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On the advantages of economically designed the Hotelling’s T2 control chart with variable sample sizes and sampling intervals Faraz, Alireza ; ; et al in Quality & Quantity (2012), 46(1), 39-53 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 ▲] Detailed reference viewed: 60 (16 ULg)A modified economic-statistical design of the T2 control chart with variable sample sizes and control limits ; Faraz, Alireza ; Heuchenne, Cédric et al in Journal of Applied Statistics (2011), 38(11), 2459-2469 Recent studies have shown that using variable sampling size and control limits (VSSC) schemes result in charts with more statistical power than variable sampling size (VSS) when detecting small to ... [more ▼] Recent studies have shown that using variable sampling size and control limits (VSSC) schemes result in charts with more statistical power than variable sampling size (VSS) when detecting small to moderate shifts in the process mean vector. This paper presents an economic-statistical design (ESD) of the VSSC T2 control chart using the general model of Lorenzen and Vance [22]. The genetic algorithm approach is then employed to search for the optimal values of the six test parameters of the chart. We then compare the expected cost per unit of time of the optimally designed VSSC chart with optimally designed VSS and FRS (fixed ratio sampling) T2 charts as well as MEWMA charts. [less ▲] Detailed reference viewed: 108 (31 ULg)On the properties of the hotelling’s T2 control chart with variable sampling intervals Faraz, Alireza ; ; in Quality & Quantity (2011), 45(3), 579-586 When T 2 control chart is used to monitor a process, it is usually assumed that the samples of size n0 is taken at constant intervals t0 . In this paper, we investigate the T 2 control chart for ... [more ▼] When T 2 control chart is used to monitor a process, it is usually assumed that the samples of size n0 is taken at constant intervals t0 . In this paper, we investigate the T 2 control chart for monitoring the process mean vector when the sampling intervals are variable. Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme Fixed Ratio Sampling (FRS). In this paper, it is assumed that the length of time the process remains in control is exponentially distributed. [less ▲] Detailed reference viewed: 42 (7 ULg)ECONOMICALLY DESIGNED HOTELLING’S T2 CONTROL CHART USING VSICL SCHEME ; ; Faraz, Alireza in Arabian Journal for Science & Engineering (2010), 35(2), 251263 The Hotelling’s T2 control chart, is the most widely used multivariate procedure for two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to ... [more ▼] The Hotelling’s T2 control chart, is the most widely used multivariate procedure for two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to moderate shifts. Recently, the variable sampling intervals (VSI) control scheme in which the length of successive sampling intervals is determined upon the preceding T2 values has been proved to have a very good performance on detecting small to moderate shifts when it is compared to the original T2 control chart . Moreover, it has been shown that the VSI scheme is more economical than the classical one. This paper studies the economic consequences of a new control scheme named variable sampling intervals and control limits (VSICL) in that the sampling interval h and control limit k vary between minimum and maximum values while keeping the sample size fixed over time. We apply the cost model proposed by Costa and Rahim [8]. Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. Finally, both VSI and VSICL T2 control charts are compared with respect to the expected cost per unit time. [less ▲] Detailed reference viewed: 121 (6 ULg)Constructing a fuzzy Shewhart control chart for variables when uncertainty and randomness are combined Faraz, Alireza ; ; et al in Quality & Quantity (2010), 44(5), 905-914 In this paper we introduce a fuzzy chart for variables which is used in situations when uncertainty and randomness are combined. It is showed that the Shewhart chart’s control limits must be adjusted in ... [more ▼] In this paper we introduce a fuzzy chart for variables which is used in situations when uncertainty and randomness are combined. It is showed that the Shewhart chart’s control limits must be adjusted in these situations. However, this chart is based on a fuzzy acceptance region and this method arises when a decision should be made by referring to the grade of a sample statistic belonging to the fuzzy acceptance region. [less ▲] Detailed reference viewed: 56 (6 ULg)Hotelling’s T 2 control chart with two adaptive sample sizes Faraz, Alireza ; 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 ▲] Detailed reference viewed: 25 (4 ULg)Fuzzy Control Chart A Better Alternative for Shewhart Average Chart Faraz, Alireza ; in Quality & Quantity (2007), 41(3), 375-385 This paper through a real illustrative example and a power test shows that designing a fuzzy control chart for process average of a continuous (variable) quality characteristic with a warning line is a ... [more ▼] This paper through a real illustrative example and a power test shows that designing a fuzzy control chart for process average of a continuous (variable) quality characteristic with a warning line is a better alternative to Shewhart ¯X chart in many respects, like providing better neural view to inspectors, offering different strategic options for company to choose, detecting the desire shifts more quickly, and more sensibility to small shifts without any complexity augmentation to the chart. [less ▲] Detailed reference viewed: 67 (10 ULg) |
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