Skip to main content

2024 | OriginalPaper | Buchkapitel

Analysis of Progressively Censored Repair Time of Airborne Communication Transceiver with Burr-Hatke Exponential Model

verfasst von : Kartik Waliya, Alka Chaudhary, Abhishek Tyagi

Erschienen in: Reliability Engineering for Industrial Processes

Verlag: Springer Nature Switzerland

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter, the parameter estimation of a Burr-Hatke exponential model based on the progressive type-II censored sample is investigated. Various methods of estimation for complete data are generalized to the case under progressive censored samples. These approaches comprise maximum likelihood, least squares, maximum product spacings, and Bayesian estimation. Interval estimate and coverage probability for the parameter are derived by the use of maximum likelihood and Bayesian estimation techniques. Markov chain Monte Carlo algorithm has been employed to obtain the Bayes estimator of the parameter with gamma prior under squared error loss function. A vast comparative analysis of the four methods is made using a Monte Carlo empirical study. The empirical findings are used in the formulation of certain suggestions, and a real-world data example is shown to illustrate how the developed theory may be applied in practice.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Lawless JF (1982) Statistical models and methods for lifetime data. Wiley, New York Lawless JF (1982) Statistical models and methods for lifetime data. Wiley, New York
2.
Zurück zum Zitat Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data (Book). In: Research supported by the U. S. Air Force and Rockwell International Corp. New York, John Wiley and Sons, Inc., 573 pp Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data (Book). In: Research supported by the U. S. Air Force and Rockwell International Corp. New York, John Wiley and Sons, Inc., 573 pp
3.
Zurück zum Zitat Sinha SK (1986) Reliability and life testing. Wiley Eastern Limited, New Delhi Sinha SK (1986) Reliability and life testing. Wiley Eastern Limited, New Delhi
4.
Zurück zum Zitat Yadav AS, Altun E, Yousof HM (2021) Burr-Hatke exponential distribution: a decreasing failure rate model, statistical inference and applications. Ann Data Sci 8:241–260CrossRef Yadav AS, Altun E, Yousof HM (2021) Burr-Hatke exponential distribution: a decreasing failure rate model, statistical inference and applications. Ann Data Sci 8:241–260CrossRef
6.
Zurück zum Zitat Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Springer Science & Business Media Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Springer Science & Business Media
7.
Zurück zum Zitat Krishna H, Kumar K (2011) Reliability estimation in Lindley distribution with progressively type II right censored sample. Math Comput Simul 82(2):281–294MathSciNetCrossRef Krishna H, Kumar K (2011) Reliability estimation in Lindley distribution with progressively type II right censored sample. Math Comput Simul 82(2):281–294MathSciNetCrossRef
8.
Zurück zum Zitat Ng HKT, Luo L, Hu Y, Duan F (2012) Parameter estimation of three-parameter Weibull distribution based on progressively type-II censored samples. J Stat Comput Simul 82(11):1661–1678MathSciNetCrossRef Ng HKT, Luo L, Hu Y, Duan F (2012) Parameter estimation of three-parameter Weibull distribution based on progressively type-II censored samples. J Stat Comput Simul 82(11):1661–1678MathSciNetCrossRef
9.
Zurück zum Zitat Krishna H, Kumar K (2013) Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. J Stat Comput Simul 83(6):1007–1019MathSciNetCrossRef Krishna H, Kumar K (2013) Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. J Stat Comput Simul 83(6):1007–1019MathSciNetCrossRef
10.
Zurück zum Zitat Dey S, Singh S, Tripathi YM, Asgharzadeh A (2016) Estimation and prediction for a progressively censored generalized inverted exponential distribution. Stat Methodol 32:185–202MathSciNetCrossRef Dey S, Singh S, Tripathi YM, Asgharzadeh A (2016) Estimation and prediction for a progressively censored generalized inverted exponential distribution. Stat Methodol 32:185–202MathSciNetCrossRef
11.
