Home / Current Issue / Paper 1702974
A Study on Extension of Double Acceptance Sampling Plans Based on Truncated Life Tests on The Inverse Rayleigh Distribution
Subject area: Science,Engineering and Technology · Area of research: Mathematics
Abstract
Sequential probability ratio test analysis (SPRT) which was the special case for multiple acceptance plans was develop using the inverse Rayleigh predicting software for the life time random variable for a truncated life test. In this paper, double acceptance sampling extend by Zoramawa et al (2018) has been extended to sequential sampling plans in terms of obtaining the minimum number of sample sizes necessary to obtained specified average life time under a given consumer?s risk. The lower proportion, higher proportion and the coefficient function where obtained, for different values of and and show the graphical performance of the model either to reject, to accept, to continue or terminate the procedure.
References
[1] Aryal,R. G and Tsokos, C. P (2011) Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution. European Journal of Pure and Applied Mathematics.4(2), 89-102
[2] Aslam, M. (2007). Double acceptance sampling based on truncated life tests in Rayleigh distribution. European Journal of Scientific Research, 17(4); 605-611.
[3] Aslam, M. and Ali, M. M (2019) Testing and inspection using acceptance sampling plans. doi.10.1007/978-981-13.9306-8
[4] B. Rao, K. G Rao, B.Rao (2013) Inverse Rayleigh software reliability growth model, International journal of computer application (0975-8887) volume 75 – No. 6. doi:10.5120/13112-0470
[5] Bacanli, S and Icen, D (2013) "Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing," Open Journal of Statistics, 3(3);195-199. doi: 10.4236/ojs.2013.33022.
[6] Baklizi, A. (2003). A conditional distribution runs test for symmetry. Nonparametric Statistics. 14(15); 713-718. 10.1080/10485250310001634737.
[7] Balakrishnan, N. (2007) Progressive Censoring Methodology: An Appraisal (with Discussion). Test, 16, 211-259.http://dx.doi.org/10.1007/s11749-007-0061-y
[8] Chen, Y., Li, X., Liu, J., & Ying, Z. (2019). Statistical analysis of complex problem-solving process data: An event history analysis approach. Frontiers in Psychology, 10(MAR), [486]. https://doi.org/10.3389/fpsyg.2019.00486
[9] Cox, D. R. (2013) A return to an old paper: tests of separate families of hypotheses. Journal of the Royal Statistical Society: Series B (Statistical Methodology)
[10] Darkhovsky, B. (2011). Optimal sequential tests for testing two composite and multiple simple hypotheses. Sequential Analysis 30 (4):479–96.
[11] Davida, M., Amsden, H. E. and Butler, R. T. A. (1991) Acceptance sampling plans doi.10.10007/978-94-011-3070-7_7
[12] Dey, S. and Dey, T. (2011). Bayesian estimation and prediction on inverse Rayleigh distribution. International Journal of Information and Management Sciences. 22(4);. 343-356.
[13] Dodge H.F. (1943) A sampling inspection plan for continuous production. Annals of Mathematical Statistics, 14, 264-279.
[14] Dodge H.F. and Torrey M.N. (1951) Additional continuous sampling inspection plans. Industrial Quality Control, 7(5); 7-12.
[15] Ewart, A. and Thomas, C (1975). A note on the sequential probability ratio test. , 40(1), 107–111. doi:10.1007/bf02291482
[16] Gardonyi , G., Por, G., and Samu, K. (2019) An Enhanced Evaluation Method of Sequential Probability Ratio Test.Mathematical Problems in Engineering. Volume 2019, Article ID 4724507, 1-12
[17] Ghosh, J. K. and R. V. Ramamoorthi (2003). Bayesian Nonparametrics. New York, NY: Springer
[18] Lens, H. and Wilrich, P. (2006). Frontiers in statisitical quality control 811 optimal two stage sequential sampling plans by attribute-, 10.1007/3-7908-1687-6(Chapter2), 21-33. doi. 10.1007/3-7908-1687-6_2
[19] Li, X., Liu, J. and Xu, J. (2016) On the Tail Asymptotics of Exponential Integrals of Gaussian Random Fields with Small Noise. Mathematics of Operations Research.
[20] Li, X., Liu, J. and Ying, Z. (2017) Generalized Sequential Probability Ratio Test for Separate Families of Hypotheses New York, NY 10027, USA
[21] Montgomery, D.C. (2013) Statistical quality control: a modern introduction.7th ed., wiley
[22] Muhammad, A., Yen, C., Chang, C and Jun, C. (2013) Multiple states repetitive group sampling plans with process loss consideration. Applied Mathematical Modelling 3(7):20-21
[23] Nakamura, T., Yamamoto, Y. and Douke, H (2016) Sequential hypothesis tests for identifying the minimum dose with a threshold effect. Communications in Statistics-Simulation and Computation 45(6):1950–70. doi:10.1080/03610918.2014.884588.
[24] Neyman, J. and Pearson, E. S. (1933) The problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 231(694–706):289–337.
