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Trend Analysis in Manufacturing for Quality ImprovementBy: Ashweni Sahni, Director of Quality & Regulatory Affairs Presented at: The 45th Annual Minnesota Quality Conference, Once we have established a manufacturing process, we want it to remain in control, with minimum variation. This is because process variation, if it is too much, more often than not, leads to non-conformance in the product, which in practical terms means a waste of time, money, and resources for the manufacturer and potential dissatisfaction for the customer. Trend analysis is a tool that we can use to monitor production processes, analyze process variation, identify its assignable causes and take corrective actions to bring processes into a state of control. These also meet the requirements of ISO 9000 and FDA's requirements, as well as maintain the quality of the products. This paper will explain the basic principals of trend analysis, a variety of unnatural data patterns and their probable causes. Trend analysis is not the only method to study process variation, but it is one of the most powerful and accepted methods. It can be conducted on many characteristics of industrial applications, but here we will limit our discussions to the analysis of manufacturing processes. Run Charts and Control Charts Trend analysis is expressed graphically as an element of the manufacturing process (e.g. processing parameters such as temperature or pressure, or output characteristics such as material strength or product dimensions) plotted over time (e.g. a shift or a day). Generally, trend analysis takes one of two forms: run charts or control charts. A run chart is the more basic of the two - it is simply a display of raw data over time (see figures 1-3). In the usual format, the horizontal axis of the run chart indicates time and the vertical axis indicates the measurement of interest. 
Figures 1-3. Run charts illustrating various data pattern trends. The term run describes changes in the direction of measured data. In Figure 1, the lines plotted from point A to point B, or from A to C, or from C to D, indicate runs. The term long run indicates that there are few changes in the direction of the data pattern, and that it rarely shifts from one side of the center line to the other (see Figure 8). By comparison, the term short run indicates that there are frequent changes in the direction of the data pattern. In Figure 9, for example, the pattern crosses the center line continuously.  
Figures 8 and 9. Stratification; systematic variation. Figures 1, 2, and 3 illustrate some of the general rules of thumb for identifying trends. In figure 1, a sequence of eight or more points on the same side of the center line indicates a shift in the process average. In Figure 2, a sequence of 14 or more points in a row, alternating up and down, suggests a bias or systematic sampling from different sources. In Figure 3, a sequence of seven or points continuously increasing or continuously decreasing indicates a drift in the process average. In general, run charts are easy to plot and interpret. They can be used for almost any process and require no statistical calculation. However, they have several limitations:
By comparison, control charts are a more sophisticated and reliable method than run charts for plotting and analyzing the causes of variation in the manufacturing process. A control chart is similar to a run chart in that it is a graphic display of some aspect of process variation over time. However, in addition to the center line, which represents the average quality measurement at which the process performs, a control chart, (see Figure 4) has lines for an upper control limit (UCL) and a lower control limit (LCL). These are calculated by applying a statistical procedure to the data from the run charts and they establish an acceptable range within which plotted points may fall. Figure 4. A natural data pattern on a control chart. Natural and Unnatural Data Patterns The control limits help to determine whether a data pattern is natural or unnatural. In a natural pattern, all data points fall within the control limits; this indicates that no abnormal, extraneous causes are working in the process, and that it is in control (see Figure 4). Another characteristic of a natural pattern is that the fluctuations of the data points are unsystematic and unpredictable. By comparison, in an unnatural pattern, outside disturbances are present that affect the process. As a result, the data patterns jump outside the control limits or form unnatural clusters of points within them (Figure 11-13). These are considered assignable causes of process variation. The more numerous the jumps or clusters, the stronger the evidence that the process is out of control.   
Figures 11-13. A sudden shift in level; a drift toward the upper control limit; instability. There are many guidelines for testing unnatural clusters of points, the best-known of which are the Western Electric Rules. When a pattern is unnatural, those familiar with the process should investigate to identify the outside disturbances and correct the problem. For this reason, control limits are often referred to as action limits. Frequently Occurring Unnatural Data Patterns Cycles. Short runs in data that occur in repeated patterns called cycles (see Figure 5). Any tendency to of the pattern to repeat, by showing a series of peaks interspersed with troughs, is an indication of an assignable cause, because the primary characteristic of random pattern is that it does not repeat often. Cycles are caused by process variables that occur on a regular basis, and include systematic environmental changes such as variation in temperature, pressure, or voltage. Other causes include operator fatigue, changes in shipping schedules, rotating a shift of machine operators, or systematically using a different set of machines. 
