Evaluation of CUSUM Charts for Finite-Horizon Processes

Int J Adv Manuf Technol

Taleb

et al. 2015

Monitoring the coefficient of variation (CV) is an effective approach to monitor a process when both the process mean and the standard deviation are not constant but, nevertheless, proportional. Until now, few contributions have investigated the monitoring of the CV for short production runs. This paper proposes an adaptive Shewhart control chart implementing a variable sample size (VSS) strategy in order to monitor the coefficient of variation in a short production run context. Formulas for the truncated average run length are derived. Moreover, a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV in order to evaluate the performance of each chart in a short run context. An example illustrates the use of this chart on real data.

Section: Truncated Run Length Propertiesmentioning

confidence: 99%

“…and c.d.f. of the usual (i.e., infinite horizon) run length (RL): It can be proven that (see Nenes and Tagaras [18])…”

Section: Truncated Run Length Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monitoring the coefficient of variation using a variable sample size control chart in short production runs

Amdouni

Int J Adv Manuf Technol

Taleb

et al. 2015

“…The measures of statistical performance of a control chart when production ends after H hours have been originally proposed by Nenes and Tagaras [19]. The average run length (ARL) in infinite production runs is typically computed for a specific state of the process without taking into account the assignable cause occurrence mechanism: for the finite horizon production, Nenes and Tagaras [19] followed the same approach. That is, the process is assumed to run either in-control or out-ofcontrol from the beginning of the production run.…”

Section: Truncated Run Length and Other Metrics Of Statistical Performentioning

confidence: 99%

“…The measure of performance proposed by Nenes and Tagaras [19] for finite runs in place of the "classical" ARL for infinite runs is the expected value of truncated run length, which represents the expected number of samples to be taken until a signal or the end of the process. We denote it as E(T RL) = T ARL.…”

Section: Truncated Run Length and Other Metrics Of Statistical Performentioning

confidence: 99%

The performance of the Shewhart sign control chart for finite horizon processes

Celano

Int J Adv Manuf Technol

Chakraborti

et al. 2015

Self Cite

In many manufacturing environments, the production horizon of the same part code between two consecutive set-ups should be limited to a few hours or shifts. When 100 % sampling is not possible, on-line quality control on a quality characteristic should be immediately started by means of a control chart. In this paper, we investigate the statistical performance of a nonparametric (distributionfree) Shewhart Sign (SN) control chart for monitoring the location of a quality characteristic in a production process with a finite horizon and a small number of scheduled inspections. The observations taken from the process are assumed to be continuous random variables. By implementing a SN control chart, any model assumption about the distribution of observations is needless to guarantee a nominal in-control (IC) performance: after each process set-up, this overcomes the important problem of lack of information about the distribution of the observations collected for the quality characteristic to be monitored. An extensive simulation study is conducted to compare the statistical performance of the distribution-free Shewhart SN control chart to the normal theory-based Shewhart Student's t control chart: several types of distributions of observations and different numbers of scheduled inspections are considered to show the advantages related to the implementation of the Shewhart SN control chart. An illustrative example presents the implementation of the Shewhart SN control chart on a real data set collected in a beverage company.

Finite Horizon Process Monitoring

Chakraborti

Celano

Wiley StatsRef: Statistics Reference Online

et al. 2021

In some industrial environments flexibility is a key for the manufacturer, that is, the ability to switch frequently from the production of one product code to another and produce batches of different items during consecutive short production time intervals, called finite production horizons; such a setting is called a finite horizon process (FHP). The frequent process changeovers may require new setup activities and machine reconfigurations every time before the beginning of a new production run. An erroneous setup or a process failure can negatively impact the quality of the manufactured products. In order to perform statistical quality control for these types of processes, practitioners have to deal with the challenging issues of designing, scheduling, and performing only a limited number of inspections. This is typically not the case in traditional quality control and monitoring applications. In this article, we highlight various aspects of statistical process monitoring (SPM) implemented in an FHP setting that need to be considered by quality practitioners. We describe available statistical process monitoring tools, such as the control charts, properly designed to monitor quality characteristics in the FHP setting. Finally, we discuss some of the still open challenges in the area of FHP monitoring.