Progressive Mean Control Chart for Monitoring Process Location Parameter

Abbas, Nasir; Zafar, Raja Fawad; Riaz, Muhammad; Hussain, Zawar

doi:10.1002/qre.1386

Cited by 60 publications

(86 citation statements)

References 15 publications

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“…This statistics is result of inspiration from PM (see Agarwal (2003) and Abbas et al (2013) for more details). Let X ij , i = 1, 2, 3, .…”

Section: The Proposed Pv Control Chartsmentioning

confidence: 95%

“…The mean and variance of PM are given as μ PM j = μ and σ PM j = σ 0 √ j , respectively, where μ and σ 0 are mean and standard deviation of the process, respectively. So ultimately, the 3-sigma limits become Abbas et al (2013) discussed that these limits are so wider (relative to the plotting statistic, i.e., PM) for the larger values of j , as a result, the control chart fails to signal once we are done with some of the initial samples. To resolve this issue, the limits are penalized by putting a simple function of "j" (i.e.…”

Section: The Proposed Pv Control Chartsmentioning

confidence: 97%

“…Later, comparisons, an illustrative example, and finally summary and conclusions are given. Downloaded by [Rutgers University] at 09:52 12 April 2015 Abbas et al (2013) proposed a new memory-type control structure named as progressive mean (PM) control chart for monitoring location parameter of the process. Agarwal (2003, p. 38) defined PM as "in progressive average, we find out the average of first two periods value and then go on adding the value for third, fourth, fifth period, etc., and calculate the averages of three, four, five, etc., period successively.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Progressive Variance Control Charts for Monitoring Process Dispersion

Zafar

Abbas

Hussain

2014

Communications in Statistics - Theory and Methods

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In a process, the deviation from location or scale parameters affects the quality of the process and waste resources. So it is essential to monitor such processes for possible changes due to any assignable causes. Control charts are the most famous tool used to meet this intention. It is useless to monitor process location until the assurance that process dispersion is in-control. This study proposes some new two-sided memory control charts named as progressive variance (P V ) control charts which are based on sample variance to monitor changes in process dispersion assuming normality of quality characteristic to be monitored. Simulation studies are made, and an example is discussed to evaluate the performance of the proposed charts. The comparison of the proposed chart is made with exponentially weighted moving average-and cumulative sum-type charts for process dispersion. The study shows that performance of the proposed charts are uniformly better than its competitors for detecting positive shifts while for detecting negative shift in the variance their performance is better for small shifts and reasonably good for moderated shifts.

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“…This statistics is result of inspiration from PM (see Agarwal (2003) and Abbas et al (2013) for more details). Let X ij , i = 1, 2, 3, .…”

Section: The Proposed Pv Control Chartsmentioning

confidence: 95%

Section: The Proposed Pv Control Chartsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Progressive Variance Control Charts for Monitoring Process Dispersion

Zafar

Abbas

Hussain

2014

Communications in Statistics - Theory and Methods

Self Cite

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“…They stand for graphical analysis and monitoring of a process regarding timewise by two characteristics: centralization -the process average and dispersion, estimated by its standard deviation or range of data (HO & QUININO, 2013). The objective of a control chart is to seek for signs of special causes affecting the process stability by visual identification of the behavior of critical quality variables (HACHICHA & GHORBEL, 2012;ABBAS et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Anaerobic Digestion Stability Test by Shewhart Control Chart

et al. 2017

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ABSTRACT:The anaerobic digestion (AD) operation complexity raise the importance of stability testing to verify whether the operating conditions are under control and whether the process is working as required. The current method of verifying process stability is by a range of the ratio between volatile fatty acidity and total alkalinity (VFA/ TA) within which stable conditions are brought about; these rates vary with the content of organic material. A few indicators as pH or constant biogas production are also used. Therefore, the aim of this study was to propose the use of Shewhart control chart for individual measures as a stability test for AD, as well as to demonstrate its use in poultry litter AD. The method showed to be advantageous since it standardizes a variation range for the process according to the average and verifies the stability by direct measures, such as organic material removal efficiency and biogas production.

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“…Ali 26 presented control charts based on the renewal process assuming that TBE follow a generalized exponential, a generalized Rayleigh, or an exponentiated Pareto distribution. Abbas et al 36 proposed a progressive mean (PM) chart for monitoring the mean of a process, and it was found very effective in detecting small and moderate shifts. Kumar and Baranwal 29 studied the design of the t r chart based on the quantiles of the run-length distribution for both the known and unknown exponential parameter case.…”

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confidence: 99%

A progressive mean control chart for monitoring time between events

Alevizakos

Koukouvinos

2019

Quality & Reliability Eng

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Control charts based on time between events (TBE) are widely used in highquality manufacturing processes where the events occur rarely. For monitoring such data, a new two-sided TBE control chart called progressive mean control chart (regarded as PM-TBE chart) is proposed in the present study. Through a simulation study and using the average run-length (ARL) measure, it is shown that the proposed chart outperforms the t r , ARL-unbiased gamma, GWMA-TBE, and DEWMA-TBE charts in detecting very small to moderate downward shifts, as well as in some cases small upward shifts. Moreover, the PM-TBE chart is very robust for moderate to large shifts when the true distribution of the TBE observations is a Weibull or a lognormal. Finally, examples are given to display the application of the proposed chart. KEYWORDSaverage run length, Erlang distribution, progressive mean, robustness, time between events | INTRODUCTIONControl charts based on time between events (TBE) are frequently used in high-quality processes where the rate of occurrences is low. The traditional Shewhart control charts for attributes, such as c chart, u chart, p chart, and np chart, are used to monitor the number or the proportion of nonconformities or defective products, 1 whereas TBE control charts are used to monitor the inter-arrival times between the occurrences of events, which are assumed to be exponentially distributed. 2 Many researchers have focused on the study of TBE control charts. Lucas 3 studied the cumulative sum (CUSUM) chart for exponentially distributed observations, while Vardeman and Ray 4 used integral equations to calculate the average run-length (ARL) of the exponential CUSUM chart. Gan 5 investigated the optimal design of the exponential CUSUM chart, and Gan and Choi 6 presented a program for calculating the ARL of the above control chart. Gan 2 proposed the exponentially weighted moving average (EWMA) control chart for exponential data computing its ARL using differential equations, and he found it slightly less sensitive than the exponential CUSUM chart. Chan et al 7 proposed a Shewhart-type chart, called cumulative quantity control chart (CQC chart) for monitoring exponential TBE data. Jones and Champ 8 studied the phase I of Shewhart-type TBE control charts. Xie et al 9 proposed a Shewhart-type control chart, namely, t r chart, based on the Erlang distribution, to monitor the time between r (r ≥ 1) failures. Borror et al 10 studied the robustness of the exponential CUSUM chart assuming that the TBE observations follow a Weibull or a lognormal distribution, and they showed that it is very robust for both small and large shifts of parameters. Liu et al 11 compared various one-and two-sided exponential TBE control charts. Liu et al 12,13 proposed CUSUM and EWMA schemes, respectively, for monitoring exponential data after transforming it to an approximate normal distribution using the double square root transformation. Zhang et al 14 proposed a TBE control chart based on gamma distribution using the Let Y t ∼ iid ExpðθÞ, t=1,2,… r...

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Progressive Mean Control Chart for Monitoring Process Location Parameter

Cited by 60 publications

References 15 publications

Progressive Variance Control Charts for Monitoring Process Dispersion

Progressive Variance Control Charts for Monitoring Process Dispersion

Anaerobic Digestion Stability Test by Shewhart Control Chart

A progressive mean control chart for monitoring time between events

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