Evaluation of Sampling Inspection Plans for Life-tests Based on Generalized Gamma Distribution

R. Vijayaraghavan¹ , K. Sathya Narayana Sharma² , C. R. Saranya³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.138-146, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.138146

Online published on Feb 28, 2019

Copyright © R. Vijayaraghavan, K. Sathya Narayana Sharma, C. R. Saranya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

637 Views    322 Downloads    75 Downloads

Abstract :
Acceptance sampling is concerned with rules for deciding about the acceptance or rejection of a lot of products submitted for inspection based on the quality of the products assessed through the testing of items drawn randomly from the lot. Sampling inspection plans which are used for taking decisions about the acceptability of the product with respect to life time are called life-test sampling plans. Lifetime of the product is considered as a continuous random variable, which is modelled by a probability distribution. The literature of sampling inspection for lifetime data provides applications of various types of continuous distributions in the studies relating to the design and evaluation of life-test sampling plans. This paper presents the procedures and tables for the selection of life-test sampling plans under the conditions for application of the generalized gamma distribution. The criteria for designing life-test plans when lot quality is evaluated in terms of mean life and hazard rate are proposed.

Key-Words / Index Term :
Acceptable mean life, Hazard rate, Generalized Gamma Distribution, Mean life, Reliability sampling

References :
[1] Aslam, M., and Jun, C. H. Group Acceptance Sampling Plans for Truncated Life Tests Based on the Inverse Rayleigh Distribution and Log-logistic Distribution, Pakistan Journal of Statistics, Vol.25,pp.107 - 119, 2009.
[2] Aslam, M., and Jun, C. H. A Group Acceptance Sampling Plan for Truncated Life Test having Weibull Distribution, Journal of Applied Statistics, Vol.39,pp.1021 - 1027, 2009.
[3] Balakrishnan, N., Leiva, V., and L´opez, J. Acceptance Sampling Plans from Truncated Life-test Based on the Generalized Birnbaum - Saunders Distribution, Communications in Statistics - Simulation and Computation, Vol.36, pp.643 - 656, 2007.
[4] Birnbaum, Z. W., and Saunders, S. C. A Statistical Model for Life – Length of Materials, Journal of the American Statistical Association, Vol.53, pp.153 - 160, 1958.
[5] Cameron, J. M. Tables for Constructing and for Computing the Operating Characteristics of Single Sampling Plans, Industrial Quality Control, Vol.9,pp.37 - 39, 1952.
[6] Choi, S. C., and Wette, R. Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and their Bias, Technometrics,Vol.4,pp.683 -690, 1969.
[7] Cohen, C. A., and Norgaard, N. J. Progressively Censored Sampling in the Three-Parameter Gamma Distribution, Technometrics,Vol.19, pp.333 - 340, 1977.
[8] Drenick, R. F. Mathematical Aspects of the Reliability Problem, Journal of the Society for Industrial and Applied Mathematics, Vol.8,pp.125 - 149, 1960.
[9] Epstein, B. Tests for the Validity of the Assumption that the Underlying Distribution of Life is Exponential, Part I, Technometrics, Vol.2,pp.83 - 101, 1960.
[10] Epstein, B. Tests for the Validity of the Assumption that the Underlying Distribution of Life is Exponential, Part II, Technometrics, Vol.2, pp.67 – 183, 1960.
[11] Glaser, R. E. Bathtub and Related Failure Rate Characterizations, Journal of the American Statistical Association, Vol.75,pp.667 - 672, 1980.
[12] Goode, H. P., and Kao, J. H. K. Sampling Plans Based on the Weibull Distribution, Proceedings of the Seventh National Symposium on Reliability and Quality Control, Philadelphia, PA., pp.24 - 40, 1961.
[13] Goode, H. P., and Kao, J. H. K. Sampling Procedures and Tables for Life and Reliability Testing Based on the Weibull Distribution (Hazard Rate Criterion), Proceedings of the Eight National Symposium on Reliability and Quality Control, Washington, DC., pp.37 - 58, 1962.
[14] Goode, H. P., and Kao, J. H. K. Hazard Rate Sampling Plans for the Weibull Distribution. Industrial Quality Control, Vol.20,pp.30 - 39, 1964.
[15] Greenwood, J. A., and Durand, D. Aids for Fitting the Gamma Distribution by Maximum Likelihood, Technometrics, Vol.2,pp.55 - 65, 1960.
[16] Gross, A. J., and Clark, V. A. Survival Distributions: Reliability Applications in the Biomedical Sciences, John Wiley & Sons, New York, 1975.
[17] Gupta, S. S. Order Statistics from the Gamma Distribution, Technometrics, Vol.2,pp.243 - 262, 1960.
[18] Gupta, S. S. Life Test Sampling Plans for Normal and Lognormal Distributions, Technometrics, Vol.4,pp.151 - 175, 1962.
[19]Gupta, S.S. and Groll, P. A. Gamma Distribution in Acceptance Sampling Based on Life Tests, Journal of the American Statistical Association, Vol.56,pp.942 - 970, 1961.
[20] 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