Zurück zum Zitat Valiollahi R, Raqab MZ, Asgharzadeh A, Alqallaf FA (2018) Estimation and prediction for power Lindley distribution under progressively type II right censored samples. Math Comput Simul 149:32–47MathSciNetCrossRef Valiollahi R, Raqab MZ, Asgharzadeh A, Alqallaf FA (2018) Estimation and prediction for power Lindley distribution under progressively type II right censored samples. Math Comput Simul 149:32–47MathSciNetCrossRef
12.
Zurück zum Zitat Zhang Z, Gui W (2019) Statistical inference of reliability of Generalized Rayleigh distribution under progressively type-II censoring. J Comput Appl Math 361:295–312MathSciNetCrossRef Zhang Z, Gui W (2019) Statistical inference of reliability of Generalized Rayleigh distribution under progressively type-II censoring. J Comput Appl Math 361:295–312MathSciNetCrossRef
13.
Zurück zum Zitat Elshahhat A, Rastogi MK (2021) Estimation of parameters of life for an inverted Nadarajah-Haghighi distribution from Type-II progressively censored samples. J Indian Soc Probab Stat 22:113–154CrossRef Elshahhat A, Rastogi MK (2021) Estimation of parameters of life for an inverted Nadarajah-Haghighi distribution from Type-II progressively censored samples. J Indian Soc Probab Stat 22:113–154CrossRef
14.
Zurück zum Zitat Kumari R, Arora S, Mahajan KK (2022) Estimation of stress-strength reliability for Dagum distribution based on progressive type-II censored sample. Model Assist Stat Appl 17(2):109–122 Kumari R, Arora S, Mahajan KK (2022) Estimation of stress-strength reliability for Dagum distribution based on progressive type-II censored sample. Model Assist Stat Appl 17(2):109–122
15.
Zurück zum Zitat Swain JJ, Venkatraman S, Wilson JR (1988) Least-squares estimation of distribution functions in Johnson’s translation system. J Stat Comput Simul 29(4):271–297CrossRef Swain JJ, Venkatraman S, Wilson JR (1988) Least-squares estimation of distribution functions in Johnson’s translation system. J Stat Comput Simul 29(4):271–297CrossRef
16.
Zurück zum Zitat Jukić D, Benšić M, Scitovski R (2008) On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution. Comput Stat Data Anal 52(9):4502–4511MathSciNetCrossRef Jukić D, Benšić M, Scitovski R (2008) On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution. Comput Stat Data Anal 52(9):4502–4511MathSciNetCrossRef
17.
Zurück zum Zitat Cheng RCH, Amin NAK (1979) Maximum product-of-spacings estimation with applications to the lognormal distribution. Math Report 791 Cheng RCH, Amin NAK (1979) Maximum product-of-spacings estimation with applications to the lognormal distribution. Math Report 791
18.
Zurück zum Zitat Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J Roy Stat Soc: Ser B (Methodol) 45(3):394–403MathSciNetCrossRef Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J Roy Stat Soc: Ser B (Methodol) 45(3):394–403MathSciNetCrossRef
19.
Zurück zum Zitat Coolen FPA, Newby MJ (1990) A note on the use of the product of spacings in Bayesian inference. University of Technology, Department of Mathematics and Computing Science Coolen FPA, Newby MJ (1990) A note on the use of the product of spacings in Bayesian inference. University of Technology, Department of Mathematics and Computing Science
21.
Zurück zum Zitat Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44(247):335–341CrossRef Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44(247):335–341CrossRef
22.
Zurück zum Zitat Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109MathSciNetCrossRef Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109MathSciNetCrossRef
23.
Zurück zum Zitat Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69–92MathSciNetCrossRef Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69–92MathSciNetCrossRef
24.
Zurück zum Zitat Balakrishnan N, Sandhu RA (1995) A simple simulational algorithm for generating progressive Type-II censored samples. Am Stat 49(2):229–230CrossRef Balakrishnan N, Sandhu RA (1995) A simple simulational algorithm for generating progressive Type-II censored samples. Am Stat 49(2):229–230CrossRef
25.
Zurück zum Zitat Chhikara RS, Folks JL (1977) The inverse Gaussian distribution as a lifetime model. Technometrics 19(4):461–468CrossRef Chhikara RS, Folks JL (1977) The inverse Gaussian distribution as a lifetime model. Technometrics 19(4):461–468CrossRef
Metadaten
Titel
Analysis of Progressively Censored Repair Time of Airborne Communication Transceiver with Burr-Hatke Exponential Model
verfasst von
Kartik Waliya
Alka Chaudhary
Abhishek Tyagi
Copyright-Jahr
2024
DOI
https://doi.org/10.1007/978-3-031-55048-5_8

Premium Partner