Optimal design of Shewhart–Lepage type schemes and its application in monitoring service quality

Mukherjee, Amitava; Sen, Rudra

doi:10.1016/j.ejor.2017.09.013

Cited by 52 publications

(29 citation statements)

References 37 publications

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“…Mukherjee and Marozzi 16 proposed the generalized version of the PML test statistic. Mukherjee and Sen 13 considered control charts using the PML statistic. We introduce two statistics in the line of Mukherjee and Sen 13 as follows: When is odd,…”

Section: The Class Of Pml Statisticmentioning

confidence: 99%

“…After that, most nonparametric joint monitoring schemes have considered the -values of the Wilcoxon test and the Mood or Ansari-Bradley test to offer a follow-up analysis after receiving a signal. Interested readers may see Chowdhury et al 11 , Mukherjee 12 and Mukherjee and Sen, 13 among others. A systematic and thorough examination of signals following an alarm is critical in joint monitoring.…”

Section: Introductionmentioning

confidence: 99%

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A class of new nonparametric circular‐grid charts for signal classification

Song

Mukherjee

et al. 2021

Quality & Reliability Eng

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In this paper, some efficient monitoring and post-signal follow-up approaches are studied and compared for joint surveillance of location and scale of a process using the notions of circular-grid (CG) schemes. Precisely, three variants of CG Cucconi schemes are introduced and compared with three variants of percentile modified Lepage (PML) schemes. One of the PML schemes is equivalent to the traditional CG Lepage scheme, while another may be viewed as the Lepage type statistic using Gastwrith score, which is also a powerful tool for process surveillance. Overall, one of the proposed CG Cucconi schemes is most effective in identifying a class of signals, whether it is a location shift or scale shift or a shift in both parameters. It also indicates the direction of the shifts in either or both the parameters. Detecting a downward scale shift is the most challenging task in joint monitoring, and to this end, a new bias-corrected CG Lepage scheme is introduced. We compare the competing schemes in terms of correct signal classification probabilities. We illustrate the use of the proposed schemes in monitoring the trip-duration data in cab services. Some concluding remarks and future research problems are offered.

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Section: The Class Of Pml Statisticmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A class of new nonparametric circular‐grid charts for signal classification

Song

Mukherjee

et al. 2021

Quality & Reliability Eng

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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%

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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“…In recent years, we see the applications of the SPM schemes far beyond manufacturing sectors. For example, we find applications in healthcare surveillance (see Woodall, 2006), in monitoring service quality (see Mukherjee and Marozzi, 2017a; Mukherjee and Sen, 2018; Mukherjee et al, 2018), for environmental assessment (see Leiva et al, 2015), and in monitoring water quality (see Chong et al, 2020). For more applications in measurement and control, we refer to Riaz and Ali (2016), who discussed monitoring the surface roughness of metal part reamed holes, and Khatun et al (2019) for short production runs.…”

Section: Introductionmentioning

confidence: 99%

“…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. Li, Xie and Zhou (2018) extended the Lepage-type joint monitoring scheme for individual observation per sample.…”

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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Optimal design of Shewhart–Lepage type schemes and its application in monitoring service quality

Cited by 52 publications

References 37 publications

A class of new nonparametric circular‐grid charts for signal classification

A class of new nonparametric circular‐grid charts for signal classification

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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