Nkemnole* | E. Bridget | Samiyu | M. Abiodun
OPEN ACCESS
Research has suggested that there are components or devices which survive due to their strength. Although, these devices survive under a certain level of stress but when a higher level of stress is applied on them, they failed because they can’t sustain it. The likelihood that these components are functional during a certain level of stress under a stated condition and a specified operational environment is regarded as its reliability, which in reliability engineering studies can be used to control, evaluate and estimate the capability and lifetime of a device. This study aims to further contribute to the estimation of the stress-strength reliability parameter, where and are independent lognormal distributions based only on the first-observed lower record values. The Maximum Likelihood Estimator (MLE) of R and its asymptotic distribution are obtained as well as the confidence interval. Different parametric bootstrap confidence intervals are also proposed. Simulation and real data set representing Block-Moulding Machine experiment data (of Tola Block industry, Lagos, Nigeria) are fitted using the lognormal distribution and used to estimate the stress-strength parameters and reliability. Empirical analysis shows that the proposed model helps to establish a proficient structure for stress-strength reliability models.
Lognormal Distribution, Reliability, Interval Estimation, Lower record values, Stress-Strength Reliability
[1] M. Ahsanullah “Extreme Value Distributions”, Atlantis Studies in Probability and Statistics; Volume 8; ISBN: 978-94-6239-222-9, 2016.
[2] S. Amal, Hiba Z., Mohammed S. “Estimation of Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution Based on Lower Record Values", British Journal of Mathematics & Computer Science, 2015; 11(2):1-14.
[3] B. Alessandro Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case. Communications in Statistics, 2011; 40(6):907-925.
[4] F. Al-Gashgari , Shawky A. Estimation of P(Y<X) Using Lower Record Data from the Exponentiated Weibull Distributions: Classical and MCMC Approaches. Life Science Journal, 2014; 11(7):768-777.
[5] A. Baklizi Estimation of Pr(X<Y) using Record Values in the One and Two-Parameter
[6] Exponential Distributions. Communications in Statistics-Theory and methods, 2008; 37:692-698.
[7] Baklizi Inference on Pr(X<Y) in the Two-Parameter Weibull Model Based on Records. ISRN Probability and Statistics, 2012; Article ID: 263612: 1-11.
[8] Baklizi A. Interval Estimation of Stress-strength reliability in the two-parameter exponential distribution based on records. Journal of Statistical Computation and Simulations, 2013; 84: 2670-2679.
[9] Baklizi Bayesian Inference for
in the Exponential Distribution Based on Records. Applied Mathematical Modelling, 2014; 38: 1698-1710.
[10] Basu The estimation of
for distributions useful in life testing. Naval Research Logistics Quarterly, 1981; 28:383-392.
[11] K. Chandler The Distribution and Frequency of record Values. Journal of Royal Society, 1952. 14:220-228.
[12] J. Church The Estimation of Reliability from Stress-Strength Relationships. Technometrics, 1970; 12: 49-54.
[13] A. Essam The Sampling Distribution of the Maximum Likelihood Estimators from type I Generalized Logistic Distribution Based On Lower Record Values. International Journal of Contemporary Math. Sciences, 2012; 24:1205-1212.
[14] Hassan et al. Estimation of Stress-Strength Reliability function Based on Lower Record
[15] Values. British Journal of Mathematics and Computer Science, 2015; 11(2):1-14.
[16] M. Khan Modified Inverse Rayleigh Distribution. Journal of statistics Applications and Probability, 2012; 2: 115-132.
[17] S. Kotz , Lumelskii Y., Pensky M. The Stress-Strength Model and Its Generalizations: Theory and Applications, London: Imperial College Press, 2003; ISBN: 978-981-238-057-9.
[18] Krishnamoorthy K. et al . New Inferential Methods for the Reliability Parameter in a Stress-
[19] strength Model; The Normal Case. Communication in Statistics Theory and Methods, 2014; 33:1715-1731.
[20] M. Mazumdar Some Estimates of Reliability using Inference Theory. Naval Research Logistics Quarterly,1970; 17:159-165.
[21] Nguimkeu P., Marie R., Augustine W. Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables. Communication in Statistics Theory and Methods, 2014; 15:23-67.
[22] R.G. Srinivasa Estimation of Stress-Strength Reliability from Inverse Rayleigh Distribution based on lower record values. Journal of Quality and Reliability Engineering, 2013; 30(4):256-263.
[23] Bahman T., Hossein K. Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution. Journal of Quality and Reliability Engineering, 2014; 2014: Article ID 192072.