Volume 32, Issue 2

Nosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number R0{R_{0}} and study its relationship with the parameters of the offspring distribution. in case of a single-type epidemic, we investigate the effect of contact tracing on the estimates for R0{R_{0}}.

We consider the Dagum distribution for estimating the reliability of a k -component stress-strength system with different shape values of the shape parameter. We assume that the system has strength modelled by k independent and identically distributed random variables, and each system’s component experiences random stress. We construct maximum likelihood estimators for the system’s reliability and study their asymptotic properties. We evaluate the small sample performance of the estimators through Monte Carlo simulation. Finally, we illustrate the procedure using real data.

This article is a comparative study between the parametric asymptotic lower confidence limits and bootstrap lower confidence limits for the basic quantile based process capability indices based on the unified super-structure CNp⁢(u,v){C_{N_{p}}(u,v)} when the distribution of the quality characteristic follows an asymmetric non-normal distribution. We illustrate this method when the distribution of the quality characteristic is a member of the family of Esscher-transformed Laplace models introduced by S. George and D. George [11]. We obtain the bias corrected and accelerated (BCa) bootstrap confidence intervals of CNp⁢(u,v){C_{N_{p}}(u,v)}, which provide lower confidence intervals with coverage probability nearer to the nominal value compared to the asymptotic confidence intervals. We conclude that for asymmetric and peaked processes, the BCa confidence interval is a better alternative compared to the usual confidence intervals under the assumption that the quality characteristic follows a Gaussian type distribution. Numerical examples are given based on some real data.

In industry when a lot of items is sent for inspection, double acceptance sampling plans (DASP) are considered as a way to decide on acceptance or rejection of the lot. If the lot contains items with high sensitivity, then the measuring of quality characteristics is destructive or costly. So we are looking for a method to decide that it has high performance. Using the ranked set sampling (RSS) method will make it stricter and more accurate whether or not to accept a lot. Moreover, it is affordable and will not burden extra costs on the buyer or the producer. In this paper, by using a special type of RSS, with the name of maxima nomination sampling (MNS), we design a DASP with regards to the total loss function. The results indicate that the total loss function, which is acquired by the MNS method, has lower values than the one using the simple random sampling (SRS) method.