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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 sequential probability ratio test (SPRT) control chart for monitoring the mean of a normal process is proposed in this paper. Its mechanism is based on the SPRT for the mean of a normal distribution that is extended for a two-sided alternative. The exact statistical performance measures of this chart are obtained using a Markov chain approach. An approach to design the chart such that it has a specified in-control performance and the optimal out-of-control performance for detecting a mean shift of a particular size is provided. The statistical performance of this chart is numerically compared with that of various competing charts in the existing literature. It is found that the proposed chart outperforms all these charts for detecting a mean shift of any size. An example to illustrate the mechanism of the chart is provided. [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]

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]

This paper develops a nonparametric sequential probability ratio test (SPRT) control chart for monitoring the process location. The chart is based on a sequential sign test. Young's algorithm to determine the properties of the SPRT for a parameter of discrete Koopman-Darmois density is used to obtain the exact statistical performance measures of the proposed chart. The proposed chart substantially outperforms the Shewhart sign, synthetic Shewhart sign, CUSUM sign, and EWMA sign charts in detecting a location shift of any size. It is a preferable alternative to the parametric SPRT chart for mean when the underlying process distribution is not precisely known. The implementation of the chart is illustrated through an example. [ABSTRACT FROM AUTHOR]

A memory-type control chart utilizes previous information for chart construction. An example of a memory-type chart is an exponentially-weighted moving average (EWMA) control chart. The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts. Meanwhile, the EWMA median chart is robust against outliers. In light of this, the economic model of the EWMA and EWMA median control charts are commonly considered. This study aims to investigate the effect of cost parameters on the out-of-control average run length (ARL1) in implementing EWMA and EWMA median control charts. The economic model was used to compute the ARL1 parameter. The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis. When the input parameters change based on a predetermined percentage, the ARL1 is affected. According to the results of the EWMA chart, nine input parameters had an effect and five input parameters had no effect on the ARL1 parameter. Further, only seven of the 14 input parameters had an effect on the ARL1 of the EWMA median chart. However, the effect of each input parameter on the ARL1 was different. Moreover, the ARL1 for the EWMA median chart was smaller than the EWMA chart. This analysis is crucial to observe and determine the input parameters that have a significant impact on the ARL1 of the EMWA and EWMA median control charts. Hence, practitioners can obtain an overview of the influence of the input parameters on the ARL1 when implementing the EWMA and EWMA median control charts. [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]

A nonparametric sequential probability ratio test control chart to monitor the process dispersion based on the sequential sign statistic is proposed. The statistical performance of this chart is evaluated by comparing it with that of the charts for dispersion based on sign statistic in the existing literature. It is found that the proposed chart outperforms all these charts uniformly in detecting a shift of any size over a wide range. An implementation of the chart is illustrated through an example. [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 compares the powers of Kolmogorov-Smirnov test under ranked set sampling (RSS) and under double ranked set sampling (DRSS) using the level-2 sampling design. The extensive simulation study showed that in a single auxiliary variable case, the test is approximately equally efficient under RSS and DRSS. In a multiple auxiliary variables case, the test under DRSS is at least as efficient as that under RSS. [ABSTRACT FROM AUTHOR]

This paper analyzes the impact of urbanization on the diversity of bird species near the city of Amravati, India. The secondary data used for analysis consist of counts of the bird species sampled over the four stages along an urbanization gradient, namely, the rural forest area, peri-urban area, suburban area, and urban area. Exploratory data analysis and analysis of variance show that the urbanization significantly impacts the diversity of bird species in the region. The richness of species decreases with an increasing level of urbanization while the evenness in the urban area is substantially lower than that in other urbanization stages. The overall diversity significantly weakens with the higher stage of urbanization. The species in the region can be classified into notably different groups according to their abundance distribution along an urbanization gradient. The comfort zone of most of the species is the rural forest area. However, some species have adapted themselves to the urbanization to the extent that their comfort zones are the higher urbanization stages. [ABSTRACT FROM AUTHOR]