Time truncated attribute control chart for the generalized Rayleigh distributed quality characteristics and beyond
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 9 January 2024
Issue publication date: 8 April 2024
Abstract
Purpose
First is to develop the time truncated median control chart for the Rayleigh distribution (RD) and generalized RD (GRD), respectively. Second is to evaluate the performance of the proposed attribute control chart which depends on the average run length (ARL) and third is to include real life examples for application purpose of the proposed attribute control chart.
Design/methodology/approach
(1) Select a random sample of size n from each subgroup from the production process and put them on a test for specified time t, where t = ? × µe. Then, count the numbers of failed items in each subgroup up to time t. (2) Step 2: Using np chart, define D = np, the number of failures, which also a random variable follows the Binomial distribution. It is better to use D = np chart rather than p chart because the authors are using number of failure rather than proportion of failure p. When the process is in control, then the parameters of the binomial distribution are n and p0, respectively. (3) Step 3: The process is said to be in control if LCL = D = UCL; otherwise, the process is said to be out of control. Hence, LCL and UCL for the proposed control chart.
Findings
From the findings, it is concluded that the GRD has smaller ARL values than the RD for specified values of parameters, which indicate that GRD performing well for out of control signal as compared to the RD.
Research limitations/implications
This developed control chart is applicable when real life situation coincide with RD and GRD.
Social implications
Researcher can directly use presented study and save consumers from accepting bad lot and also encourage producers to make good quality products so that society can take benefit from their products.
Originality/value
This article dealt with time truncated attribute median control chart for non-normal distributions, namely, the RD and GRD, respectively. The structure of the proposed control chart is developed based on median lifetime of the RD and GRD, respectively.
Keywords
Acknowledgements
The author appreciates the Managing Editor and Reviewers for their attentive reading and helpful suggestions that improved the earlier version of this essay. The Tables [1-9] and the Figures [1-3] reported here are made through the study and these are not taken from any sources. And all the calculations and the Figures are made by using the R Software [Open Source] and are cited in the article.
Since submission of this article, the following author(s) have updated their affiliations: Mahendra Saha is at the Department of Statistics, University of Delhi, Delhi, India.
Citation
Saha, M., Pareek, P., Tripathi, H. and Devi, A. (2024), "Time truncated attribute control chart for the generalized Rayleigh distributed quality characteristics and beyond", International Journal of Quality & Reliability Management, Vol. 41 No. 5, pp. 1400-1416. https://doi.org/10.1108/IJQRM-02-2023-0049
Publisher
:Emerald Publishing Limited
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