The Fixed v. Variable Sampling Interval Shewhart X-Bar Control Chart in the Presence of Positively Autocorrelated Data

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This study uses simulation to examine differences between fixed sampling interval (FSI) and variable sampling interval (VSI) Shewhart X-bar control charts for processes that produce positively autocorrelated data. The influence of sample size (1 and 5), autocorrelation parameter, shift in process mean, and length of time between samples is investigated by comparing average time (ATS) and average number of samples (ANSS) to produce an out of control signal for FSI and VSI Shewhart X-bar charts. These comparisons are conducted in two ways: control chart limits pre-set at ±3σ_x / √n and limits computed from the sampling process. Proper interpretation of ... continued below

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xx, 299 leaves : ill.

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Harvey, Martha M. (Martha Mattern) May 1993.

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  • Harvey, Martha M. (Martha Mattern)

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This study uses simulation to examine differences between fixed sampling interval (FSI) and variable sampling interval (VSI) Shewhart X-bar control charts for processes that produce positively autocorrelated data. The influence of sample size (1 and 5), autocorrelation parameter, shift in process mean, and length of time between samples is investigated by comparing average time (ATS) and average number of samples (ANSS) to produce an out of control signal for FSI and VSI Shewhart X-bar charts. These comparisons are conducted in two ways: control chart limits pre-set at ±3σ_x / √n and limits computed from the sampling process. Proper interpretation of the Shewhart X-bar chart requires the assumption that observations are statistically independent; however, process data are often autocorrelated over time. Results of this study indicate that increasing the time between samples decreases the effect of positive autocorrelation between samples. Thus, with sufficient time between samples the assumption of independence is essentially not violated. Samples of size 5 produce a faster signal than samples of size 1 with both the FSI and VSI Shewhart X-bar chart when positive autocorrelation is present. However, samples of size 5 require the same time when the data are independent, indicating that this effect is a result of autocorrelation. This research determined that the VSI Shewhart X-bar chart signals increasingly faster than the corresponding FSI chart as the shift in the process mean increases. If the process is likely to exhibit a large shift in the mean, then the VSI technique is recommended. But the faster signaling time of the VSI chart is undesirable when the process is operating on target. However, if the control limits are estimated from process samples, results show that when the process is in control the ARL for the FSI and the ANSS for the VSI are approximately the same, and exceed the expected value when the limits are fixed.

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xx, 299 leaves : ill.

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UNT Theses and Dissertations

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  • May 1993

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  • March 26, 2014, 9:30 a.m.

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  • Feb. 9, 2015, 2:51 p.m.

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Harvey, Martha M. (Martha Mattern). The Fixed v. Variable Sampling Interval Shewhart X-Bar Control Chart in the Presence of Positively Autocorrelated Data, dissertation, May 1993; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc278763/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .