Volume 33, Issue 1

This paper describes the application of simple quality control charts to monitor the traffic intensity of single server queues, a still uncommon use of what is arguably the most successful statistical process control tool. These charts play a vital role in the detection of increases in the traffic intensity of single server queueing systems such as the M/G/1{M/G/1}, G⁢I/M/1{GI/M/1} and G⁢I/G/1{GI/G/1} queues. The corresponding control statistics refer solely to a customer-arrival/departure epoch as opposed to several such epochs, thus they are termed short-memory charts. We compare the RL performance of those charts under three out-of-control scenarios referring to increases in the traffic intensity due to: a decrease in the service rate while the arrival rate remains unchanged; an increase in the arrival rate while the service rate is constant; an increase in the arrival rate accompanied by a proportional decrease in the service rate. These comparisons refer to a broad set of interarrival and service time distributions, namely exponential, Erlang, hyper-exponential, and hypo-exponential. Extensive results and striking illustrations are provided to give the quality control practitioner an idea of how these charts perform in practice.

The log-logistic distribution is a right skewed distribution of a random variable whose logarithm has the logistic distribution. In this paper, characterizations based on truncated moments, functions of order statistics and record values are obtained. Also, limiting distributions for the extreme order statistics are studied.

This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.

In this paper, a generalization of the Harris family of distributions, namely, the Harris generalized linear exponential distribution is discussed. The use of the model is established by fitting it to a real data set. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution.

Reliability sampling plans are used for determining the acceptability of any product. In this paper, reliability sampling plans for acceptance or rejection of a lot of products submitted for inspection are developed when the lifetimes follow the Gumbel-uniform distribution. The sampling plan proposed here can save the test time in practical situations. Some tables are also provided for the new sampling plans so that this method can be used conveniently by practitioners. Operating characteristic values and minimum ratios of the true value and the required value of the parameter with a given producers risk with respect to the newly developed sampling plans are also presented. The new test plan is applied to ordered failure times of software release to illustrate its use in industrial contexts.