In this article, we consider the estimation of the parameters and reliability characteristics of Kumaraswamy distribution using progressive first Failure censored samples. First, we derive the maximum likelihood estimates using an expectationmaximization algorithm and compute the observed information of the parameters that can be used for constructing asymptotic confidence intervals. We also compute the Bayes estimates of the parameters using Lindley approximation as well as the Metropolis-Hastings algorithm. Furthermore, we derive the highest posterior density credible intervals. Simulation studies are conducted to evaluate the performance of the point and interval estimators. Finally, two examples of real data sets are provided to illustrate the proposed procedures.

One of the most important quality characteristics in a production process is the product lifetime. The production of highly reliable products is a concern of manufacturers. Since it is time-consuming and costly to measure lifetime data, designing a control chart seems difficult. To solve the problem, lifetime tests are employed. In the present study, one-sided and two-sided EWMA control charts are designed under a type II censoring (Failure censoring) life test. Product lifetime is a quality characteristic dealt with in this study. It is assumed to follow the Weibull distribution with a fixed shape parameter and a variable scale parameter. In order to design a control chart, first, the control chart limits are calculated for different parameters, and then the Average Run Length (ARL) in the out-of-control state is used to evaluate the performance of the proposed control chart. Next, a comprehensive sensitivity analysis is performed for the different parameters involved. The computational results show that the one-sided control chart has better performance to detect the shift of lifetime data than the two-sided control chart. The average run length curve of the two-sided control chart is biased, while that of the one-sided control chart is unbiased. A very effective parameter that increases the performance of a control chart is found to be the number of Failures in the Failure censoring process. Finally, simulated and real examples are provided to show the performance of the proposed control chart.

This paper considers the Type I hybrid censoring and investigates the optimal value for the sample size which is assumed as a truncated binomial random variable‎. ‎Rayleigh distribution is considered for the lifetime distribution‎. ‎Towards this end‎, ‎various factors can be considered and the most important is the sampling cost criterion‎. ‎Since the sample size is a random variable‎, ‎the optimal parameter of the random sample size is determined so that the total cost of the test does not exceed a pre-determined value‎. ‎Numerical calculations and a simulation study have been performed to evaluate the obtained results‎. ‎Finally‎, ‎the conclusion of the article is presented.