TY - JOUR

T1 - The effects of large round-off errors on the performance of control charts for the mean when the quality characteristic is normally distributed with a known variance

AU - Diamanta, Benson Karhi

AU - Michal, Ben David

AU - Ofer, Levi

AU - Edna, Schechtman

N1 - Publisher Copyright:
© 2023 The Authors. IET Science, Measurement & Technology published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.

PY - 2023/12/22

Y1 - 2023/12/22

N2 - This research discusses the effects of large round-off errors on the performance of control charts for means when a process is normally distributed with a known variance and a fixed sample size. Quality control in practice uses control charts for means as a process monitoring tool, even when the data is significantly rounded. The objective of this research is to demonstrate how ignoring the round-off errors and using a standard Shewhart chart affects the quality control of a measured process. The first part of the research includes theoretical calculations for estimating the values of alpha and beta, relating to the unrounded data and the large-rounded data. For the rounded data, normality can no longer be assumed because the data is discrete; therefore, the multinomial distribution is used. The results show that given an in-control process, alpha indicates that false alarms are more frequent, whereas given an out-of-control process, the influence on beta is minor and inconsistent. For some rounding levels, there is a decline in the control chart performances, and in others, there is an improvement. In the second part, a simulation study is used to evaluate the performances of the control chart based on a single sample, checking whether the conclusion (reject or fail to reject) for a sample is consistent for rounded and unrounded data. The results of the simulation match the theoretical calculations.

AB - This research discusses the effects of large round-off errors on the performance of control charts for means when a process is normally distributed with a known variance and a fixed sample size. Quality control in practice uses control charts for means as a process monitoring tool, even when the data is significantly rounded. The objective of this research is to demonstrate how ignoring the round-off errors and using a standard Shewhart chart affects the quality control of a measured process. The first part of the research includes theoretical calculations for estimating the values of alpha and beta, relating to the unrounded data and the large-rounded data. For the rounded data, normality can no longer be assumed because the data is discrete; therefore, the multinomial distribution is used. The results show that given an in-control process, alpha indicates that false alarms are more frequent, whereas given an out-of-control process, the influence on beta is minor and inconsistent. For some rounding levels, there is a decline in the control chart performances, and in others, there is an improvement. In the second part, a simulation study is used to evaluate the performances of the control chart based on a single sample, checking whether the conclusion (reject or fail to reject) for a sample is consistent for rounded and unrounded data. The results of the simulation match the theoretical calculations.

KW - measurement errors

KW - measurement theory

KW - normal distribution

KW - process monitoring

UR - http://www.scopus.com/inward/record.url?scp=85180214779&partnerID=8YFLogxK

U2 - 10.1049/smt2.12171

DO - 10.1049/smt2.12171

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AN - SCOPUS:85180214779

SN - 1751-8822

VL - 18

SP - 103

EP - 115

JO - IET Science, Measurement and Technology

JF - IET Science, Measurement and Technology

IS - 3

ER -