An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

Hany, Maureen; Mahmoud, Mahmoud A.

doi:10.1002/qre.1916

Cited by 5 publications

(8 citation statements)

References 33 publications

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“…To this end, for 100 000 simulation runs, we count the number of correct signals, out‐of‐control samples, false alarms, and in‐control samples. Step 3: Assess the conditional control chart performance To assess the performance of a conditional control chart during updating, we determine the CTAP and CFAP as follows:

C T A P = \frac{# correct signals}{# out‐of‐control samples},

and

C F A P = \frac{# false signals}{# in‐control samples} .

To assess the conditional performance of a conditional control chart after updating, we determine the conditional false alarm probability ( CFAR ) and the conditional average run length ( CARL ). For the Shewhart chart, these values can be obtained by

C F A R = normalΦ false(\frac{{\overset{L C L}{true}}_{t} - μ}{σ false/ \sqrt{n}} false) + 1 - normalΦ false(\frac{{\overset{U C L}{true}}_{t} - μ}{σ false/ \sqrt{n}} false),

and

C A R L = 1 false/ C F A R .

For the CUSUM and EWMA control charts, CFAR is assessed by determining the number of false alarms on an interval of 100 000 samples, and CARL is determined by the Markov chain approaches given by Hany and Mahmoud and Saleh et al Step 4: Assess the overall control chart performance To assess the unconditional control chart performance during updating, we determine the average true alarm percentage ( ATAP ) and the average false alarm percentage ( AFAP ) by averaging the CTAP and CFAP values for the R simulation runs.The expected average run length after updating ( AARL ) and the expected false alarm rate after updating ( AFAR ) are determined by averaging the corresponding conditional values obtained in the R simulation runs. Moreover, we determine the 10th and 90th percentiles of the CARL and CFAR values, which are indicated by CARL 10 , CARL 90 , CFAR 10 , and CFAR 90 .…”

Section: Simulation Proceduresmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

“…For the CUSUM and EWMA control charts, CFAR is assessed by determining the number of false alarms on an interval of 100 000 samples, and CARL is determined by the Markov chain approaches given by Hany and Mahmoud 19 and Saleh et al 20 Step 4: Assess the overall control chart performance To assess the unconditional control chart performance during updating, we determine the average true alarm percentage (ATAP) and the average false alarm percentage (AFAP) by averaging the CTAP and CFAP values for the R simulation runs.…”

Section: Step 3: Assess the Conditional Control Chart Performancementioning

confidence: 99%

See 2 more Smart Citations

The effect of continuously updating control chart limits on control chart performance

Huberts

Schoonhoven

Does

2019

Quality & Reliability Eng

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An open topic within statistical process monitoring is the effect on control chart properties of updating the control chart limits during the monitoring period. The challenge is to use the correct data for updating the control limits as in‐control data could be incorrectly classified as out of control and therefore not used for re‐estimating the parameters, and out‐of‐control data could be classified as in control and therefore used for re‐estimating. In the present article, we study the effect of updating the Shewhart, cumulative sum, and exponentially weighted moving average control chart limits. We simulate different scenarios: the monitoring data could be in or out of control, and the practitioner may or may not be able to find out whether the process is indeed out of control when the control chart gives a signal. The results reveal that the variation in the performance of the conditional control charts decreases significantly as a result of updating the control chart limits when the updating data are in control and also when the updating data are out of control and the practitioner is able to classify correctly data samples that produce a signal. However, when a practitioner is not able to classify a signal correctly, the advisability of updating depends on the type of control chart and the level of data contamination.

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C T A P = \frac{# correct signals}{# out‐of‐control samples},

and

C F A P = \frac{# false signals}{# in‐control samples} .

C F A R = normalΦ false(\frac{{\overset{L C L}{true}}_{t} - μ}{σ false/ \sqrt{n}} false) + 1 - normalΦ false(\frac{{\overset{U C L}{true}}_{t} - μ}{σ false/ \sqrt{n}} false),

and

C A R L = 1 false/ C F A R .

