Abstract
Paper aims This paper studies the influence of process variation on deviation from nominal control chart performance and proposes some adjustments on the control limits to make it enable on small batches. Originality Specific methods were developed to monitor small batches, mainly due to unavailability of data for precise parameters estimation, like the deviation from nominal control charts. However, Montgomery (2014) highlights some essential aspects, such as the influence of process variation on its performance. Research method The method used was mathematical modeling and computer simulation. Main findings The results validated that there is a significant influence of the process variation on the control chart performance. It has been demonstrated that small adjustments on the control limits can make it enable on lean environments. Implications for theory and practice The main contribution is demonstrating the use of deviation from nominal control chart, through the valid control limits definition regardless of the samples size.
Highlights
The control charts, originally proposed by Shewhart, were intended solely to monitor the variation of processes in order to detect the occurrence of special causes as soon as possible
Some steps were established: i) calculate the Average Run Length (ARL) of a control chart constructed under ideal conditions, that is, with known mean and standard deviation; ii) determine the ARL of a control chart of the deviation from the nominal with estimated parameters, without changing the standard deviation of the products; iii) determine the ARL of the same control chart with a gradual variation of 0.5, 1, 5 and 10% in the standard deviation of the products; iv) compare the ARL obtained from each chart with the ARL of the ideal control chart; v) identify the influence of process variation on the chart’s ARL; vi) propose adjustments to the value of k to calculate new control limits
If the process is in control when δ =0, the Run Length (RL) is geometric with probability P(δ,n), the ARL of control chart KK is calculated according to Equation 10 bellow: ARL =
Summary
The control charts, originally proposed by Shewhart, were intended solely to monitor the variation of processes in order to detect the occurrence of special causes as soon as possible. According to the literature, it is recommended to apply the DNOM control chart in cases where the process variation, measured through the standard deviation, has to be the same, or close, for all products manufactured by the monitored equipment (Cullen & Bothe, 1989; Crowder, 1992; Sower et al, 1994; Ho & Trindade, 2009; Celano et al, 2012; Capizzi & Masarotto, 2012) This condition restricts the use of DNOM control chart and the literature does not specify an acceptable range of variability for its use, which seems to be a theoretical gap to be filled. Some steps were established: i) calculate the ARL of a control chart constructed under ideal conditions, that is, with known mean and standard deviation; ii) determine the ARL of a control chart of the deviation from the nominal with estimated parameters, without changing the standard deviation of the products; iii) determine the ARL of the same control chart with a gradual variation of 0.5, 1, 5 and 10% in the standard deviation of the products; iv) compare the ARL obtained from each chart with the ARL of the ideal control chart; v) identify the influence of process variation on the chart’s ARL; vi) propose adjustments to the value of k to calculate new control limits
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