[25] Opperman, L. and Ning, W. (2019) Sequential probability ratio test for skew normal distribution. Communications In Statistics Simulation and Computation https://doi.org/10.1080/03610918.2019.1614623
[26] Prasad, R. S., Ramadevi, B. and Sridevi, G (2015) Detection of Burr type XII Reliable Software Using SPRT on Interval Domain Data. (IJCSIT) International Journal of Computer Science and Information Technologies, 6 (2); 1806-1811
[27] Rayleigh J.W.S (1880) On the resultant of a large number of vibrations of the same pitch and arbitrary phase philosophical magazine, 5th series, 10, pp,73-78
[28] Rosaiah, K. and Kantam, R.R.L (2005). Acceptance sampling plan on the inverse Rayleigh distribution. Economic quality control, 20(2) 277-286.
[29] Rosaiah, K., Kantam, R. and Kumar, S. (2006). Reliability Test Plans for Exponentiated Log-Logistic Distribution. Economic Quality Control 21(2); 279-289.
[30] Rosaiah, K., Kantam, R., Prasad, S. and Reddy, J. (2008). Reliability Estimation in Type-II Generalized Log-Logistic Distribution. International Journal of Agricultural and Statistics Sciences 4(2); 283-292.
[31] Russell, E., Koren, G., Rieder, M., Van Uum, S., (2012). Hair cortisol as a biological marker of chronic stress: current status, future directions and unanswered questions. Psychoneuroendocrinology 37, 589–601.
[32] Shi, J., Siegmund, D. and Yakir, B. (2007) Importance sampling for estimating p values in linkage analysis. Journal of the American Statistical Association. 102(479):929–937
[33] Singh, N., Singh, N. and Kaur, H. (2019). Acceptance sampling plans for truncated life test have generalized Pareto distribution, life cycle reliability and safety engineering. doi:10.1007/s41872-019-00075-2
[34] Steland, A. (2015). Sampling Plans for Control-Inspection Schemes Under Independent and Dependent Sampling Designs with Applications to Photovoltaics. Frontiers in Statistical Quality Control 11, 287–317. doi:10.1007/978-3-319-12355-4_18
[35] Stute, W (1996), The sequential probability ratio test under random censorship metrika, 44(1), 1-8 doi.10.1007/bf02614050
[36] Sudamani, R. R, and Sutharani, R. (2013) Designing Double Acceptance Sampling Plans Based on Truncated Life Tests in Rayleigh Distribution Using Minimum Angle Method, American Journal of Mathematics and Statistics, 3(4),227-236. doi: 10.5923/j.ajms.20130304.07.
[37] Sukhdev, A., Vol, J., Brandt, K., and Yeoman, R. (2019): Cities in the Circular Economy: The Role of Digital Technology, Ellen MacArthur Foundation ANBI, Cowes, UK, 10, available at: https://www.ellenmacarthurfoundation.org/assets/downloads/ Cities-in-the-Circular-Economy-The-Role-of-Digital-Tech.pdf (last access: 5 June 2020),
[38] Tapiero, C.S (1996) Inspection and acceptance sampling in the management of quality and its contrl. Springer, Boston, MA.http//doi.org/10.1007/978-1-4615 -2055-9_5
[39] Teh, M. A, P., Aziz, N and Zain, Z, (2016) Time truncated group chain sampling plans for Rayleigh distribution. Research Journal of Applied Science 11(11); 1432-1435
[40] Wald, A. (1947). Sequential Analysis. John Wiley and Sons.
[41] Wald, A. and Wolfowitz, J. (1948) Optimum Character of the Sequential Probability Ratio Test. Annals of Mathematical Statistics, 19, 326-339.http://dx.doi.org/10.1214/aoms/1177730197
[42] Walter, B. (1943) “Multiple Sampling with Constant Probability," The Annals of Mathematical Statistics, 14; 363-377
[43] Yahya, C. (2007). Using Artificial Neural networks for the modelling of a distillation column. International Journal of Computer Science & Applications. https://www.researchgate.net/publication/26621941_Using_Artificial_Neural_networks_for_the_modelling_of_a_distillation_column
[44] Zoramawa, A. B., Gulumbe S. U, Kantam, R. R. L., and Musa, Y (2018) Developing double acceptance sampling plans for percentiles based on inverse Rayleigh distribution 3(1):39 –44
[45] Zoramawa, A.B.,Musa, Y and Usman U. (2018) Double acceptance sampling plans based on truncated life tests for inverse Rayleigh distribution 13(2)18 –28. doi:10.5281/zenodo.1418607
How to cite this paper
@article{1702974,
author = {Ibrahim, Sylvester, A.B. Zoramawa, N. S. Dauran, M.M Hamza, David Saiki Suru},
title = {A Study on Extension of Double Acceptance Sampling Plans Based on Truncated Life Tests on The Inverse Rayleigh Distribution},
journal = {Iconic Research And Engineering Journals},
year = {2021},
volume = {5},
number = {5},
pages = {155-182},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/17029742.pdf},
abstract = {Sequential probability ratio test analysis (SPRT) which was the special case for multiple acceptance plans was develop using the inverse Rayleigh predicting software for the life time random variable for a truncated life test. In this paper, double acceptance sampling extend by Zoramawa et al (2018) has been extended to sequential sampling plans in terms of obtaining the minimum number of sample sizes necessary to obtained specified average life time under a given consumer?s risk. The lower proportion, higher proportion and the coefficient function where obtained, for different values of and and show the graphical performance of the model either to reject, to accept, to continue or terminate the procedure.},
month = {November},
}