Distribution-free Lepage Type Circular-grid Charts for Joint Monitoring of Location and Scale Parameters of a Process

Self Cite

Weibull distribution is one of the most important probability models used in modeling time between events, system reliability, and particle sizes, among others. Therefore, efficiently and consequently monitoring certain changes in Weibull process is considered as an important research topic. Various statistical process monitoring schemes have been developed for monitoring different process parameters, including some for Weibull parameters. Most of these schemes are, however, designed to monitor and control a single process parameter, although there are two important model parameters for Weibull distribution. Recently, several researchers studied various schemes for jointly monitoring the mean and variance of a normally distributed process using a single plotting statistic. Nevertheless, there is still dearth of researches in joint monitoring of non‐normal process parameters. In this context, we develop some control schemes for simultaneously monitoring the scale and shape parameters of processes that follow the Weibull distribution. Implementation procedures are developed, and performance properties of various proposed schemes are investigated. We also offer an illustrative example along with a summary and recommendations.

“…Nevertheless, we can consider the Mahalanobis distance that takes appropriate account of the covariance between

{\overset{truê}{k}}_{MLE}

and

{\overset{truê}{λ}}_{MLE}

. Readers may refer to Mukherjee and Marozzi for more discussion on the Mahalanobis distance in developing a process control scheme.…”

Section: Some Shewhart‐type Joint Schemesmentioning

confidence: 99%

Design and comparison of some Shewhart‐type schemes for simultaneous monitoring of Weibull parameters

Gong

Mukherjee

2018

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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

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.

“…Among the more recent articles, we recommend Li et al, Qiu and Li, Graham et al, Abbasi et al, Mukherjee et al, Graham et al, Liu et al, Chowdhury et al, Mukherjee and Sen, Qiu and Zhang, Mukherjee, Chong et al, and Huang et al Clearly, in the last few years, research on NSPM techniques has gained considerable momentum. Mukherjee and Marozzi outlined the phenomenal growth of works on NSPM schemes. Searching through Google Scholar database, during early September 2015, they noted that “ 246 articles on distribution‐free control charts during 2000–2009 and 466 articles in the following years.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric cost‐minimized Shewhart‐type process monitoring with restricted false alarm probability

Mukherjee

2019

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Traditional Duncan-type models for cost-efficient process monitoring often inflate type I error probability. Nevertheless, controlling the probability of type I error or false alarms is one of the key issues in sequential monitoring of specific process characteristics. To this end, researchers often recommend economic-statistical designs. Such designs assign an upper bound on type I error probability to avoid excessive false alarms while achieving cost optimality. In the context of process monitoring, there is a plethora of research on parametric approaches of controlling type I error probability along with the cost optimization. In the nonparametric setup, most of the existing works on process monitoring address one of the two issues but not both simultaneously. In this article, we present two distribution-free cost-efficient Shewhart-type schemes for sequentially monitoring process location with restricted false alarm probability, based, respectively, on the sign and Wilcoxon rank-sum statistics. We consider the one-sided shift in location parameter in an unknown continuous univariate process. Nevertheless, one can easily extend our proposed schemes to monitor the two-sided process shifts. We evaluate and compare the actual performance of the two monitoring schemes employing extensive computer simulation based on Monte Carlo. We investigate the effects of the size of the reference sample and the false alarm constraint. Finally, we provide two illustrative examples, each based on a realistic situation in the industry.