Some distribution-free Lepage-type schemes for simultaneous monitoring of one-sided shifts in location and scale

Chong, Zhi Lin; Mukherjee, Amitava; Khoo, Michael B. C.

doi:10.1016/j.cie.2017.11.029

Cited by 31 publications

(8 citation statements)

References 51 publications

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“…Chowdhury et al 25 proposed a distribution‐free Shewhart‐Cucconi (

SC

) scheme for jointly monitoring the location and scale parameters of a process. Chong et al 26,27 proposed a fuzzy monitoring scheme that combines two versions of the

SL

chart and a class of

SL

type schemes for one‐sided joint monitoring. Mukherjee and Marozzi 28 introduced a circular‐grid chart based on some Lepage‐type statistics.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive distribution‐free scheme for tri‐aspect surveillance of complex processes

Mukherjee

Qiu

Marozzi

2021

Appl Stoch Models Bus & Ind

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Distribution-free charting schemes for process monitoring are more robust and reliable than their parametric counterparts when the process distributions are unknown and complicated. Most of the existing control charts are uni-aspect schemes because they can detect a shift in only one aspect of the process distribution, like location or scale. Research on schemes for simultaneous surveillance of location and scale parameters has been very active in recent years, leading to many bi-aspect schemes. These schemes do not explicitly deal with the shape of the process distribution. However, a shift in the shape parameter with or without a location or scale shift can occur in practice, especially in production or time-to-event processes. Note that there are nonparametric schemes for detecting general shifts based on goodness-of-fit test statistics or empirical likelihood ratio statistics, which cannot isolate if there is a shift in location, scale, shape, or combination of these parameters. This article introduces a new distribution-free process monitoring scheme that can detect a shift in the location, scale or shape parameters, or any combinations of them. The new scheme is based on a combined statistic designed via Euclidean distance of the standardized Wilcoxon statistic for location, the standardized Ansari-Bradley statistic for scale, and the standardized Savage-type statistic for shape. We discuss the implementation design using the average run-length as the performance metric and investigate the proposed scheme's in-control performance. It is shown that the new charting scheme is in-control robust irrespective of the underlying process distribution and therefore applicable to monitor any univariate continuous processes. An out-of-control performance comparison study of the new scheme with many existing schemes shows that the new scheme is preferable to the existing schemes. We illustrate the proposed chart with real data to monitor a passenger train's arrival delays in Italy's regional route. The proposed scheme is comprehensive because it integrates the follow-up procedure via integrated sub-charts for classifying the signaling component.

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“…Chowdhury et al 25 proposed a distribution‐free Shewhart‐Cucconi (

SC

) scheme for jointly monitoring the location and scale parameters of a process. Chong et al 26,27 proposed a fuzzy monitoring scheme that combines two versions of the

SL

chart and a class of

SL

type schemes for one‐sided joint monitoring. Mukherjee and Marozzi 28 introduced a circular‐grid chart based on some Lepage‐type statistics.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive distribution‐free scheme for tri‐aspect surveillance of complex processes

Mukherjee

Qiu

Marozzi

2021

Appl Stoch Models Bus & Ind

Self Cite

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“…Recent approaches to monitor location and scale changes include the Shewhart‐type control charts of Chong et al and Mukherjee and Sen . Mukherjee and Marozzi followed a similar approach, but they used a circular grid to monitor the coordinates of location and scale statistics simultaneously with the standardized Wilcoxon statistic and the standardized Mood statistic.…”

Section: Introductionmentioning

confidence: 99%

“…Mahmood et al compared the performance of Shewhart‐type control charts under Cucconi and Lepage statistic, concluding that the Cucconi approach had better performance under light‐tailed distributions while the Lepage approach is a better alternative when dealing with heavy‐tailed distributions. Related approaches as the one presented by Chong et al proposed the monitoring of one side changes in mean and variance. A different approach was proposed by Zhang et al where a goodness‐of‐fit test (Cramér‐Von Mises) is used instead of a traditional Lepage or Cucconi statistic.…”

Section: Introductionmentioning

confidence: 99%

A distribution‐free CUSUM chart for joint monitoring of location and scale based on the combination of Wilcoxon and Mood statistics

Tercero-Gómez

Aguilar-Lleyda

Cordero-Franco

et al. 2020

Quality & Reliability Eng

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We propose a distribution-free cumulative sum (CUSUM) chart for joint monitoring of location and scale based on a Lepage-type statistic that combines the Wilcoxon rank sum and the Mood statistics. Monte Carlo simulations were used to obtain control limits and examine the in-control and out-of-control performance of the new chart. A direct comparison of the new chart was made with the original CUSUM Lepage based on Wilcoxon rank sum and Ansari-Bradley statistics. The result is a more powerful chart in most of the considered scenarios and thus a more useful CUSUM chart. An example using real data illustrates how the proposed control chart can be implemented.

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“…Recently, Sanusi and Mukherjee (2019) extended the premier Shewhart-Lepage schemes for joint monitoring of time between events and event magnitudes. Chong, Mukherjee and Khoo (2018, 2020) proposed some Lepage-type schemes to monitor one-sided shifts in location-scale. Moreover, Mukherjee and Sen (2018) introduced some generalized SL scheme based on percentiles modification.…”

Section: Introductionmentioning

confidence: 99%

Performance comparisons of distribution-free Shewhart-type Lepage and Cucconi schemes in monitoring complex process distributions

Chong

Huang

Mukherjee

et al. 2020

Transactions of the Institute of Measurement and Control

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In recent years, researchers introduced several distribution-free schemes for simultaneously monitoring the location and scale parameters of distribution in the literature related to process monitoring and control. To this end, the Shewhart-Lepage (SL) and Shewhart-Cucconi (SC) schemes are two fundamental distribution-free schemes. These schemes are primarily designed to monitor the location-scale family of densities. In practice, apart from the location and scale parameters, we often encounter the presence of a shape (or skewness) parameter. In this article, we investigate the performance of the SL and SC schemes in monitoring such models. We consider some skewed distributions in the location-scale family with one or two additional parameters, some three-parameter time-to-event processes, such as three-parameter Weibull and Gamma, which are very common in various measurement and control literature. First, we present the in-control performance of the two competing schemes and then carry out a comprehensive out-of-control performance study by considering different combinations of shifts. Several recent investigations showed that the SC scheme performs just as well or better than the SL scheme in joint monitoring of the location and scale parameters for a large number of process distributions. The current study shows that in the presence of an additional parameter, especially when the shift in the shape parameter is substantial, the SL scheme is better; for a small change in shape, the SC scheme is more competitive. In general, the SL scheme performs better in monitoring the three-parameter distributions for time-to-event processes. Finally, a real application and some concluding remarks are presented.

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Some distribution-free Lepage-type schemes for simultaneous monitoring of one-sided shifts in location and scale

Cited by 31 publications

References 51 publications

A comprehensive distribution‐free scheme for tri‐aspect surveillance of complex processes

A comprehensive distribution‐free scheme for tri‐aspect surveillance of complex processes

A distribution‐free CUSUM chart for joint monitoring of location and scale based on the combination of Wilcoxon and Mood statistics

Performance comparisons of distribution-free Shewhart-type Lepage and Cucconi schemes in monitoring complex process distributions

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