Section: Simulation Proceduresmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

Section: Step 3: Assess the Conditional Control Chart Performancementioning

confidence: 99%

See 1 more Smart Citation

The effect of continuously updating control chart limits on control chart performance

Huberts

Schoonhoven

Does

2019

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…For example, Zhao et al [22] proposed a method by combining two different CUSUM charts, namely, the dual CUSUM (DC) charts which are used to detect a range of shifts. Hany and Mahmoud [23] provided Crosier CUSUM (CC) control chart that performs better than the classical CUSUM chart. Similarly, Haq and Munir [24] suggested proposed CC and Shewhart-CUSUM (SC) charts for the process mean under ranked set sampling (RSS) scheme.…”

Section: Introductionmentioning

confidence: 99%

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Arslan

Ashraf

Anwar

et al. 2022

Mathematical Problems in Engineering

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The classical cumulative SUM (CUSUM) chart is commonly used to monitor a particular size of the mean shift. In many real processes, it is assumed that the shift level varies within a range, and the exact level of the shift size is mostly unknown. For detecting a range of shift size, the dual-CUSUM (DC) and dual-Crosier CUSUM (DCC) charts are used to provide better detection ability as compared to the CUSUM and Crosier CUSUM (CC) charts, respectively. This paper introduces a new mixed exponentially weighted moving average (EWMA)-DCC (EDCC) chart to monitor process mean. In addition, AIB-based EWMA-DC (EDC) and EDCC charts (namely, AIB-EDC and AIB-EDCC charts) are suggested to detect shifts in the process mean level. Monte Carlo simulations are used to compute the run length (RL) characteristics of the proposed charts. A detailed comparison of the proposed schemes with other competing charts is also provided. It turns out that the proposed chart provides better performance than the counterparts when detecting a range of mean shift sizes. A real-life application is also presented to illustrate the implementation of the existing and proposed charts.

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“…Jones [21] stated that the EWMA chart that fails to account for processparameter estimates, has an increase in the false alarm rate and a reduction in the detection ability of process changes. To address these problems, much efforts have been devoted to design control charts by accurately accounting for process-parameter estimates (see, for example, Hany and Mahmoud [22]; Lim et al [23]; Saleh et al [24]; Teoh et al [25]; Zhang et al [26]). Since control charts with the VSI feature are more sensitive to small shifts, Jensen et al [16] noted that these type of control charts are more seriously influenced by process parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

The Variable Sampling Interval EWMA X¯ Chart with Estimated Process Parameters

Teoh

Ong

Khoo

et al. 2021

Journal of Testing and Evaluation

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The exponentially weighted moving average (EWMA) ̅ chart with the variable-samplinginterval (VSI) feature is usually scrutinized under the assumption of known process parameters. However, in practice, process parameters are usually unknown and they need to be estimated from the in-control Phase-I dataset. With this in mind, this paper proposes the VSI EWMA ̅ chart where the process parameters are estimated. A Markov Chain approach is adopted to derive the run-length properties of the VSI EWMA ̅ chart with estimated process parameters.The standard deviation of the average time to signal (SDATS) is employed to measure the practitioner-to-practitioner variation in the control chart's performance. This variation occurs because different Phase-I datasets are used among practitioners to estimate the process parameters. Based on the SDATS criterion, this paper provides recommendations regarding the minimum number of required Phase-I samples. For an optimum implementation, this paper develops two optimization algorithms for the VSI EWMA ̅ chart with estimated process parameters, i.e. by minimizing the (i) out-of-control AATS (expected value of the average time to signal) and (ii) out-of-control EAATS (expected value of the AATS), for the cases of deterministic and unknown shift sizes, respectively. With the implementation of these new design procedures, the VSI EWMA ̅ chart with estimated process parameters is not only able to achieve a desirable in-control performance, but it is also able to quickly detect changes in the process. Keywords: expected value of the average time to signal, known and unknown shift sizes, optimization design, parameter estimation, standard deviation of the average time to signal, standard deviation of the time to signal

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An Evaluation of the Crosier's CUSUM Control Chart with Estimated Parameters

Cited by 5 publications

References 33 publications

The effect of continuously updating control chart limits on control chart performance

The effect of continuously updating control chart limits on control chart performance

Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

The Variable Sampling Interval EWMA X¯ Chart with Estimated Process Parameters

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