Application of a three-parameter Lindley distribution in quality control

G, Veena; Tomy, Lishamol; Chesneau, Christophe

doi:10.47974/JSMS-1374

Open Access Research Article

Application of a three-parameter Lindley distribution in quality control

^*Veena GCorresponding authorveenagpillai@hotmail.comDepartment of Mathematics GITAM (Deemed to be) UniversityBengaluru, Karnataka, 561203, IndiaView full profile → , Lishamol Tomylishatomy@gmail.comDepartment of Statistics Deva Matha CollegeKuravilangad, Kerala, 686633, IndiaView full profile → , Christophe Chesneauchristophe.chesneau@gmail.comUniversité de Caen Laboratoire de Mathématiques Nicolas Oresme Campus II, Science 3Caen, 14032, FranceView full profile →

* Corresponding author · click or hover a name for details

pp. 839–853Vol. 28Issue 5July 2025DOI: 10.47974/JSMS-1374XML

Received:: 08 Nov 2023
Published Online:: 15 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1374
Pages:: 839–853

Abstract

Statistical quality control in industries enables businesses to improve product quality, reduce defects, optimize processes, increase customer satisfaction, and gain a competitive edge in the market. It provides a systematic and data-driven approach to quality management, enabling industries to consistently deliver high-quality products and services while driving continuous improvement across all operations. This paper examines the applications of the Harris extended modified Lindley distribution, a generalization of the well-known Lindley distribution. We demonstrate the practical utility of this distribution in the field of quality control. Using the lifetime distribution, an acceptance sampling plan is devised that can determine whether a large batch of products submitted for inspection should be accepted or rejected. The operational characteristic functions that were generated allow for a greater understanding of the performance of the sampling plan. Computed tables show sample sizes and parameters in the article. To demonstrate the efficacy of the proposed methodology, two distinct datasets pertaining to the ordered product failure times of a software development project and ball bearing failure times are utilized.

Keywords

Acceptance sampling plan Harris family of distributions Operating characteristic function Truncated life tests Lindley distribution

