obtained using a Markov chain approach. The numerical comparisons revealed that the performance of a CSE chart lies within the range of the Shewhart sign and EWMA sign charts for identifying a process change of any magnitude. A real‐data example is provided to illustrate the mechanism of the chart. [ABSTRACT FROM AUTHOR]

This paper investigates the statistical performance of a sequential probability ratio test control chart for monitoring the dispersion of a normally distributed process. The expressions for statistical performance measures of the chart are derived using a Markov chain approach. It is shown through numerical comparisons that the overall statistical performance of this chart is superior to that of the existing competitor charts for dispersion. An example illustrating an application of the chart in practice is provided. [ABSTRACT FROM AUTHOR]