Abstract
Censoring schemes have received much attention over the past decades. Hybrid censoring schemes are censoring schemes mixed of type-I (T-1) and type-II (T-2) censoring schemes, a most popular area of study in life-testing or reliability experiments. More precisely, hybrid censoring can be described as a mixture of T-I and T-2 schemes. Gamma distribution is widely used, and its connection has more distributions. Mixture and single gamma distribution will be studied to estimate parameters, based on type-II hybrid censoring schemes (T-2HCS). We will apply algorithms to compute the maximum likelihood (ML) estimators and Bayesian approaches, using statistics, such as Markov chain Monte Carlo methods. Bayes estimators and corresponding highest posterior density confidence intervals will be tabled. Also, Markov chain Monte Carlo simulation is implemented to compare the performances of the different methods and the real dataset is analyzed for illustrative purposes.
Highlights
Over the last century, monitoring items and products are incredibly important tasks for managers in companies and different institutions
Childs et al [11] suggested a new approach to the schemes and is called T-2HCS. e definition of data is to suppose n identical products or items on the experiment, and the experiment will be stopped at the random time, say T∗ maxxr: n, T, where 0 ≤ r ≤ n and T are chosen numbers and xr: n indicates the time of r-th failure item in a sample of size n
Bayes estimators are proposed to estimate unknown parameters of gamma distribution based on T-2HCS
Summary
Over the last century, monitoring items and products are incredibly important tasks for managers in companies and different institutions. E definition of data is to suppose n identical products or items on the experiment, and the experiment will be stopped at the random time, say T∗ maxxr: n, T, where 0 ≤ r ≤ n and T are chosen numbers and xr: n indicates the time of r-th failure item in a sample of size n Under this definition, it is clear to extricate three cases:. (2) Case II is to collect r-th failure of products, which occurs between two prefixed times, and the experiment terminated at the last failure item xr: n (3) Case III is to collect the r-th failure occurring before time T2 is reached is type of investigation might arise in a case when the examiner decides to add a specific condition Childs et al [11], for example, at least number of failures r must be collected and this might cost for the use of the testing facility until the moment of units time T1.
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