Reliability Test Plan for an Extended Birnbaum-Saunders Distribution

  • Jiju Gillariose Department of Statistics, St.Thomas College, Pala, Kerala-686574, India
  • Lishamol Tomy Department of Statistics, Deva Matha College, Kuravilangad, Kerala-686633, India
Keywords: irnbaum-Saunders distribution, maximum likelihood estimation, operating characteristics function, reliability test plan, truncated negative binomial distribution.


Birnbaum-Saunders distribution has been widely studied in statistical literature because this distribution accommodates several interesting properties. The purpose of this paper is to introduce a new parametric distribution based on the Birnbaum-Saunders model and develop a new acceptance sampling plans for derived extended Birnbaum-Saunders distribution when the mean lifetime test is truncated at a predetermined time. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean lifetime worked out. The results are illustrated by a numerical example. The operating characteristic functions of the sampling plans and producer’s risk and the ratio of true mean life to a specified mean life that ensures acceptance with a pre-assigned probability are tabulated. This paper presents relevant characteristics of the new distribution and a new acceptance sampling plans when the lifetime of a product adopts an extended Birnbaum-Saunders distribution. Based on this study, the optimal number of testers demanded is decreases as test termination time increases. Moreover, the operating characteristic values increases as the mean life ratio increases, which indicate that items with increased mean life will be accepted with higher probability compared with items with lower mean life ratio.


Download data is not yet available.

Author Biographies

Jiju Gillariose, Department of Statistics, St.Thomas College, Pala, Kerala-686574, India

Jiju Gillariose is a Ph.D holder from the Department of Statistics, St. Thomas College, Palai, Kerala, India affiliated to MG University, Kottayam. She is currently pursuing her post-doctoral works. Her research deals with Distribution Theory, Data Analysis, Time Series and Statistical Quality Control.

Lishamol Tomy, Department of Statistics, Deva Matha College, Kuravilangad, Kerala-686633, India

Lishamol Tomy, Ph.D., is an Associate Professor in the Department of Statistics, Deva Matha College Kuravilangad, Kerala State, South India. She is an approved Doctoral Research Supervisor of Mahatma Gandhi University Kottayam, in the Research Centre of Statistics, St. Thomas College Pala. She is a winner of the Jan Tinbergen Award for the Young Statisticians instituted by the International Statistical Institute, Netherlands. Her research interests are in Distribution Theory, Statistical Inferences, Time Series and Data Analysis.


Al-Omari, A., Al-Nasser, A. and Ciavolino, E. (2019), “Acceptance sampling plans based on truncated life tests for Rama distribution”, International Journal of Quality & Reliability Management, Vol. 36 No. 7, pp. 1181–1191.

Babu, M.G. (2016), “On a generalization of Weibull distribution and its applications”, International Journal of Statistics and Applications, Vol. 6, pp. 168–176.

Baklizi, A., El Masri, A.E.Q. (2004) “Acceptance Sampling Based on Truncated Life Tests in the Birnbaum Saunders Model”, Risk Analysis, Vol. 24, pp. 453–1457.

Balakrishnan, N., Gupta, R.C., Kundu, D., Leiva, V., Sanhueza, A. (2010), “On some mixture models based on the Birnbaum-Saunders distribution and associated inference”, Journal of Statistical Planning and Inference, Vol. 141, 2175–2190.

Birnbaum, Z. W., Saunders, S. C. (1969a). “ Estimation for a family of life distributions with applications to fatigue”, Journal of Applied Probability, Vol. 6, pp. 28–347.

Birnbaum, Z. W., Saunders, S. C. (1969b). “ A new family of life distributions”, Journal of Applied Probability, Vol. 6, pp. 319–327.

Desmond, A.F., Cintora Gonzalez, C.L., Singh, R.S., Lu, X.W. (2012), “A mixed effect log-linear model based on the Birnbaum-Saunders distribution”, Computational Statistics and Data Analysis, Vol. 56, pp. 399–407.

Epstein, B. (1954), “Truncated life test in the exponential case”, Annals of Mathematical Statistics, Vol. 25, pp. 555–564.

Gillariose, J., Tomy. L. (2018), “A New Lifetime Model: The Generalized Rayleigh-Truncated Negative Binomial Distribution”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 5, pp. 1–12.

Jayakumar, K., Sankaran, K.K. (2016), “On a generalization of Uniform distribution and its Properties”, Statistica, Vol. 6, pp. 83–91.

Jayakumar, K., Sankaran, K.K. (2017), “Generalized Exponential Truncated Negative Binomial distribution”, American Journal of Mathematical and Management Sciences, Vol. 36, pp. 98–111.

Jose, K.K., Sivadas, R. (2015), “Negative binomial Marshall-Olkin Rayleigh distribution and its applications”, Economic Quality Control, Vol. 30, pp. 89–98.

Leiva, V. (2016), “The Birnbaum-Saunders Distribution”, Academic Press, New York, US.

Marshall, A.W., Olkin, I., 1997, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families”, Biometrica, Vol. 84, pp. 41–652.

Nadarajah, S. (2008), “A truncated inverted beta distribution with application to air pollution data”, Stochastic Environmental Research and Risk Assessment, Vol. 22, pp. 285–289.

Nadarajah, S., Jayakumar, K., Ristić, M.M. (2012), “A new family of lifetime models”, Journal of Statistical Computation and Simulation, Vol. 83, pp. 1–16.

Ng, H.K.T., Kundu, D., Balakrishnan, N. (2003). “Modified moment estimation for the two-parameter Birnbaum-Saunders distribution”, Computational Statistics and Data Analysis, Vol. 43, pp. 283–298.

Sobel, M. Tischendrof, J.A. (1959), “Acceptance sampling with new life test objectives”, In Proceedings of the Fifth National Symposium on Reliability and Quality Control, Philadelphia, PA, USA, pp. 108–118.

Wood, A. 1996, “Predicting software reliability”, IEEE Transactions on Software Engineering, Vol. 22, pp. 69–77.