Estimation of Reliability in a Multicomponent Stress–Strength Model for a General Class of Inverted Exponentiated Distributions Under Progressive Censoring

Tripathi Y. M., KIZILASLAN F., Mahto A. K.

Journal of Statistical Theory and Practice, vol.14, no.4, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1007/s42519-020-00123-6
  • Journal Name: Journal of Statistical Theory and Practice
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Inverted exponentiated distributions, Multicomponent stress-strength reliability, Progressive type-II censoring, Lindley approximation, Tierney-Kadane method, UPPER RECORD VALUES, BATHTUB SHAPE, RAYLEIGH DISTRIBUTION, BAYESIAN-ESTIMATION, PARAMETER, INFERENCE, PREDICTION, SYSTEM
  • Marmara University Affiliated: Yes

Abstract

We consider estimation of the multicomponent stress-strength reliability for a general class of inverted exponentiated distributions under progressive type-II censoring. We assume that both stress and strength variables follow this general class of distributions with a common parameter. Different point and interval estimates for the reliability of this system are obtained by using maximum likelihood and Bayesian approaches when the common parameter is known and unknown. The uniformly minimum variance unbiased estimate and exact Bayes estimate under the squared error loss function are derived when the common parameter is known. Bayes estimates are also obtained by using Lindley, Tierney-Kadane and Markov chain Monte Carlo methods. The asymptotic confidence and highest posterior density credible intervals are constructed. Proposed methods are compared numerically using Monte Carlo simulations. Finally, a progressively censored real data set is analyzed for illustration purposes.