The Hotelling's T2 Control Chart with variable parameters: Markov Chain Approach

in Archives des Sciences (2012), 65(6),

The Hotelling’s T2 control chart with variable parameters (VP T2) has been shown to have improved performance in detecting small process shifts when compared to the original fixed parameter T2 control ... [more ▼]

The Hotelling’s T2 control chart with variable parameters (VP T2) has been shown to have improved performance in detecting small process shifts when compared to the original fixed parameter T2 control chart (FRS T2). Practically, though, there are some difficulties in implementation since one needs to use two different measuring scales with the VP T2 chart. In this paper, we propose an alternative sampling scheme to the VP T2 chart. Here we allow the sampling interval h, the sample size n and control limit k to vary between minimum and maximum values while keeping the warning line fixed over time. This proposed method uses only one measurement scale instead of two, greatly increasing its ease of use. Using a mathematical model, we show that this proposed method yields designs that have properties of rapid detection of small and moderate shifts in the process and, in addition, are easy to apply. [less ▲]

Optimal T2 control chart with double sampling scheme - an alternative to the MEWMA chart

in Quality & Reliability Engineering International (2012), 28(7), 751-760

Recent studies have shown that the double sampling (DS) scheme yields rapid detection of out of control situations, but the economic consequences of applying the proposed method are not discussed in the ... [more ▼]

Recent studies have shown that the double sampling (DS) scheme yields rapid detection of out of control situations, but the economic consequences of applying the proposed method are not discussed in the literature yet. In this paper, the economic statistical design of the DS T2 control chart is designed to address this issue. In this regard, upon the Lorenzen and Vance (1986)’s economic model, the problem is formulized and then the cost function is minimized using the genetic algorithm search method to obtain the optimal design parameters. Besides, we assumed that the length of the time that process remains in control is exponentially distributed. Through an illustrative example we show that by applying the proposed method relatively large benefits can be achieved in a comparison with the classical T2 and the statistical DS T2 charts. Furthermore the performance of the ESD DS T2 charts is compared to the MEWMA and other variable ratio sampling (VRS) T2 control charts in the literature. [less ▲]

Statistical design of the variable parameters Hotelling's T2 control chart with run rules: using Genetic Algorithms approach

E-print/Working paper (2012)

Monitoring delivery chains using multivariate control charts

in Proceedings of the 2nd International Symposium on Statistical Process Control, Rio de Janeireo, 13-15 July 2011 (2011, July)

Statistical Merits and Economic Evaluation of T2 Control Charts with the VSSC Scheme

in Arabian Journal for Science and Engineering (2011), 36(7), 1461-1470

An application of fuzzy random variables to control charts

in Fuzzy Sets & Systems (2010), 161

The two most significant sources of uncertainty are randomness and incomplete information. In real systems, we wish to monitor processes in the presence of these two kinds of uncertainty. This paper aims ... [more ▼]

The two most significant sources of uncertainty are randomness and incomplete information. In real systems, we wish to monitor processes in the presence of these two kinds of uncertainty. This paper aims to construct a fuzzy statistical control chart that can explain existing fuzziness in data while considering the essential variability between observations. The proposed control chart is an extension of Shewhart ¯X − S2 control charts in fuzzy space. The proposed control chart avoids defuzzification methods such as fuzzy mean, fuzzy mode, fuzzy midrange, and fuzzy median. It is well known that using different representative values may cause different conclusions to be drawn about the process and vague observations to be reduced to exact numbers, thereby reducing the informational content of the original fuzzy sets. The out-of-control states are determined based on a fuzzy in-control region and a simple and precise graded exclusion measure that determines the degree to which fuzzy subgroups are excluded from the fuzzy in-control region. The proposed chart is illustrated with a numerical example. [less ▲]

On the advantages of economically designed the Hotelling’s T2 control chart with variable sample sizes and sampling intervals

in Quality & Quantity (2010)

Faraz and Parsian (Statistical Paper, 47: 569–593, 2006) have shown that the double warning lines (DWL) scheme detects process shifts more quickly than the other variable ratio sampling schemes such as ... [more ▼]

Faraz and Parsian (Statistical Paper, 47: 569–593, 2006) have shown that the double warning lines (DWL) scheme detects process shifts more quickly than the other variable ratio sampling schemes such as variable sample sizes (VSS), variable sampling intervals (VSI) and variable sample sizes and sampling intervals (VSSVSI). In this paper, the DWLT2control chart for monitoring the process mean vector is economically designed. The cost model proposed by Costa and Rahim (Journal of Applied Statistics, 28: 875–885, 2001) is used here and is minimized through a genetic algorithm (GA) approach. Then the effects of the model parameters on the chart parameters and resulting operating loss is studied and finally a comparison between all possible variable ratio sampling (VRS) schemes are made to choose the best option economically. [less ▲]

The Optimal Design of the VSI T2 Control Chart

in Journal of Iranian Statistical Society (2010), 9(1), 1-19

Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme (FRS). In this paper, the economically and ... [more ▼]

Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme (FRS). In this paper, the economically and statistically optimal design of the VSI T2 control chart for monitoring the process mean vector is investigated. The cost model proposed by Lorenzen and Vance (1986) is minimized through a genetic algorithm (GA) approach. Then the effects of the costs and operating parameters on the optimal design (OD) of the chart parameters and resulting operating loss through a fractional factorial design is systematically studied and finally, based on the ANOVA results, a Meta model to facilitate implementation in industry is proposed to determine the OD of the VSI T2 control chart parameters from the process and cost parameters [less ▲]

Economic and Economical Statistical Design of Hotelling’s T2 Control Chart with Two-State Adaptive Sample Size

in Journal of Statistical Computation & Simulation (2010), 80(12), 12991316

The Hotelling’s T 2 control chart, a direct analogue of the univariate Shewhart ¯X chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics ... [more ▼]

The Hotelling’s T 2 control chart, a direct analogue of the univariate Shewhart ¯X chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics. Recent studies have shown that using variable sampling size (VSS) schemes results in charts with more statistical power when detecting small to moderate shifts in the process mean vector. In this paper, we build a cost model of a VSS T 2 control chart for the economic and economic statistical design using the general model of Lorenzen and Vance [The economic design of control charts: A unified approach, Technometrics 28 (1986), pp. 3–11].We optimize this model using a genetic algorithm approach.We also study the effects of the costs and operating parameters on theVSS T 2 parameters, and show, through an example, the advantage of economic design over statistical design forVSS T 2 charts, and measure the economic advantage of VSS sampling versus fixed sample size sampling. [less ▲]

Hotelling’s T 2 control chart with two adaptive sample sizes

in Quality & Quantity (2009), 43

Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling’s T 2 ... [more ▼]

Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling’s T 2 control chart for monitoring the mean vector of the process. It is a direct analog of the univariate shewhart ¯ x chart. As in the case of univariate, the ARL improvements are very important particularly for small process shifts. In this paper, we study the T 2 control chart with two-state adaptive sample size, when the shift in the process mean does not occur at the beginning but at some random time in the future. Further, the occurrence time of the shift is assumed to be exponentially distributed random variable. [less ▲]