Nonparametric control chart techniques represent a rather neglected area in Statistical Process Control, in particular with respect to monitoring process variability. There are only very few relevant papers published. The reason for not regarding nonparametric techniques for controlling process...

Consider a Γ-distributed random variable X and a random variable Y with a probability distribution of exponential, Γ, Weibull, Pareto or log-normal type. In this paper the exact distributions of the products XY for the different cases with respect to Y are derived. For illustration an...

In this paper, a maintenance strategy is proposed for a multi-state deteriorating system subject to both aging and fatal shocks under continuous inspection. The strategy allows one of the three actions “do nothing”, “maintenance” or “replacement” to be taken at each state of the...

The so-called confidence interval for the first moment (expectation) of a random variable X based on the t-distribution and the confidence interval for the variance based on the χ 2-distribution are two very important statistical methods. They allow to determine the value μ of E[X] and the...

Critical values for the significance levels α=0.0100, 0.0500, and 0.1000 and sample sizes from n = 3 to n = 30 for Dixon's outlier test have been calculated using Monte Carlo simulation. For the one-sided and two-sided case critical values are determined, which are accurate to within ±0.00001...

A truncated version of the bivariate t distribution is introduced. Unlike the t distribution, this possesses finite moments of all orders and could, therefore, be a better model for real-world situations, as it becomes possible to incorporate always available knowledge about the range of...

We propose frailty regression models in mixture distributions assuming the distribution of frailty to be a gamma distribution. We consider Weibull mixture as an example. There are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births...

Some classes of lifetime distributions based on the failure rate are considered, namely new better than used failure rate (NBUFR), new better than average renewal failure rate (NBARFR) and generalized new better than average renewal failure rate (GNBARFR). Moment inequalities and moment...

This paper proposes an efficient heuristic approach to solving the constrained redundancy optimization problem in multi-state systems (MSS) with multi-state components using minimal path vectors. A discrete multi-state model is considered, where the system state depends on the discipline of the...

Imprecise measurements may seriously affect the efficiency of process control and production cost. For two dependent processes, the in-coming quality variable in the first process may influence the out-going quality variable in the second process. To effectively monitor and distinguish the state...