Improved Shewhart-Type Charts for Monitoring Times Between Events

Kumar, Nirpeksh; Chakraborti, S.; Rakitzis, Athanasios C.

doi:10.1080/00224065.2017.11917995

Cited by 37 publications

(21 citation statements)

References 35 publications

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“…In an effort to increase the sensitivity of the Shewhart charts, supplementary runs‐rules have been incorporated to these charts to improve their performance in detection of small shifts; see for instance Koutras et al for earlier research work on these. For more recent research work on runs‐rules, see for instance, Abbasi et al, Zaman et al, Khoo et al, Malela‐Majika et al, Kumar et al, Rakitzis, Arshad et al, Shongwe and Graham, Tran, Maravelakis et al, Lee and Khoo, and Mehmood et al…”

Section: Introductionmentioning

confidence: 99%

One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

Shongwe

Malela‐Majika

Molahloe³

2019

Quality & Reliability Eng

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In some industrial or health-related processes, it makes more practical sense to monitor either an increase only or a decrease only in the quality characteristic of interest. Consequently, in this paper, we propose four one-sided Shewhart X charts supplemented with runs-rules to monitor the mean of autocorrelated normally distributed samples using a stationary first-order autoregressive model. To counteract the negative effect of autocorrelation, we implement a sampling strategy which involves sampling of non-neighboring observations to form rational subgroups. The Markov chain technique is used to derive zero-state and steady-state closed-form expressions of the specific shift performance metric, ie, average run-length (ARL). Moreover, we compute the expected ARL metric which evaluates each monitoring scheme based on all specified range of possible values of the shift parameter, or more specifically, from a global point of view and thus gives a different perspective from the specific shift ARL metric. We observed that the steady-state improved w-of-w and the improved 2-of-(H + 1) schemes yield a better overall performance than their corresponding basic counterparts for all different levels of autocorrelation. A real-life example is provided to illustrate the implementation of the monitoring schemes proposed here.

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Section: Introductionmentioning

confidence: 99%

One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

Shongwe

Malela‐Majika

Molahloe³

2019

Quality & Reliability Eng

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“…Supplementary runs-rules have been used since the 1950s to improve the performance of the basic Shewhart control charts; see some detailed discussions of some of these earlier works in [2][3][4][5][6]. Some of the commonly cited and recent research works on runs-rules are done in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. For a literature review on the parametric runs-rules charts that cover articles up to 2006, a reader is referred to Koutras et al [22], whereas, for the full discussion of nonparametric runs-rules charts until 2017, see the book by Chakraborti and Graham [23].…”

Section: Introductionmentioning

confidence: 99%

One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

Shongwe

Malela‐Majika

Rapoo

2019

Journal of Probability and Statistics

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The one-sided and two-sided Shewhart w-of-w standard and improved runs-rules monitoring schemes to monitor the mean of normally distributed observations from independent and identically distributed (iid) samples are investigated from an overall performance perspective, i.e., the expected weighted run-length (EWRL), for every possible positive integer value of w. The main objective of this work is to use the Markov chain methodology to formulate a theoretical unified approach of designing and evaluating Shewhart w-of-w standard and improved runs-rules for one-sided and two-sided X- schemes in both the zero-state and steady-state modes. Consequently, the main findings of this paper are as follows: (i) the zero-state and steady-state ARL and initial probability vectors of some of the one-sided and two-sided Shewhart w-of-w standard and improved runs-rules schemes are theoretically similar in design; however, their empirical performances are different and (ii) unlike previous studies that use ARL only, we base our recommendations using the zero-state and steady-state EWRL metrics and we observe that the steady-state improved runs-rules schemes tend to yield better performance than the other considered competing schemes, separately, for one-sided and two-sided schemes. Finally, the zero-state and steady-state unified approach run-length equations derived here can easily be used to evaluate other monitoring schemes based on a variety of parametric and nonparametric distributions.

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“…Also, Scariano and Calzada proposed and studied a lower‐sided synthetic‐type chart for exponential data, while Yen et al studied one‐sided synthetic‐type charts based on the t ‐ and t r ‐charts. Recently, Kumar et al incorporated various runs rules into the two‐sided t r ‐chart to increase the sensitivity to detect small shifts. A comparative study between various one‐ and two‐sided charts for TBE data was conducted by Liu et al…”

Section: Introductionmentioning

confidence: 99%

Shewhart‐type Phase II control charts for monitoring times to an event with a guaranteed in‐control and good out‐of‐control performance

Kumar

Baranwal

Chakraborti

2019

Quality & Reliability Eng

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Monitoring time to event (failure) data is important in many applications. Proper monitoring and control can make the production process more efficient and provide economic advantages. In this paper, we consider the efficacy of a class of Shewhart‐type control charts for monitoring time to event data following an exponential distribution with an unknown mean, which is estimated from a class of estimators. An estimator is chosen within this class, so that the in‐control performance is maximized with respect to a number of popular criteria in the recent literature, and the proposed optimal charts are compared on the basis of their in‐control and out‐of‐control performance. The comparisons include the traditional Phase II exponential Shewhart chart using the maximum likelihood estimator. Improved in‐control and out‐of‐control performances of these charts can enhance the quality and productivity of manufacturing processes. Since no chart is best under all the criteria, a ranking system is used to choose a chart to use in practice with a good overall performance. Two illustrative examples using real data are given; summary and conclusions are offered.

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Improved Shewhart-Type Charts for Monitoring Times Between Events

Cited by 37 publications

References 35 publications

One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

Shewhart‐type Phase II control charts for monitoring times to an event with a guaranteed in‐control and good out‐of‐control performance

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