Joint Economically Optimal Design of X\bar and R Control Charts

In this paper, we develop an expected cost model for a process whose mean is controlled by an X\bar chart and whose variance is controlled by an R chart. The expected cost comprises the fixed and variable costs of sampling, the cost of investigating and correcting the process when at least one control chart indicates that the process parameters have shifted, and the cost of producing defective units. We use a search procedure to determine the sample size, interval between samples and control limits for both charts that minimize the expected cost. Optimal solutions to numerical examples are presented. A sensitivity analysis of the model is performed. In addition, we find the optimal interval between samples and the expected cost for several examples with large shifts in the mean and variance where Shewhart's heuristic design is used in place of the optimal design. Comparison of the expected cost of the optimal design to the expected cost of Shewhart's design shows an increase in expected cost of only 0.4 to 8.2 percent for the latter design. But other situations are discussed and examples presented which indicate that the optimal design is preferred.

A note on the distribution types of financial ratios in the commercial banking industry

Bedingfield, Reckers and Stagliano (1985) have shown that financial ratios in the commercial banking industry are not generally normally distributed. This paper uses separate systems proposed by Karl Pearson [see Elderton and Johnson (1969) and Johnson (1949)] to determine the distributional forms for eleven financial ratios for each year 1976-1983. Some potential applications to regulatory surveillance in commercial banking are discussed. © 1989

A Statistically adaptive sampling policy to the Hotelling's T2 Control Chart: Markov Chain Approach

We present an alternative sampling scheme for the Hotelling's T2 control chart with variable parameters (VP T2) which allows the sampling interval h, the sample size n, and control limit k to vary between minimum and maximum values while keeping the warning line fixed over time. Our method uses only one measurement scale to overcome the difficulties of using two scales in practice. Later, we demonstrate the merits of the method in terms of its performance in detecting small-to-moderate shifts and its ease of application