Abstract
Acceptance sampling or sampling inspection is an essential quality control technique that describes the rules and procedures for making decisions about the acceptance or rejection of a batch of commodities based on inspection of one or more samples. When quality of an item is evaluated based on the lifetime of the item, which can be adequately described by a continuous-type probability distribution, the plan is known as life test sampling plan. In this article, a reliability double sampling plan with smaller acceptance number is formulated under time censoring by assuming the lifetime of the item follows Marshall–Olkin extended exponential distribution. A procedure for selection of the plan parameters to protect both the producer as well as the consumer indexed by the acceptable mean life and operating ratio is evolved.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Epstein, B.: Tests for the validity of the assumption that the underlying distribution of life is exponential, Part I. Technometrics 2, 83–101 (1960)
Epstein, B.: Tests for the validity of the assumption that the underlying distribution of life is exponential, Part II. Technometrics 2, 167–183 (1960)
Handbook H-108.: Sampling procedures and tables for life and reliability testing. Quality Control and Reliability, Office of the Assistant Secretary of Defense. US Department of Defense, Washington, D.C. (1960)
Goode, H.P., Kao, J.H.K.: Sampling plans based on the weibull distribution. In: Proceedings of the seventh national symposium on reliability and quality control, pp. 24–40. Philadelphia, PA (1961)
Goode, H.P., Kao, J.H.K.: Sampling procedures and tables for life and reliability testing based on the weibull distribution (Hazard Rate Criterion). In: Proceedings of the Eight National Symposium on Reliability and Quality Control, pp. 37–58. Washington, DC (1962)
Goode, H.P., Kao, J.H.K.: Hazard rate sampling plans for the weibull distribution. Ind. Qual. Control. 20, 30–39 (1964)
Gupta, S.S., Groll, P.A.: Gamma distribution in acceptance sampling based on life tests. J. Am. Stat. Assoc. 56, 942–970 (1961)
Schilling, E.G., Neubauer, D.V.: Acceptance sampling in quality control. Chapman and Hall, New York, NY (2009)
Gupta, S.S.: Life test sampling plans for normal and lognormal distributions. Technometrics 4, 151–175 (1962)
Kantam, R.R.L., Rosaiah, K., Rao, G.S.: Acceptance sampling based on life tests: log-logistic models. J. Appl. Stat. 28, 121–128 (2001)
Baklizi, A., El Masri, A.E.Q.: Acceptance sampling based on truncated life tests in the Birnbaum Saunders model. Risk Anal. 24, 1453–1457 (2004)
Jun, C.-H., Balamurali, S., Lee, S.H.: Variables sampling plans for weibull distributed lifetimes under sudden death testing. IEEE Trans. Reliab. 55, 53–58 (2006)
Tsai, T.-R., Wu, S.-J.: Acceptance sampling based on truncated life-tests for generalized rayleigh distribution. J. Appl. Stat. 33, 595–600 (2006)
Balakrishnan, N., Leiva, V., López J.: Acceptance sampling plans from truncated life-test based on the generalized Birnbaum–Saunders distribution. Commun. Stat.–Simul. Comput. 36:643–656 (2007)
Aslam, M., Jun, C.H.: A group acceptance sampling plan for truncated life test having weibull distribution. J. Appl. Stat. 39, 1021–1027 (2009)
Aslam, M., Kundu, D., Jun, C.H., Ahmad, M.: Time truncated group acceptance sampling plans for generalized exponential distribution. J. Test. Eval. 39, 968–976 (2011)
Kalaiselvi, S., Vijayaraghavan, R.: Designing of Bayesian Single Sampling Plans for Weibull-Inverted Gamma Distribution, pp. 123–132. Recent Trends in Statistical Research, Publication Division, M. S. University, Tirunelveli (2010)
Kalaiselvi, S., Loganathan, A., Vijayaraghavan, R.: Reliability Sampling Plans under the Conditions of Rayleigh–Maxwell Distribution—A Bayesian Approach, pp. 280–283. Recent Advances in Statistics and Computer Applications, Bharathiar University, Coimbatore (2011)
Loganathan, A., Vijayaraghavan, R., Kalaiselvi, S.: Recent Developments in Designing Bayesian Reliability Sampling Plans—an Overview, pp. 61–68. New Methodologies in Statistical Research, Publication Division, M. S. University, Tirunelveli (2012)
Vijayaraghavan, R., Chandrasekar, K., Uma, S.: Selection of sampling inspection plans for life test based on weibull-poisson mixed distribution. Proceedings of the International Conference on Frontiers of Statistics and its Applications, pp. 225–232. Coimbatore (2012)
Vijayaraghavan, R., Uma, S.: Selection of sampling inspection plans for life tests based on lognormal distribution. J. Test. Eval. 44, 1960–1969 (2016)
Al-Zahrani.: Reliability test plan based on Dagum distribution. Int. J. Adv. Stat. Probab. 4, 75–78 (2016)
Marshall, A.W., Olkin, I.: A new method for adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika 84, 641–652 (1997)
Marshall, A.W., Olkin, I.: Life Distributions. Structure of Nonparametric, Semiparametric and Parametric Families. Springer, New York, US (2007)
Dodge, H.F.: Chain sampling inspection plans. Ind. Qual. Control. 11, 10–13 (1955)
Vijayaraghavan, R.: Minimum size double sampling plans for large isolated lots. J. Appl. Stat. 34, 799–806 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Vijayaraghavan, R., Saranya, C.R., Sharma, K.S.N. (2022). Double Sampling Plans for Life Test Based on Marshall–Olkin Extended Exponential Distribution. In: Das, B., Patgiri, R., Bandyopadhyay, S., Balas, V.E. (eds) Modeling, Simulation and Optimization. Smart Innovation, Systems and Technologies, vol 292. Springer, Singapore. https://doi.org/10.1007/978-981-19-0836-1_20
Download citation
DOI: https://doi.org/10.1007/978-981-19-0836-1_20
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0835-4
Online ISBN: 978-981-19-0836-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)