Double sampling control chart for a first order autoregressive process

Claro, Fernando Antônio Elias; Costa, Antônio Fernando Branco; Machado, Marcela Aparecida Guerreiro

doi:10.1590/s0101-74382008000300008

Cited by 15 publications

(7 citation statements)

References 28 publications

(27 reference statements)

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“…They studied for a variable sample size and sampling interval. Claro et al (2008) proposed the double sampling (DS) X control chart for monitoring processes in which the observations followed a first order autoregressive model, AR (1). They considered sampling intervals that are sufficiently long to meet the rational subgroup concept.…”

Section: Detection Of Shift In Process Meanmentioning

confidence: 99%

Detection of shift in process mean withX¯chart for autocorrelated data

Singh¹,

Prajapati

2013

Int J Qual & Reliability Mgmt

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Purpose -The purpose of this paper is to study the performance of the X-bar chart on the basis of average run lengths (ARLs) for the positively correlated data. The ARLs at various sets of parameters of the X-bar chart are computed by simulation. The performance of the chart at the various shifts in the process mean is compared with the X-bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes suggested in this paper are also compared with variable parameters (VP) chart and double sampling (DS) X-bar chart suggested by Costa and Machado. Design/methodology/approach -Positively correlated observations having normal distribution are generated with the help of the MATLAB software. The performance of the X-bar chart in terms of ARLs at the various shifts in the process mean is compared with the X-bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes are also compared with VP X-bar chart and DS X-bar chart suggested by Costa and Machado. Findings -The suggested optimal schemes of X-bar chart perform better at the various shifts in the process mean than the X-bar chart suggested by Zang and residual chart suggested by Zang. It was concluded that, although the suggested schemes for X-bar chart detect shifts later than the VP and DS X-bar charts proposed by Costa and Machado, they involved a much smaller number of parameters that are to be adjusted. So the time required for adjustment in case of optimal scheme is very small compared to the VP and DS charts.Research limitations/implications -The optimal schemes of X-bar chart are developed for the normally distributed autocorrelated data. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover, the optimal schemes for chart can be developed for variable sample size and for variable sampling intervals. Originality/value -Although it is the extension of previous work, it can be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.

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Section: Detection Of Shift In Process Meanmentioning

confidence: 99%

Detection of shift in process mean withX¯chart for autocorrelated data

Singh¹,

Prajapati

2013

Int J Qual & Reliability Mgmt

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“…If the results are not clear‐cut, a second random sample is selected and inspected and a final decision is taken using the results of the two samples (Balakrishnan et al, 2006). Claro et al (2008) proposed the double sampling control chart for the autoregressive process. Torng and Lee (2009) discussed the performances of a double sampling (DS)

\overset{X}{true}

chart under nonnormality assumptions in comparison with a Shewhart

\overset{X}{true}

chart.…”

Section: Introductionmentioning

confidence: 99%

Refined double sampling scheme with measures and application

Khired

Aslam

Dobbah

2021

Stat

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In this study, we propose a design for a control chart for the normal distribution using a modified double sampling scheme. The probability of in control, out of control, the average run length (ARL), and the standard deviation of run length (SDRL) of the proposed control chart is derived. The proposed control chart using the modified double sampling scheme is found to be more efficient in detecting small shifts of a process in comparison with existing, single, and double sampling control charts. The efficiency of the proposed control chart is investigated in terms of ARL and SDRL via simulation and application to a real data set.

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“…Some of these models are known as autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), etc; see Box et al for more thorough discussion on these. In this paper, we only consider the well‐known first‐order AR model (ie, AR(1)) as a starting point (other models will be discussed in upcoming articles) and because according to Alwan and Radson, this is the most commonly used time series model in SPM applications; see also Wardell et al, Runger and Willemain, Claro et al, Kazemzadeh et al, Costa and Machado, Chang and Wu, Keramatpour et al, Franco et al, Hu and Sun, Osei‐Aning et al, Garza‐Venegas et al, Shongwe et al, Ahmad et al, etc, for additional indication that AR(1) is the most used model in SPM due to its simplicity as compared with other stationary time series processes.…”

Section: Introductionmentioning

confidence: 99%

On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

Shongwe

Malela‐Majika

Castagliola

2020

Quality & Reliability Eng

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Runs‐rules have been widely used since the 1950s in industrial and nonindustrial process monitoring applications to improve the performance of basic and other traditional monitoring schemes. However, none of the studies on runs‐rules have accounted for a process with a combined effect of measurement errors and autocorrelation. Hence, in this paper, the use of the w‐of‐w runs‐rules to improve the performance of the Shewhart trueX¯ scheme using an additive model with a constant variance and a first‐order autoregressive model is proposed. To reduce the combined negative effect of measurement errors and autocorrelation, we implement a sampling strategy based on rational subgroups in which (a) multiple measurements per item are taken (instead of a standard single measurement) and (b) non‐neighboring observations are gathered. Moreover, the latter sampling strategy is incorporated into the values of probability elements of a Markov chain matrix which is used to derive some closed‐form expressions for the zero‐ and steady‐state run‐length distribution. The main finding of this study is that, with respect to some overall performance measures, the proposed scheme outperforms the existing Shewhart trueX¯ scheme by a significant margin. A real‐life example is used to illustrate the practical implementation of the proposed scheme.

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Double sampling control chart for a first order autoregressive process

Cited by 15 publications

References 28 publications

Detection of shift in process mean withX¯chart for autocorrelated data

Detection of shift in process mean withX¯chart for autocorrelated data

Refined double sampling scheme with measures and application

On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

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