[21] Hong, C. W., Lee, W. C., and Wu, J. W. Computational Procedure of Performance Assessment of Life-time Index of Products for the Weibull Distribution with the Progressive First-failure Censored Sampling Plan, Journal of Applied Mathematics, Vol.2012,pp.1 - 13, 2012.
[22] Johnson, N. L., Kotz, S., and Balakrishnan, N. Continuous Univariate Distribution, Vol. 1, Second Edition, Wiley, New York, 1995.
[23] Jun, C.-H., Balamurali, S., and Lee, S.H. Variables Sampling Plans for Weibull Distributed Lifetimes under Sudden Death Testing, IEEE Transactions on Reliability, Vol.55,pp.53 - 58, 2006.
[24] Kantam, R. R. L., Rosaiah, K., and Rao, G. S. Acceptance Sampling Based on Life Tests: Log-Logistic Models, Journal of Applied Statistics, Vol.28, pp.121 - 128, 2001.
[25] Kalaiselvi, S., and Vijayaraghavan, R. Designing of Bayesian Single Sampling Plans for Weibull-Inverted Gamma Distribution, Recent Trends in Statistical Research, Publication Division, M. S. University, Tirunelveli, India, pp.123 - 132, 2010.
[26] Kalaiselvi, S., Loganathan, A., and Vijayaraghavan, R. Reliability Sampling Plans under the Conditions of Rayleigh – Maxwell Distribution – A Bayesian Approach, Recent Advances in Statistics and Computer Applications, Bharathiar University, Coimbatore, India, pp.280 - 283, 2011.
[27] Loganathan, A., Vijayaraghavan, R., and Kalaiselvi, S. Recent Developments in Designing Bayesian Reliability Sampling Plans – An Overview, New Methodologies in Statistical Research, Publication Division, M. S. University, Tirunelveli, India, pp.61 - 68, 2012.
[28] Marshall, A.W., and Olkin, I. Life Distributions, Springer Series in Statistics, Springer, 2007.
[29] McDonald, J. B., and Richards, D. O. Hazard Rates and Generalized Beta Distributions, IEEE Transactions on Reliability, Vol.36,pp.463 - 466, 1987.
[30] Pearson, K. Contributions to the Mathematical Theory of Evolution – II: Skew Variations in Homogeneous Material, Philosophical Transactions of the Royal Society of London, pp.343 - 414, 1895.
[31] Schilling, E. G., and Neubauer, D. V. Acceptance Sampling in Quality Control. Chapman and Hall, New York, NY., 2009.
[32] Stacy E. W. A Generalization of the Gamma Distribution, The Annals of Mathematical Statistics,Vol.33, pp.1187 - 1192, 1962.
[33] Tsai, T.-R., and Wu, S.-J. Acceptance Sampling Based on Truncated Life-tests for Generalized Rayleigh Distribution, Journal of Applied Statistics, Vol.33,pp.595 - 600, 2006.
[34] United States Department of Defense, Military Standard, Sampling Procedures and Tables for Inspection by Attributes (MIL-STD-105D), U. S. Government Printing Office, Washington D. C., 1963.
[35] United States Department of Defense, Sampling Procedures and Tables for Life and Reliability Testing Based on the Weibull Distribution (Mean Life Criterion), Quality Control and Reliability Technical Report (TR 3), Office of the Assistant Secretary of Defense Installation and Logistics), U. S. Government Printing Office, Washington D. C., 1961.
[36] United States Department of Defense, Sampling Procedures and Tables for Life and Reliability Testing Based on the Weibull Distribution (Hazard Rate Criterion), Quality Control and Reliability Technical Report (TR 4), Office of the Assistant Secretary of Defense Installation and Logistics), U. S. Government Printing Office, Washington D. C., 1962.
[37] United States Department of Defense, Sampling Procedures and Tables for Life and Reliability Testing Based on the Weibull Distribution (Reliability Life Criterion), Quality Control and Reliability Technical Report (TR 6), Office of the Assistant Secretary of Defense Installation and Logistics), U. S. Government Printing Office, Washington D. C., 1963.
[38] United States Department of Defense, Factors and Procedures for Applying MIL-STD-105D Sampling Plans to Life and Reliability Testing, Quality Control and Reliability Assurance Technical Report (TR 7), Office of the Assistant Secretary of Defense (Installations and Logistics), Washington D. C., 1965.
[39] Vijayaraghavan, R., Chandrasekar, K., and Uma, S. Selection of Sampling Inspection Plans for Life-test Based on Weibull - Poisson Mixed Distribution, Frontiers of Statistics and its Applications, Bonfring, Coimbatore, India, pp.225 - 232, 2012.
[40] Vijayaraghavan, R., and Uma, S. Evaluation of Sampling Inspection Plans for Life Test Based on Exponential - Poisson Mixed Distribution, Frontiers of Statistics and its Applications, Bonfring, Coimbatore, India, pp.233 - 240, 2012.
[41] Vijayaraghavan, R., and Uma, S. Selection of Sampling Inspection Plans for Life Tests Based on Lognormal Distribution, Journal of Testing and Evaluation, Vol.44,pp.1960 - 1969, 2016.
[42] Wu, J. W., and Tsai, W. L. Failure Censored Sampling Plan for the Weibull Distribution, Information and management Sciences, Vol.11,pp.13 - 25, 2000.
[43] Wu, J. W., Tsai, T. R., and Ouyang, L. Y. Limited Failure-Censored Life Test for the Weibull Distribution, IEEE Transactions on Reliability, Vol.50, pp.197 - 111, 2001.