Hakan S. Sazak

Monitoring reliability for a three-parameter Weibull distribution

Control charts are widely used to monitor production processes in the manufacturing industry and are also useful for monitoring reliability. A method to monitor reliability has recently been proposed when the distributions of inter-failure times are exponential and Weibull with known parameters. This method has also been extended to monitor the cumulative time elapsed between a fixed number of failures for the exponential distribution. In this paper, we consider a three-parameter Weibull distribution to model inter-failure times, use a robust estimation technique to estimate the unknown parameters, and extend the proposed method to monitor the cumulative time elapsed between r failures using the three-parameter Weibull distribution. Since the distribution of the sum of independent Weibull random variates is not known (except in specific cases with known parameters), we give two useful moment approximations to be able to apply their scheme. We show how effective the approximations are and the usefulness of the method in detecting a possible instability during production.

Absolute quantification of carnosine in human calf muscle by proton magnetic resonance spectroscopy

Carnosine has been shown to be present in the skeletal muscle and in the brain of a variety of animals and humans. Despite the various physiological functions assigned to this metabolite, its exact role remains unclear. It has been suggested that carnosine plays a role in buffering in the intracellular physiological pHi range in skeletal muscle as a result of accepting hydrogen ions released in the development of fatigue during intensive exercise. It is thus postulated that the concentration of carnosine is an indicator for the extent of the buffering capacity. However, the determination of the concentration of this metabolite has only been performed by means of muscle biopsy, which is an invasive procedure. In this paper, we utilized proton magnetic resonance spectroscopy (1H MRS) in order to perform absolute quantification of carnosine in vivo non-invasively. The method was verified by phantom experiments and in vivo measurements in the calf muscles of athletes and untrained volunteers. The measured mean concentrations in the soleus and the gastrocnemius muscles were found to be 2.81 +/- 0.57/4.8 +/- 1.59 mM (mean +/- SD) for athletes and 2.58 +/- 0.65/3.3 +/- 0.32 mM for untrained volunteers, respectively. These values are in agreement with previously reported biopsy-based results. Our results suggest that 1H MRS can provide an alternative method for non-invasively determining carnosine concentration in human calf muscle in vivo.

Estimation in bivariate nonnormal distributions with stochastic variance functions

Data sets in numerous areas of application can be modelled by symmetric bivariate nonnormal distributions. Estimation of parameters in such situations is considered when the mean and variance of one variable is a linear and a positive function of the other variable. This is typically true of bivariate t distribution. The resulting estimators are found to be remarkably efficient. Hypothesis testing procedures are developed and shown to be robust and powerful. Real life examples are given.

Double-looped maximum likelihood estimation for the parameters of the generalized gamma distribution

The generalized gamma distribution (GGD) is a very popular distribution since it includes many well known distributions. Estimation of the parameters of the GGD is quite problematic because of the complicated structure of its density function. We introduce two new estimation methods called maximum likelihood with goodness of fit test (MLGOFT) and double-looped maximum likelihood (ML) estimation. We show through simulations under several situations that the MLGOFT method is more efficient than the Method of Moments with goodness of fit test (MMGOFT) technique especially for small and moderate sample sizes whereas the double-looped ML is the superior estimation method for all cases. The double-looped ML method is also very fast, practical and straightforward.

A Robust Control Chart for Monitoring the Mean of an Autocorrelated Process

Residual control charts are frequently used for monitoring autocorrelated processes. In the design of a residual control chart, values of the true process parameters are often estimated from a reference sample of in-control observations by using least squares (LS) estimators. We propose a robust control chart for autocorrelated data by using Modified Maximum Likelihood (MML) estimators in constructing a residual control chart. Average run length (ARL) is simulated for the proposed chart when the underlying process is AR(1). The results show the superiority of the new chart under several situations. Moreover, the chart is robust to plausible deviations from assumed distribution of errors.