Improved Wald Transformation p-Chart for Nonconforming Fraction

Saichon  Sinsomboonthong; Juthaphorn  Sinsomboonthong

doi:10.6180/jase.202504_28(4).0010

Improved Wald Transformation p-Chart for Nonconforming Fraction

$Estimates of ARL1 for four control charts in the case of p0 = 0.01 and different shifts of nonconforming fraction$

Saichon Sinsomboonthong¹ and Juthaphorn Sinsomboonthong²This email address is being protected from spambots. You need JavaScript enabled to view it.

¹Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

²Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand

Received: January 11, 2024
Accepted: April 15, 2024
Publication Date: June 11, 2024

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202504_28(4).0010

This study proposes a new improved transformation p-chart for nonconforming fraction of a production process, called improved Wald transformation p-chart. Via a simulation study, the efficiency of the proposed control chart was compared with the traditional p-chart, the improved square root transformation p-chart, and the Wilson p-chart. The simulation was conducted using the Monte Carlo technique for 180 situations and 10,000 times for each situation. The studied situations were as follows: the nonconforming fraction was set to be 0.01, 0.02, 0.05, 0.07, and 0.09 ; the shift of the nonconforming fraction was set to be 1.1, 1.3, 1.5, 2.0, 3.0, and 4.0; and the sample size (n) was set to be 30, 50, 100, 300, 500, and 1000 . The efficiency measures were out-of-control average run length and standard deviation of the run length. The results showed that the proposed chart was the most efficient among the four tested charts for a large sample size. In addition, the proposed chart tended to perform with the best efficiency for large sample sizes, n ≥ 500, and small nonconforming fraction below 0.1. It performed well with all the tested shifts of nonconforming fraction. However, the sensitivity to detect out-of-control items in the production process seemed to be same among the tested charts for smaller sample size, n < 500.

Keywords: nonconforming fraction; p-chart; run length; transformation

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