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The effect of measurement error on the performance of Mann‐Whitney and Signed‐Rank nonparametric control charts
Author(s) -
Nojavan Majid,
Alishahi Massoud,
Rezaee Maryam,
Rahaee Mohammad Amin
Publication year - 2021
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2862
Subject(s) - control chart , nonparametric statistics , statistics , type i and type ii errors , parametric statistics , mathematics , rank (graph theory) , observational error , variance (accounting) , algorithm , computer science , process (computing) , accounting , combinatorics , business , operating system
Mann‐Whitney and Signed‐Rank control charts are two well‐known nonparametric charts used for controlling the center of the process when the distribution of the process parameter is unknown or nonnormal. Considering the effect of measurement error on the performance of control charts, the mentioned effect with additive model is investigated on Mann‐Whitney and Signed‐Rank charts. Furthermore, a comparison is made between the two charts and a Shewhart‐type X ¯ chart (as a parametric one) in the presence of the error. To do so, a simulation program is used and average run length (ARL) of the charts are calculated under three distributions. The results for all three distributions show that the existence of measurement error weakens the performances of both nonparametric charts and larger values of the variance of the error will increase the effect. A numerical example is also discussed to show the effect on the performance of the charts. Multiple measurements is used as a way to decrease the effect of measurement error. Knowing the fact that it requires extra time and money, it can be used in real cases depending on the financial limitations of the user.