A non-parametric CUSUM control chart for process distribution change detection and change type diagnosis

Hou, Shiwang; Yu, Keming

doi:10.1080/00207543.2020.1721588

Cited by 21 publications

(12 citation statements)

References 45 publications

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“…2,25 As a feature, it poses optimal properties that makes it more sensitive when compared to other charts. [3][4][5] Considering the above, the plotting statistic of the CUSUM is…”

Section: Design With Known Parametersmentioning

confidence: 99%

“…CUSUM charts, by design, offer greater sensitivity to small and sustained alterations for mean processes if compared to other charts. [3][4][5] One of their perceptible aspects is the fact that they accumulate the drift of observations to spot changes in processes more quickly compared to traditional Shewhart charts. 6,7 Under normal conditions, implementation follows a phase I analysis, where parameters are estimated based on a set of in-control (IC) historical data 8 or by assuming parameters as known.…”

Section: Introductionmentioning

confidence: 99%

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A CUSUM control chart for gamma distribution with guaranteed performance

Madrid‐Alvarez,

García‐Díaz,

Tercero‐Gómez

2023

Quality & Reliability Eng

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Even though most control chart developments have revolved around the normal distribution, productive operations, in fact, often use non‐normal data, and some even use skewed distributions. This occurs with cycle times and many processes with a single specification limit. Under these conditions, gamma distributions often offer a better characterization where CUSUM schemes provide optimal performance to detect changes of a known in‐control (IC) parameter. In practice, gamma parameters have to be estimated, and limited phase I samples have undesirable effects on the phase II average run length (ARL) that has not been examined. To address this situation, this study uses Markovian models to assess the ARL of a CUSUM developed to monitor scale changes when IC parameters are estimated. This paper discusses the conditional ARL performance and proposes an adaptation of a stochastic estimation algorithm to guarantee a minimum performance. IC and out‐of‐control performance is compared with the conditional performance of a traditional approach where no corrections are made to guarantee a specific behavior. To demonstrate the practical application of this new approach, an implementation was made in a packaging process using multihead weighing machines. Practitioners interested in using reliable monitoring schemes will find, in this proposal, several implementation guidelines such as algorithms and look up tables to facilitate their implementations.

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“…2,25 As a feature, it poses optimal properties that makes it more sensitive when compared to other charts. [3][4][5] Considering the above, the plotting statistic of the CUSUM is…”

Section: Design With Known Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A CUSUM control chart for gamma distribution with guaranteed performance

Madrid‐Alvarez,

García‐Díaz,

Tercero‐Gómez

2023

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…As a general approach in most of the developed approaches, a distributionindependent (distribution-free) statistic such as Mann-Whitney statistic is defined and the performance has been evaluated in a robust condition against distribution by considering a few assumptions to it [35]. Six different categories of non-parametric statistics of quality characteristics have been introduced in Hou and Yu 36 and interested readers are referred to them. Due to main aim of this paper which is to monitor the profiles that have different IC and OC shape, the other literature of non-parametric method in monitoring quality characteristics are neglected and this type of profiles which is called non-parametric profiles hereafter is thus chosen for the focus of the literature review.…”

Section: Literature Review Of Non-parametric Profilesmentioning

confidence: 99%

Monitoring Non-Parametric Profiles using Adaptive EWMA Control Chart

Yeganeh

Shongwe

2022

Preprint

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To monitor the quality of a process in statistical process control (SPC), considering a functional relationship between a dependent variable and one or more independent variables which is denoted as profile monitoring is becoming an increasingly common approach. Most of the studies in the SPC literature have dealt with cases in which the functional relationship has the same form in the in-control (IC) and out-of-control (OC) situation or considered parametric approaches. Non-parametric profiles, which have different relationship in OC conditions is also very common. This paper designs a novel control chart to monitor not only the regression parameters but also the variation of the profile in phase II applications, using an adaptive approach. Adaptive control charts adjust the final statistic with regard to information of previous samples and the proposed method considers the relative distance of the chart statistic to the control limits as a tendency index and provides some outcomes about the process condition. The results of Monte Carlo simulations show the superiority of the proposed monitoring scheme in comparison with the common non-parametric control chart.

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“…The literature on the nonparametric CUSUM scheme continues to flourish and has been widely studied in the last few years. See, for example, Liu et al., 32 He et al., 33 Hou and Yu, 34 Triantafyllou and Ram, 35 Xue and Qiu 36 and Brown 37 . While far too little attention has been paid to single (combined) CUSUM schemes for tri‐aspect process quality surveillance.…”

Section: Introductionmentioning

confidence: 99%

An optimally designed distribution‐free CUSUM procedure for tri‐aspect surveillance of continuous processes

Tang

Mukherjee

2023

Quality & Reliability Eng

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In the past few decades, research on nonparametric process monitoring schemes mainly dealt with the uni‐aspect or bi‐aspect schemes, focusing on monitoring process location or scale separately or jointly. Another critical process characteristic, namely, the process shape, is not explicitly dealt with in‐depth in most existing charting schemes. In classical hypothesis testing, some recent literature clearly showed that the multi‐aspect test statistics, although designed for very restrictive alternatives, often perform as well or better than many statistics for arbitrary distributional shifts. They are often better than Kolmogorov‐Smirnov or Cramér‐von Mises statistics and some empirical likelihood‐based test statistics. The current paper aims to use a tri‐aspect statistic to design a distribution‐free Phase‐II Cumulative Sum (CUSUM) charting scheme for monitoring any arbitrary process changes in the process. The proposal is nonparametric and is equivalent to an unknown standard case. It reflects, in addition, which parameters, among location, scale, or shape, are more responsible for a signal. The construction of the CUSUM scheme from an existing tri‐aspect Shewhart‐type chart is simple, so significant attention is devoted to determining a near‐optimal reference parameter of the chart in keeping an unknown shift type in mind. Comparisons of the optimal performance of various competitors are considered in terms of the median run length (MRL) metric. The proposed charting scheme designed with the tri‐aspect statistic compares highly favorably with many existing SPM schemes. The same is evident from our findings based on the Monte‐Carlo simulation. Finally, the proposed schemes are illustrated with a flow‐width measurement monitoring example.

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A non-parametric CUSUM control chart for process distribution change detection and change type diagnosis

Cited by 21 publications

References 45 publications

A CUSUM control chart for gamma distribution with guaranteed performance

A CUSUM control chart for gamma distribution with guaranteed performance

Monitoring Non-Parametric Profiles using Adaptive EWMA Control Chart

An optimally designed distribution‐free CUSUM procedure for tri‐aspect surveillance of continuous processes

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