Improved Phase I Control Charts for Monitoring Times Between Events

Kumar, Nirpeksh; Chakraborti, S.

doi:10.1002/qre.1623

Cited by 18 publications

(41 citation statements)

References 15 publications

(44 reference statements)

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“…and Eq. (11) for a and b , and c and d , respectively, but this becomes complicated quickly because m can be very large in Phase‐I application as discussed by Human et al . Therefore, we use an alternative approach to find the values of these constants.…”

Section: Statistical Calculations and Resultsmentioning

confidence: 99%

“…To this end, the FAP for Phase‐I | S | chart (see, Human et al

F A P = Pr ((), U_{max} \geq b true| I C) + Pr ((), U_{m i n} \leq a true| I C) - Pr ((), U_{max} \geq b and U_{m i n} \leq a true| I C)

where U max and U min denote the maximum and the minimum order statistic of U i , i = 1, 2, …, m .…”

Section: Statistical Calculations and Resultsmentioning

confidence: 99%

“…These constants should not be used in a Phase‐I study where parameters are estimated from preliminary samples. In this case one approach is to design the Phase‐I control chart based on the specified false alarm probability (FAP) and on the joint dependent distribution of the signaling events (Human et al …”

Section: Monitoring Bivariate Process Dispersionmentioning

confidence: 99%

“…). Other recent studies on the Phase‐I control charts include Chakraborti et al ., Human et al ., Saghir, Jones‐Farmer et al ., Kumar and Chakraborti, Ning et al ., Zwetsloot et al ., etc.…”

Section: Introductionmentioning

confidence: 99%

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The Phase I Dispersion Charts for Bivariate Process Monitoring

Saghir

Khan

Chakraborti

2015

Qual. Reliab. Engng. Int.

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Multivariate control charts are usually implemented in statistical process control to monitor several correlated quality characteristics. Process dispersion charts are used to determine the stability of process variation (which is typically done before monitoring the process location/mean). A Phase-I study is generally used when population parameters are unknown. This article develops Phase-I |S| and |G| control charts, to monitor the dispersion of a bivariate normal process. The charting constants are determined to achieve the required nominal false alarm probability (FAP 0 ). The performance of the proposed charts is evaluated in terms of (i) the attained false rate and (ii) the probability of signaling for out-of-control situations. The analysis shows that the proposed Phase-I bivariate charts correctly control the FAP (the false alarm probability) and detect a shift occurring in the bivariate dispersion matrix with adequate probability. An example is given to explain the practical implementation of these charts.

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Section: Statistical Calculations and Resultsmentioning

confidence: 99%

“…To this end, the FAP for Phase‐I | S | chart (see, Human et al

F A P = Pr ((), U_{max} \geq b true| I C) + Pr ((), U_{m i n} \leq a true| I C) - Pr ((), U_{max} \geq b and U_{m i n} \leq a true| I C)

where U max and U min denote the maximum and the minimum order statistic of U i , i = 1, 2, …, m .…”

Section: Statistical Calculations and Resultsmentioning

confidence: 99%

Section: Monitoring Bivariate Process Dispersionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Phase I Dispersion Charts for Bivariate Process Monitoring

Saghir

Khan

Chakraborti

2015

Qual. Reliab. Engng. Int.

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“…Other developments on TBE charts include the economic design of the charts, the Phase I TBE charts, the bivariate TBE chart, the runs rules based TBE charts, and the TBE chart for sampling inspection …”

Section: Introductionmentioning

confidence: 99%

Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

Yen

Khoo

Teh

et al. 2015

Quality & Reliability Eng

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Control charting methods for time between events (TBE) is important in both manufacturing and nonmanufacturing fields. With the aim to enhance the speed for detecting shifts in the mean TBE, this paper proposes a generalized group runs TBE chart to monitor the mean TBE of a homogenous Poisson failure process. The proposed chart combines a TBE subchart and a generalized group conforming run length subchart. The zero‐state and steady‐state performances of the proposed chart were evaluated by applying a Markov chain method. Overall, it is found that the proposed chart outperforms the existing TBE charts, such as the T, Tr, EWMA‐T, Synth‐Tr, and GR‐Tr charts. Copyright © 2015 John Wiley & Sons, Ltd.

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Time Between Events Monitoring with Control Charts

Chakraborti¹,

Kumar²,

Rakitzis³

et al. 2023

Wiley StatsRef: Statistics Reference Online

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Time between events (TBE) control charts play an important role in many applications, particularly in the monitoring of high‐yield processes. In this article, we discuss the most common types of control charts for time between events monitoring, along with some illustrations of their practical implementation. The usual distributional assumption for the time between events is that of the exponential distribution. We also briefly discuss the case where the TBE follows a Weibull distribution. Finally, for both distributions, the cases of known and unknown parameters are discussed.

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Improved Phase I Control Charts for Monitoring Times Between Events

Cited by 18 publications

References 15 publications

The Phase I Dispersion Charts for Bivariate Process Monitoring

The Phase I Dispersion Charts for Bivariate Process Monitoring

Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

Time Between Events Monitoring with Control Charts

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