INTRODUCTION TO STATISTICAL PROCESS

146 APPLYING STATISTICAL PROCESS CONTROL Common-Cause Variation Special-Cause Signal a b Figure 10.1 Dart board comparison of a common-cause variation and b special-cause variation. Shewhart began studying several manufacturing processes in depth. As a practical engineer, he understood that in real life sit- uations, laws and theories are not exact. Shewhart concluded that all processes exhibit variation that can be classified into two dis- tinct types: 1. inherent or common-cause variation and 2. intermittent or special-cause variation. To concisely demonstrate the difference between these types of variation, a dartboard may be used as an example, as shown in Figure 10.1. The goal of each dart throw is to hit the center of the board. Common-cause variation is subject to chance with un- discoverable random causes. This is illustrated in Figure 10.1a by a random distribution of hits clustered around the center of the dartboard. Special-cause variation, however, does not fit into this predictable random variation, as shown in Figure 10.1b. Special- cause variation can be assigned directly to some event or phenom- enon. Shewhart believed that these assignable causes could be discovered and removed with an economic benefit. Once sources 10.1 INTRODUCTION TO STATISTICAL PROCESS CONTROL 147 a b Figure 10.2 Dart board comparison showing a reduction in common-cause variation from a to b. of special-cause variation are eliminated, improvements can be made to the system to reduce common-cause variation. This is illustrated in Figure 10.2. The random cluster of hits around the center of the dartboard Figure 10.2a may be made tighter Figure 10.2b by stepping closer to the dartboard. With this understanding, Shewhart worked to develop a method that would differentiate between the two types of variation. He believed that only through the use of statistics could one obtain an accurate picture of varying physical phenomena. Shewhart toyed with several statistical tools and found success when com- bining probability analysis with sampling. On May 16, 1924, Shewhart generated the first basic control chart that used statistically generated graphs to display variations in the quality of manufactured parts. Control charts offered work- ers the ability to track the performance of a process over time and presented the data in a manner that could be understood at a glance. If the process exhibited common-cause variation, nothing was done. If special-cause variation was identified on the control chart, workers would take action. The result at Western Electric was lower scrap rates and reduced inspection, the economic ben- efits of which are clear. In 1925, Shewhart joined Bell Laboratories and continued to apply and refine the control chart. In 1931, Shewhart published the Economic Control of Quality of Manufactured Products. 2 This 148 APPLYING STATISTICAL PROCESS CONTROL detailed book introduced the rudimentary concepts of what would become known as statistical process control.

10.2 SPC CHARACTERISTIC TYPES

Process variation can be quantified directly by measuring a pro- cess characteristic or indirectly by measuring a product character- istic. With variation quantified, statistical methods can be applied to determine the common-cause and special-cause variations within a process. Statistical monitoring of product characteristics product SPC is the most common application of statistical methods in manu- facturing today and can offer insight into the behavior of a process indirectly. Product SPC operates under the premise that a process is in statistical control when a particular product characteristic created by the process is in statistical control. Even though the customers of manufacturers often require that select product char- acteristics be monitored using statistical methods, data are often collected solely to meet the requirement. Statistical process con- trol in this case becomes statistical process recording. Less common is the statistical control of process characteristics. Process SPC offers direct insight into the behavior of a process. Process characteristics in some cases are static, such as liquid metal temperature in a holding furnace. However, many processes characteristics are dynamic with a predictable repeating cycle once the process has reached its steady state. When using traditional process SPC methods to control these dynamic characteristics, a measurement is typically taken at an event that repeats during each batch or cycle. An example of such a characteristic is the maxi- mum plunger pressure reached during metal intensification. Al- though this information may prove useful, it offers little understanding of the entire process. Process data curves, that is, plots of dynamic process charac- teristics as a function of time over one cycle, can be examined in order to increase the understanding of a process. Applying statis- tical methods to entire process data curves, although not feasible a decade ago, can be performed using current computer technol- ogy. Process SPC through the analysis of process data curves has been documented in the literature. 3,4 10.3 SPC APPLIED TO DYNAMIC PROCESS CHARACTERISTICS 149 Sample Number Figure 10.3 Example chart commonly used for SPC. x

10.3 SPC APPLIED TO DYNAMIC PROCESS

CHARACTERISTICS The most common SPC method used in the industry is the chart. x These charts are typically used to determine if a process is exhib- iting common-cause variation or special-cause variation. Figure 10.3 is an example of a typical chart. These charts are prepared x by 1. sampling subgroups of four or five individuals, 2. measuring a characteristic on each individual, 3. calculating and plotting the average of each subgroup, x 4. repeating the above three steps for 25 or more samples, 5. calculating the average of each and plotting as a line, x x x and 6. calculating the upper and lower control limits at three stan- dard deviations from and plotting the control limits as x lines. 5 This SPC method requires that subgroups of multiple samples be formed from data collected under the same conditions and from the same batch or lot. Through the interpretation of charts, special-cause variation x can be identified by using the following guidelines: 1. a point falls outside the control limits, 2. 9 consecutive points occur within one standard deviation, 3. 6 points in a row show a continuous increase or decrease,