[attachment=15179]
Statistical Process Control
Introduction
The purpose of this lab was to determine whether a continuous mixing process was “in control” by analyzing control charts and quantifying the benefits of an in-line mixer in the process. Statistical process control is a frequently used analytical tool for quality improvement programs. In this lab, the quality of the product stream (green dye and water solution) was analyzed using control charts (X-bar for the operating process level and R for variability) which were created by (1) an estimation method in JMP and (2) a standard deviation method. The resulting control charts were then compared to make quality control suggestions for the operating system.
Methods
The experimental apparatus for the Statistical Process Control lab is shown below in Figure 1. The apparatus consists of a large 20L container that holds the 0.2 wt% dye solution. Connected to this container is the recycle pump that mixes the solution to a uniform concentration. A peristaltic pump is also connected to the outlet of the container. This pump generates the continuous flow rate of dye solution to the rest of the apparatus. The water used for the dye and water mixture enters from the top left of the apparatus (as shown in Fig 1) at a junction before entering the first spectrometer. The mixed solution travels past the pre-mixer spectrometer before entering the in-line mixer. After the mixer, there is a second (post-mixer) spectrometer. The mixed solution then enters into a large graduated cylinder before exiting the system to the drain (Mullet, 2007).
Figure 1: Process Flow Diagram
The two detectors in this lab are spectrophotometers, or spectrometers for short, but they have slightly different path lengths (the length that the detecting light passes through the fluid). The first spectrometer has a path length of 0.56 cm, and the second spectrometer has a path length of 0.54 cm. Each of the two detectors uses the same tungsten halogen lamp as a light source. The light is directed from the lamp to the detectors by means of a fiber optic cable. Once the light reaches the spectrometer, it enters the flow cell and is emitted through the flowing fluid to a detector on the other side. The spectrometer measures the intensity of light passing through the fluid. The negative logarithm of the ratio of the intensity of the light that exits the flow cell versus the intensity of light of some reference is the absorbance (shown as Equation 1).
As the weight percent of the solution changes, the absorbance changes. A larger weight percent of dye means a larger absorbent peak due to the presence of more dye, and hence the less light that is able to pass through it. The absorbance is only a function of the amount of dye in the solution because it was “zeroed out” by taking measurements with a stream of pure water. The measurements taken with the pure water stream are then used as the reference intensity for absorbance calculations. The relationship between the amount of absorbance and the concentration is known as Beer’s Law, shown in Equation 2 below:
where c is the concentration, l is the path length of the flow cell, A is the absorbance, and ε is the extinction coefficient. Beer’s Law shows that a larger concentration is directly proportional to a larger absorbance (Mullet, 2007).
Before the dye solution could be mixed with the tap water, a calibration curve needed to be created using a series of settings for the rotameter. The rotameter flow rate was measured at settings of 26%, 36%, and 51% of the maximum flow rate. The flow rate of the peristaltic pump was also measured by use of a bucket and stopwatch method. Dye solution was sent through the system without mixing with tap water, and the absorbance was taken before and after the in-line mixer. Then, dye solution and tap water were mixed, and the absorbance was measured before and after the in-line mixer. All the intensity data collected by the computer were then used to calculate the absorbance, and hence concentration, by Beer’s Law. Finally, control charts were created using the estimation and standard deviation methods.
Random fluctuations in a process are always present, so processes are studied to determine if non-random variations exist. Non-random variations mean that the process can be modified to obtain statistically better data because the problems are from “assignable causes.” Control charts are an excellent way to interpret the data to determine what types of fluctuations are present. When looking at a control chart, the process is said to be “in control” if the data is varying only by random fluctuations. The term “in control” only corresponds to the statistical data, not the specifications needed on the product. A system is said to be out of control when there are both random and non-random variations. The capability index incorporates specified quality limits and predicts the product quality that can be expected from a process (Mullet, 2007).