Subject Classifications

62E9960E0560E10

References

[1] B. Ahmed and H. Yousof, “A New Group Acceptance Sampling Plans based on Percentiles for the Weibull Fréchet Model,” Statistics, Optimization & Information Computing, vol. 11, no. 2, pp. 409-421, Mar. (2022), doi: https://doi.org/10.19139/soic-2310-5070-1320. “
[2] B. Ahmed, M. M. Ali, and H. M. Yousof, “A Novel G Family for Single Acceptance Sampling Plan with Application in Quality and Risk Decisions,” Annals of Data Science, vol. 11, no. 1, pp. 181-199, Oct. (2022), doi: https://doi.org/10.1007/s40745-022-00451-3.
[3] A. D. Al-Nasser and A. I. Al-Omari, “Acceptance Sampling plan based on Truncated life tests for Exponentiated Fréchetdistribution,” Journal of Statistics & Management Systems, vol. 16, no. 1, pp. 13-24, Jan. (2013), doi: https://doi.org/10.1080/09720510.2013.777571.
[4] A. D. Al-Nasser, A. I. Al-Omari, A. Bani-Mustafa, and K. Jaber, “Developing Single-Acceptance Sampling plans based on a Truncated lifetime test for an Ishita Distribution,” Statistics in Transition New Series, vol. 19, no. 3, pp. 393-406, Sep. (2018), doi: https://doi.org/10.21307/stattrans-2018-022.
[5] A. I. Al-Omari, “Acceptance Sampling Plan based on Truncated life tests for Three Parameter Kappa Distribution,” Economic Quality Control, vol. 29, no. 1, Jan. (2014), doi: https://doi.org/10.1515/eqc-2014-0006.
[6] A. I. Al-Omari, “Time truncated Acceptance Sampling plans for generalized inverted Exponential Distribution,” Electronic Journal of Applied Statistical analysis, vol. 8, no. 1, pp. 1-12, Apr. (2015), doi: https://doi.org/10.1285/i20705948v8n1p1.
[7] A. I. Al-Omari, “Time truncated acceptance sampling plans for Generalized Inverse Weibull Distribution,” Journal of Statistics and Management Systems, vol. 19, no. 1, pp. 1-19, Jan. (2016), doi: https://doi.org/10.1080/09720510.2013.867703.
[8] M. Aslam and C.H. Jun, “A double Acceptance Sampling Plan for generalized log-logistic distributions with known shape parameters,” Journal of Applied Statistics, vol. 37, no. 3, pp. 405-414, Mar. (2010), doi: https://doi.org/10.1080/02664760802698979.
[9] C. Chesneau, L. Tomy, and M. Jose, “Wrapped modified Lindley Distribution,” Journal of Statistics and Management Systems, vol. 24, no. 5, pp. 1025-1040, Apr. (2021), doi: https://doi.org/10.1080/09720510.2020.1796313.
[10] G. M. Cordeiro, M. Mansoor, and S. B. Provost, “The Harris Extended Lindley Distribution for modeling Hydrological data,” Chilean Journal of Statistics, vol. 10, no. 1 (2019).
[11] M. Elgarhy, V. K. Sharma, and I. Elbatal, “Transmuted Kumaraswamy Lindley distribution with application,” Journal of Statistics and Management Systems, vol. 21, no. 6, pp. 1083-1104, Sep. (2018), doi: https://doi.org/10.1080/09720510.2018.1481003.
[12] F. Jamal, H. Reyad, C. Chesneau, A. Nasir, and S. Othman, “The Marshall-Olkin odd Lindley-G family of Distributions: Theory and applications,” Punjab University Journal of Mathematics, vol. 51, no. 7, pp. 111-125 (2019).
[13] K. K. Jose and R. Sebastian, “Marshall-Olkin Gumbel-maximum Distribution”, Far East Journal of Theoretical Statistics, submitted.
[14] K. K. Jose, L. Tomy, and S. P. Thomas, “On a Generalization of the Weibull Distribution and Its Application in Quality Control,” Stochastics and Quality Control, vol. 33, no. 2, pp. 113-124, Dec. (2018), doi: https://doi.org/10.1515/eqc-2018-0011.
[15] R. R. L. Kantam, K. Rosaiah, and Govind Pratap Rao, “Acceptance Sampling based on life tests: Log-logistic model,” Journal of Applied Statistics, vol. 28, no. 1, pp. 121-128, Jan. (2001), doi: https://doi.org/10.1080/02664760120011644.
[16] E. Krishna, K. K. Jose, and M. M. Ristić, “Applications of Marshall-Olkin Fréchet Distribution,” Communications in statistics. Simulation and computation, vol. 42, no. 1, pp. 76-89, Jan. (2013), doi: https://doi.org/10.1080/03610918.2011.633196.
[17] J. F. Lawless, Statistical Models and Methods for Lifetime Data. John Wiley & Sons, (2011).
[18] Y. L. Lio, T.-R. Tsai, and S.-J. Wu, “Acceptance Sampling plans from truncated life tests based on the Burr type XII percentiles,” Journal of the Chinese Institute of Industrial Engineers, vol. 27, no. 4, pp. 270-280, Jul. (2010), doi: https://doi.org/10.1080/10170661003791029.
[19] R. Maya, Muhammed Rasheed Irshad, Muhammed Ahammed, and Christophe Chesneau, “The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control,” AppliedMath, vol. 3, no. 1, pp. 221-242, Mar. (2023), doi: https://doi.org/10.3390/appliedmath3010013.
[20] H. A. Noughabi, “Sample entropy applied to test of fit for Lindley Distribution and power comparison,” Journal of Statistics and Management Systems, vol. 25, no. 8, pp. 1781-1802, Jul. (2022), doi: https://doi.org/10.1080/09720510.2021.1984568.
[21] G. S. Rao and R. R. L. Kantam, “Acceptance Sampling Plans from Truncated Life Tests Based on the Log-Logistic Distributions for Percentiles,” Economic Quality Control, vol. 25, no. 2, Jan. (2010), doi: https://doi.org/10.1515/eqc.2010.008.
[22] K. Rosaiah and R. R. L. Kantam, “Acceptance Sampling Based on the Inverse Rayleigh Distribution,” Economic Quality Control, vol. 20, no. 2, Jan. (2005), doi: https://doi.org/10.1515/eqc.2005.277.
[23] M. S. Ravikumar, R. R. L. Kantam, and A. N. Durgamamba,``Acceptance Sampling Plans for Burr Type X Distribution,” International Journal of Advanced Technology in Engineering and Science, vol. 4, no. 8, pp. 36-44 (2016).
[24] P. Thomas, L. Tomy, and K. K. Jose, “Harris Extended Two Parameter Lindley Distribution and Applications in Reliability”, Reliability: Theory & Applications, vol. 16(3 (63)), 302-321, Jan. (2021). doi: 10.24412/1932-2321-2021-363-302-321.
[25] L. Tomy, G. Veena, and C. Chesneau, “A new three-parameter lifetime Distribution for environmental data analysis: the Harris extended modified Lindley distribution,” International Journal of Data Science and Analytics, Feb. (2024), doi: https://doi.org/10.1007/s41060-024-00505-0.
[26] A. R. Wood, “Predicting Software reliability,” IEEE Computer, vol. 29, no. 11, pp. 69-77, Nov. (1996), doi: https://doi.org/10.1109/2.544240.

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