Control charting and survey sampling techniques in process monitoring

2017

The maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for simultaneously detecting both increases and decreases in the mean and/or dispersion of a process. In this paper, we propose a new auxiliary information-based (AIB) MaxEWMA control chart, called the AIB-MaxEWMA chart. The AIB-MaxEWMA chart encompasses the existing MaxEWMA chart. Extensive Monte Carlo simulations are performed to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the AIB-MaxEWMA chart. An extensive comparison reveals that the AIB-MaxEWMA chart performs uniformly better than the MaxEWMA chart. An example is also used to explain the implementation and working of the AIB-MaxEWMA chart.A. HAQ research papers on the AIB control charts now exist in the literature. Riaz 10 constructed a new AIB Shewhart chart using the regression estimator for improved process mean monitoring, and it has been shown that the AIB Shewhart chart surpasses the classical Shewhart chart. On similar lines, Riaz and Does 11 suggested a Shewhart-type dispersion chart using a ratio-type variance estimator for phase-I quality control. It turned out that the AIB dispersion chart is more powerful than the existing Shewhart unbiased sample variance chart. Ahmad et al. 12 compared the performances of several AIB Shewhart-type dispersion charts-based on the ratio-type variance estimators-with that of the existing process variance control charts, and have suggested using AIB dispersion charts for precisely monitoring the process dispersion. The AIB EWMA chart for monitoring the process mean was suggested by Abbas et al. 13 -the AIB EWMA chart is at least as sensitive as the classical EWMA chart. For efficiently monitoring the process median, Ahmad et al. 14 have suggested several improved AIB Shewhart charts using different ratio-type estimators. Recently, Riaz 15 has proposed improved Shewhart-type charts using AIB location estimators. For more interesting works on the AIB charts, we refer to Haq and Khoo, Abbasi and Riaz, Arshad et al., Riaz et al., Riaz, and Riaz et al.,[16][17][18][19][20][21] to name a few.In this paper, we propose a new MaxEWMA chart for simultaneously monitoring the process mean and dispersion of a normally distributed process using the auxiliary information on a single correlated auxiliary variable, named the AIB-MaxEWMA chart. Monte Carlo simulations are used to compute the run length profiles, including the average run length (ARL) and standard deviation of the run length (SDRL) of the proposed control chart. We show that the AIB-MaxEWMA chart encompasses the existing MaxEWMA chart. In addition, the AIB-MaxEWMA chart turns out to be as sensitive as the MaxEWMA chart.The rest of the paper is organized as follows: the MaxEWMA chart is reviewed in Section 2. Section 3 suggests an AIB-MaxEWMA chart. The performance and comparative studies are conducted in Section 4. An illustrative example is given in Section 5 to explain the working and implementation of ...

Section: Introductionmentioning

confidence: 99%

A New Maximum EWMA Control Chart for Simultaneously Monitoring Process Mean and Dispersion Using Auxiliary Information

2017

“…Following Haq and Khoo, an unbiased estimator of μ Y , say

{\overset{μ}{true}}_{Y}

, is

{\hat{μ}}_{Y} = \overline{Y} + ρ (σ_{Y} / σ_{X}) (μ_{X} - \overline{X}),

with its mean and variance, respectively, given by

\begin{matrix} alignleft \\ align-1 E ({\hat{μ}}_{Y}) & align-2 = μ_{Y} and \\ align-1 V ({\hat{μ}}_{Y}) & align-2 = \frac{σ_{Y}^{2}}{n} (1 - ρ^{2}) . \end{matrix}

It can be observed that

{\overset{μ}{true}}_{Y}

is always more precise than

\overset{Y}{true}

given that ρ ≠ 0. Using this fact, several authors have constructed more sensitive quality control charts to monitor the process parameter(s), see Riaz, Ahmad et al, Riaz et al, Abbas et al, Ahmad et al, Riaz, Haq, Haq and Khoo, Adegoke et al, and Ahmad et al In the subsequent subsections, we consider the synthetic and DS charts based on

{\overset{μ}{true}}_{Y}

.…”

Section: The Existing Control Chartsmentioning

confidence: 99%

“…On similar lines, Haq and Khoo introduced the AIB DS chart, which is a DS chart with the plotting statistics that utilize information from the study and auxiliary variables, and found that the former outperforms the latter in detecting process mean shifts. Other related studies on the AIB control charts can be found in Riaz et al, Ahmad et al,() Abbas et al, Riaz, Adegoke et al, Haq,() and Sanusi et al, to name a few.…”

Section: Introductionmentioning

confidence: 98%

A synthetic double sampling control chart for process mean using auxiliary information

Khoo

2019

A control chart is a simple yet powerful tool that is extensively adopted to monitor shifts in the process mean. In recent years, auxiliary-information-based (AIB) control charts have received considerable attention as these control charts outperform their counterparts in monitoring changes in the process parameter(s). In this article, we integrate the conforming run length chart with the existing AIB double sampling (AIB DS) chart to propose an AIB synthetic DS chart for the process mean. The AIB synthetic DS chart also encompasses the existing synthetic DS chart. A detailed discussion on the construction, optimization, and evaluation of the run length profiles is provided for the proposed control chart. It is found that the optimal AIB synthetic DS chart significantly outperforms the existing AIB Shewhart, optimal AIB synthetic, and AIB DS charts in detecting various shifts in the process mean. An illustrative example is given to demonstrate the implementation of the existing and proposed AIB control charts. KEYWORDSauxiliary information, average run length, conforming run length, double sampling chart, synthetic chart Qual Reliab Engng Int. 2019;35:1803-1825. wileyonlinelibrary.com/journal/qre

“…For efficiently monitoring the process median, Ahmad et al have suggested several improved AIB‐Shewhart charts using different ratio‐type estimators. Recently, Riaz has proposed improved Shewhart‐type charts using AIB location estimators. For more interesting works on the AIB charts, we refer to the literature() to name a few.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Riaz 18 has proposed improved Shewhart-type charts using AIB location estimators. For more interesting works on the AIB charts, we refer to the literature [18][19][20][21][22][23] to name a few.…”

Section: Introductionmentioning

confidence: 99%

New EWMA control charts for monitoring process dispersion using auxiliary information

2017

The exponentially weighted moving average (EWMA) control chart is a well‐known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary‐information–based (AIB) EWMA (AIB‐EWMA) charts. These AIB‐EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB‐EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB‐Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB‐EWMA charts.