International Journal of Mathematical, Engineering and Management Sciences Vol. 4, No. 4, 882–894, 2019 https://dx.doi.org/10.33889/IJMEMS.2019.4.4-070 882 Bayesian Estimation of Stress Strength Reliability using Upper Record Values from Generalised Inverted Exponential Distribution Ritu Kumari a* , Kalpana K. Mahajan b , Sangeeta Arora c Department of Statistics Panjab University, Chandigarh, India E-mails: a stats.ritu@gmail.com, b mahajan_kr@pu.ac.in, c sarora131@gmail.com * Corresponding author (Received December 26, 2018; Accepted April 12, 2019) Abstract The paper develops Bayesian estimators and HPD intervals for the stress strength reliability of generalised inverted exponential distribution using upper record values. For prior distribution, informative prior as well as non-informative prior both are considered. The Bayes estimators are obtained under both symmetric and asymmetric loss functions. A simulation study is conducted to obtain the Bayes estimates of stress strength reliability. Simulated data sets are also considered here for illustration purpose. Keywords- Bayesian estimators, Record values, HPD intervals, Loss functions. 1. Introduction The exponential distribution is the most commonly used distribution in reliability field due to its simple form and a characteristic of constant hazard rate. Let random variable Y has an exponential distribution then the random variable  = 1/ will have the inverted exponential distribution. Lin et al. (1989); Keller et al. (1982) have discussed the inverted exponential distribution. Dey (2007) considered Bayesian estimations of the parameters of inverted exponential distribution under symmetric and asymmetric loss functions. A shape parameter was introduced in the inverted exponential distribution to get the Generalised inverted exponential distribution (Abouammoh and Alshinigiti 2009). Abouammoh and Alshinigiti (2009) also pointed out that generalised inverted exponential distribution gives better fit than inverted exponential, gamma, weibull and generalised exponential distribution in many situations. Nadarajah and Kotz (2000) also discussed the generalised inverted exponential distribution. Dey and Pradhan (2014) considered generalised inverted exponential distribution under hybrid censoring. These models have applications not only in the field of reliability but are also used in the system reliability as well (Li, 2016; Deepika et al., 2017; Kumar and Ram, 2018; Li et al., 2019; Chopra and Ram, 2019). Record values have an abundant role in daily life problems concerning data relating to numerous fields such as economics, weather and sports data. Chandler (1952) introduced the main idea of record values, inter-record times and started the statistical study of record values as a model for successive extremes in a sequence of independently and identically distributed random variables. The record values can be categorized into the lower and the upper records. An observation   will be called an upper record value if its value is greater than all of previous observations (i.e.,   >   for every  > ) and it will be called a lower record value if its value is less than all of previous observations (i.e.,   <  for every  >).