The detection of upward shifts in a process parameter using a CUSUM scheme can be improved by using an upper one-sided combined CUSUM–Shewhart scheme. Considerable advantage is to be gained since combined schemes take advantage of two well known facts: the Shewhart schemes behave well in case of a large shift, while CUSUM schemes allow a fast detection of small and moderate shifts. Having this in mind, upper one-sided combined CUSUM–Shewhart schemes for binomial data are discussed in detail in this paper. Numerical comparisons between upper one-sided combined CUSUM–Shewhart schemes and upper onesided CUSUM schemes with a 50% head start are also carried out, leading to – what we believe – surprising results.
We usually assume
that counts of nonconforming items have a binomial distribution with parameters (n,p), where n and p represent the sample size and the fraction nonconforming, respectively.
The non-negative, discrete and usually skewed character and the target mean of this distribution may prevent the quality control engineer to deal with a chart to monitor p with:
a pre-specified in-control average run length (ARL), say ;
a positive lower control limit;
the ability to control not only increases but also decreases in p in an expedient fashion.
Furthermore, as far as we have investigated, the np- and p-charts proposed in the Statistical Process Control literature are ARL-biased, in the sense that they take longer, in average, to detect some shifts in the fraction nonconforming than to trigger a false alarm.
Having all this in mind, this paper explores the notions of uniformly most powerful unbiased tests with
randomization probabilities to eliminate the bias of the ARL function of the np-chart and to bring its in-control ARL exactly to .
Joint schemes for the process mean and the variance are essential to determine if unusual
variation in the location and spread of a quality characteristic occurred.
This paper comprises a systematic study on the phenomena of misleading, unambiguous and simultaneous signals while dealing with Shewhart and EWMA joint schemes for the process mean and the variance of a normally distributed quality characteristic.
Examples have been added to illustrate how the R statistical software can be used to assess the performance of joint schemes in practice, namely when it comes to the occurrence of those valid signals.
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 , and 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 traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server.
Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in ρ. In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015). We confront the performances of these charts in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.