This paper focuses on the application of Markov Chain Monte Carlo (MCMC) technique for estimating the parameters of log-logistic (LL) distribution which is dependent on a complete sample. To find Bayesian estimates for the parameters of the LL model OpenBUGS—established software for Bayesian analysis based on MCMC technique, is employed. It is presumed that samples for independent non informative set of priors for estimating LL parameters are drawn from posterior density function. A proposed module was developed and incorporated in OpenBUGS to estimate the Bayes estimators of the LL distribution. It is shown that statistically consistent parameter estimates and their respective credible intervals can be constructed through the use of OpenBUGS. Finally comparison of maximum likelihood estimate and Bayes estimates is carried out using three plots. Additively through this research it is established that computationally MCMC technique can be effortlessly put into practice. Elaborate procedure for applying MCMC, to estimate parameters of LL model, is demonstrated by making use of real survival data relating to bladder cancer patients.

The present study focuses on the multi-component stress-strength (MCSS) model based on inverse Weibull distribution (IWD). Both stress and strength are assumed to follow IWD with a common shape parameter. In such a system, reliability is obtained by the maximum likelihood (ML) method. The results are extracted using Monte Carlo simulation for comparing the performance of the reliability component R_s,k using different sample sizes and different combinations of the parameters (s,k). The procedure is further illustrated through a real data set to show how the proposed technique may be employed to study the strength and stress of multicomponent model.

In this paper, a control chart scheme has been introduced for the mean monitoring using gamma distribution for belief statistics using multiple dependent (deferred) state sampling under the neutrosophic statistics. The coefficients of the control chart and the neutrosophic average run lengths have been estimated for specific false alarm probabilities under various process conditions. The offered chart has been compared with the existing classical chart through simulation and the real data. From the comparison, it is concluded that the performance of the proposed chart is better than that of the existing chart in terms of average run length under uncertain environment. The proposed chart has the ability to detect a shift quickly than the existing chart. It has been observed that the proposed chart is efficient in quick monitoring of the out-of-control process and a cherished addition in the toolkit of the quality control personnel.

The performance and potential of a process of industrial products is assessed under lower specification limit L by lifetime performance index (C_L ). In this paper, under consideration the independent lifetimes Chen products with known one shape parameters the C_L of the performance of a process is evaluated. For the hybrid censoring scheme the maximum likelihood (ML) estimate of C_L is constructed as well as confidence interval for C_L is developing. Also, Bayesian approach is adopted to estimates C_L and credibly interval is constructed. Some theoretical results of hypothesis tests of C_L is adopted. Finally, our obtaining results will be assessed and compared through Monte Carlo simulation study and numerical example.

One of the main statistical process control tools is a control chart. The latter constructed under the hypothesis that the quality characteristics processes belong a normal distribution, but in the most real situation, the set of data are not following a normal distribution. Thus, the control limits will give misleading results. Therefore, it is important to use an alternative control chart approach. In this paper, a quantile approach has been discussed to construct the quality control chart for the log-logistic model. Properties of log-logistics and parameter estimation have been considered and compared with the existing control chart. Real data is used to apply the proposed control chart.