Time Series Control Charts for Correlated and Contaminated Data

This paper discusses the development of control charts for correlated and contaminated data. For illustration the charts were applied to a set of maximum principal-stress data at two locations on a blast furnace shell. The Dynamic Data System (DDS) approach was used to model the correlated data which contained several types of discrepancies. After the standard DDS models were found, control charts for the averages and variances of the model residuals were constructed for two data sets. For more effective analysis, two methods for calculating the control limits for both charts are given. With this approach, dynamic process change, such as an increase in the production rate or the wearing out of the sacrificial lining, can be detected and separated from data with collection errors from instrument malfunctions. Furthermore, the tap hole opening timing is identified from the DDS model parameters, to help verify the time series model.

Optimization of Multipass Turning With Constraints

Single pass operation is not always the most economical or the most productive, for under such practical constraints as available horsepower, desired surface finish, minimum tool life and maximum permissible feed and speed, it can be shown that two passes, or sometimes even three passes, can be cheaper or take less production time. The objective of this paper is to illustrate when multipass turning is optimum and what ratios of rough to finishing depths of cut will give the optimum. The optimizing is determined by geometrical programming combined with linear programming. This mathematical approach can handle as many constraints as required, and any combination of them can be tight or loose at the optimum solution. Several examples are given to demonstrate the application of the method and the advantage of the process optimizing technique.

Optimization of the Constrained Machining Economics Problem by Geometric Programming

A more complete solution to the machining economics problem is one that takes into account several constraints of the actual machining operation. The object of the paper is to illustrate how a relatively new mathematical programming method called geometric programming can be used to determine the optimum machining conditions when the solution is restricted by one or more inequality constraints. This optimizing method is especially effective in machining economics problems, where the constraints may be nonlinear and the objective function of more than second degree. Furthermore, the geometric programming approach furnishes a unique insight into how the optimizing criterion is distributed among its components for a given set of input parameter values.

The Effect of Experimental Error on the Determination of the Optimum Metal-Cutting Conditions

The effect of experimental error in tool life testing on the determination of the minimum cost cutting speed (Vmin) is investigated by using the concept of statistical inference. It is shown that Vmin is not uniquely defined but lies within a probable interval of cutting speeds, and that this interval is affected by the cost and time parameters and the experimental range of feed in tool life testing. The selection of a specific speed from the Vmin confidence interval is illustrated by a decision rule based on the minimax principle.

Maximum Profit as the Criterion in the Determination of the Optimum Cutting Conditions

Maximum profit is an appropriate criterion for the selection of the optimum machining conditions rather than the conventional criteria of minimum cost or maximum production rate. A simple example is presented to illustrate the determination of the maximum-profit cutting speed by application of a fundamental economic principle that maximum profit occurs at the production rate where the marginal revenue equals the marginal cost. The effects of the demand function, feed, and cost and time parameters on the determination of the maximum-profit cutting speed are analyzed. Emphasis is given to the investigation of a range of optimum cutting speeds, instead of the theoretical optimum speed, for practical applications.

An Exploratory Study of Taylor’s Tool-Life Equation by Power Transformations

Transformations of both dependent and independent variables are employed to investigate the linearization of Taylor’s tool-life equation. This exploratory study indicates that a logarithmic transformation, which is a special case of the general class of power transformations, gives the best fit for HSS tool-life data. However, the study does not show that a logarithmic transformation is the best for carbide tool-life data. For a wide cutting range, where Taylor’s tool-life equation does not hold, a linear equation instead of a second-order relationship for the prediction of tool life can be determined by the proper transformation.