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This paper considers a single server queue in which the service time is exponentially distributed and the service station may breakdown according to a Poisson process with the rates γ and γ' in busy period and idle period respectively. Repair will be performed immediately following a breakdown. The repair time is assumed to have an exponential distribution. Let g(t) and G(t) be the probability density function and the cumulative distribution function of the interarrival time respectively. When t tends to infinity, the rate of g(t)/[1 -G(t)] will tend to a constant. A set of equations will be derived for the probabilities of the queue length and the states of the arrival, repair and service processes when the queue is in a stationary state. By solving these equations, numerical results for the stationary queue length distribution can be obtained.

The Jarque-Bera test is a test based on the coefficients of skewness (S) and kurtosis (K) for testing whether the given random sample is from a normal population. When the random sample of size n contains m outliers, we use the remaining n-m observations to compute two statistics S* and K* which mimic the statistics S and K. The statistics S* and  K* are next  transformed to z1 and z2 which are uncorrelated and having standard normal distributions when the original population is normal. We show that the acceptance region given by a circle in the (z1, z2) plane is suitable for testing the normality assumption.

The Hotelling T 2 control chart is widely used to monitor the process mean vector in multivariate quality control. However, this control chart is relatively insensitive to small and moderate shifts in the process mean as it uses information only from the current sample. A new type of control chart is proposed to detect shift of the mean of a vector of two quality characteristics which are normally distributed. The acceptance region for declaring that the process is in control is a circle of which the centre depends on the mean based on the all the previous data. By using simulation, the performance of the new chart as measured by the average run length is found to be better than that of the Hotelling T 2 control chart.

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