Search

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]

A Shewhart control chart is highly effective for detecting large process shifts, however, it is relatively less sensitive to the small shifts. A CUSUM chart is more efficient than a Shewhart chart for detecting small process shifts but it is inferior to that for detecting the large ones. This paper proposes the nonparametric combined Shewhart-CUSUM (CSC) control charts based on the sign statistic. By appropriately choosing the design parameters, a CSC chart exhibits a trade-off statistical performance between that of the Shewhart and CUSUM sign charts. That is, its performance lies between the performances of the Shewhart and CUSUM sign charts for detecting a process shift of any size. The expressions for the zero-state and steady-state average run lengths of the CSC chart are obtained using a Markov chain approach. An example illustrating the implementation of this chart is provided. [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]

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]