Experiments and Statistical Process Control

The topics of this chapter involve a certain amount of mathematics and many associated texts are full of mind-numbing pages of equations. The object here is to introduce the reader to the subjects, explain their importance and give some sense of how they are used. Some use of mathematics is necessary, but every attempt will be made to keep the examples simple so we can keep focused on the larger picture of why these techniques are useful. 

We can get some idea of the variability of these nvunbers by calculating the standard deviation. The standard deviation is the square root of the variance. The variance is the sum of the squares of the difference of each value from the mean divided by the number of samples. By squaring the numbers, the sign 

Fundamentals of Industrial Chemistry Pharmaceuticals, Polymers, and Business, First Edition. John A. Tyrell. 2014 John TOley Sons, Inc. Published 2014 by John Wiley Sons, Inc. 

Sometimes the sample standard deviation is used when the numbers represent a sampling. In that instance, the sample standard deviation is calculated by taking the square root of the sum of the squares of each of the individual variances divided by one less than the number of samples. In the above example, we would divide by three (4-1) rather than four. This removes a bias so it is sometimes referred to as the unbiased standard deviation. Unfortunately, the term standard deviation is used to refer to both versions. To keep things simple, I will not use the sample standard deviation in the examples, but you should be aware of it because it might be used in other texts. 

It seems that the blue airplanes fly further than the white airplanes. There are statistical tests that can be used to determine whether the blue airplane results differ from the white airplane results in a significant way. Note that in this context, the term significant means statistically significant and is not the same as important. For example, a change in a polymer process may result in a statistically significant difference in polymer tensile elongation. 

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The PAT guidance facilitates introduction of new measurement and control tools in conjunction with well-established statistical methods such as design of experiments and statistical process control. It, therefore, can provide more effective means for product and process design and control, alternate efficient approaches for quality assurance, and a means for moving away from the corrective action to a continuous improvement paradigm. 

Once these links and meaningful process control plans are made, operators can for the first time experience true statistical process control beginning with the critical few parameters that control color quality for the final product. 

One approach for using DOE on more complex processes is to do the majority of the process development on smaller, representative sections of material, such as test panels, rather than on full-scale parts, and then to scale up with a more limited experimental matrix. There is no guarantee that experience on small-scale test panels will directly translate to large parts because dimensions and thickness of the part are important variables in their own right. Another way to save on costs is to start with a satisfactory process and to continue, via careful monitoring of process variations and results, to extend the range of experience. This method is variously called statistical process control or statistical quality control. 

The recent trend towards total quality management (TQM) has generated a great deal of interest in statistical process control (SPC). This technique has been applied with good success in the discrete parts manufacturing industries. In the chemical process industries experience has been mixed, partly because of misunderstandings about its applicability to chemical processes and its interrelation to conventional process control. 

Models can often be used to guide the designed experiments that need to be run on the commercial process as part of the qualification effort. Out of this activity come the aims and limits of the process variables, which either directly or indirectly are under closed-loop feedback control and some of which are then monitored by statistical process control techniques (Ref 2). 

Statistically designed experimentation is used to obtain maximum information at a minimum cost of time and resources. Conclusions drawn from experiments determine the best course of action in establishing a process. Therefore, controllable variables of the process can be set at optimum levels in an objective manner — supported by data to produce the desired outcome. Once the process is stable, it should be monitored using statistical process control (SPC). To achieve best-in-class performance, it is vital to monitor the process to prevent defect occurrences. 

The AML supports faculty Instruction in seven different courses, and as a support facility, the equipment may be used on a stand-alone basis. The Mitutoyo Coordinate Measuring Machine of the AML is used by students in the "Metal Processes II" course for precision measurement experiments and to evaluate their final projects. The same machine is used in "Statistical Quality Control" for developing statistical process control (SPC) charts and for conducting process capability studies on the machine tools in the AML. 

There are a number of mathematical tools that are used in the world of manufacturing. Statistical Process Control is used to monitor and control the process parameters that are used to manufacture parts. Tolerance Analyses are used to analyze and predict fit and function of final assemblies. Pareto Analysis techniques are used to assess the contribution of various factors in problem situations. Design of Experiments techniques are used to quantify the variables in a given process or application. 

There is a tendency among control and statistics theorists to refer to trial and error as one-variable-at-a-time (OVAT). The results are often treated as if only one variable were controlled at a time. The usual trial, however, involves variation in more than one controlled variable and almost always includes uncontrolled variations. The trial-and-error method is fortunately seldom a random process. The starting cycle is usually based on manufacturers specifications or experience with a similar process and/or material. Trial variations on the starting cycle are then made, sequentially or in parallel, until an acceptable cycle is found or until funds and/or time run out. The best cycle found, in terms of one or a combination of product qualities, is then selected. Because no process can be repeated exactly in all cases, good cure cycles include some flexibility, called a process window, based on equipment limitations and/or experience. 

SPC or statistical quality control (SQC) is similar to DOE in that it is a statistical, rather than mechanistic, method. Both SPC/SQC and DOE rely on the theory that there is a direct relationship between variations in process controls and resulting changes in product quality. In SPC, however, the experiments are not forced on the process like they are in DOE. The variations in product quality and the random process variations are traced over time instead. The variations in end product are then correlated, if possible, with changes in the process that have occurred during that time. SPC techniques are usually applied to the process after some baseline process has been established by other methods. 

The last twenty years of the last millennium are characterized by complex automatization of industrial plants. Complex automatization of industrial plants means a switch to factories, automatons, robots and self adaptive optimization systems. The mentioned processes can be intensified by introducing mathematical methods into all physical and chemical processes. By being acquainted with the mathematical model of a process it is possible to control it, maintain it at an optimal level, provide maximal yield of the product, and obtain the product at a minimal cost. Statistical methods in mathematical modeling of a process should not be opposed to traditional theoretical methods of complete theoretical studies of a phenomenon. The higher the theoretical level of knowledge the more efficient is the application of statistical methods like design of experiment (DOE). 

Before the special causes are fully identified and controlled, PpK estimates the process performance that the customer currently experiences, and CpK estimates the potential process capability attainable when the process is brought more closely into a state of statistical control. As the process approaches a state of statistical control, PpK approaches Cpk- Similarly, the estimates Pp and Cp are used when the process is centered within two-sided specification limits, or to reflect what the capability would be if the process were centered. 

Formulation and process optimization can be done statistically with the use of experimental design for estimates of the best processing parameters and excipient and lubricant levels. Controllable variables in tableting are mainly the precompression and compression forces and tablet press speed, as well as the formulation component levels. Response variables include the ejection force, tablet hardness and friability, dissolution rate, and drug stability. The purpose of an experimental design is to perform a series of experiments in... 

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