Figure 5. A cyclic data pattern. Freaks. Defined as isolated data units or measurements greatly different than the others, freaks are among the easiest data patterns to recognize (see Figure 6). In most cases, freaks are produced by an extraneous system of causes and do not indicate that a process is out of control. A common source of freaks is a mistake in calculation, an error in plotting, or an omitted step in an operation. Occasionally, measurements that look like freaks are in reality a normal element in the process. For example, on occasion parts being tested for a quality such as tensile strength will dramatically exceed the normal failure limits. Accidental damage to or mishandling of products being measured can also result in freaks. 
Figure 6. Freaks. Mixtures. In a mixture pattern, the data points tend to fall near the upper and lower limits, with an absence of normal fluctuations near the middle. This pattern can be recognized by the unnatural length of the lines joining the points, which tends to create a seesaw effect. There are two general types of mixtures, stable and unstable. When the component distributions maintain the same relative positions and proportions, the pattern is called a stable mixture (see Figure 7). Stable mixtures frequently occur because of the way samples are taken, and do not necessarily indicate a process that is out of control. 
Figure 7. A stable mixture. A stable mixture often results from samples being taken from more than one distribution, each of which varies on average slightly from the others, but all of which fall within the control limits -- for example products from multiple assembly lines, from machines of slightly different design, or from different personnel shifts. Stable mixtures often occur when the product is measured near the end of the production cycle rather than early. Two forms of stable mixtures -- stratification and systematic variation - result from a special systematic way of taking samples. Stratification is a form of stable mixture that is characterized by an artificial constancy. Instead of fluctuating naturally inside the control limits, with occasional points approaching the upper and lower limits, a stratification pattern consists of small fluctuations that hug the center line, with few deviations or excursions at any distance from it (see Figure 8). Stratification often occurs as a result of samples being consistently taken from widely different distributions, in such a way that at least one unit comes from each. For example, the person taking the sample might select one unit from each operator among a group of operators. When sampling is done in this manner, the selection of the units is not random, and consequently the pattern will not fluctuate in a natural fashion.
Figure 8. Stratification. Because natural patterns are random in nature, another indication of an unnatural pattern is that it is systematic or predicable (for example, a low point is always followed by a high point), indicating the presence of systematic variable in either the process or the data. The most common appearance of such a pattern is a regular sawtooth effect (see Figure 9). Cycles (Figure 5) are also examples of a systematic patterns. Systematic variation is often caused by differences in worker shifts and differences between test sets.
Figure 9. Systemic variation.
Figure 5. A cyclic data pattern. An unstable mixture is one of the most common types of unnatural data patterns. In an unstable mixture, the component distributions do not maintain the same positions and proportions, and occasional vary in the extreme (see Figure 10). Unstable mixtures almost invariably are an indication that the process is out of control. 
Figure 10. An unstable mixture. Sudden Shifts in Level. A sudden shift in level, one of the easiest patterns to spot, is indicated by a change in distribution toward either the upper or lower control limit (see Figure 11).
Figure 11. A sudden shift in level. Typical causes of a sudden shift in a level include a change to a different quality of raw material, a change in setup or method, a change in machine operator skill or motivation, or a new inspector, test set, or machine setting. Drifts. A drift is a long series of points that move gradually toward either the upper or lower control limit (see Figure 12). In general, drifts are fairly easy to identify. They are caused by a variety of factors that work on the manufacturing process gradually. The most frequent causes of drifts include tool wear, machine aging, seasonal effects (such as temperature and humidity), and operator fatigue.
Figure 12. A drift toward the upper control limit. Instability. An unstable data pattern is characterized by unnaturally large fluctuations, with erratic ups and downs that extend outside both control limits (see Figure 13). An unstable pattern can arise from either a single case that operates on the process erratically or a group of causes that operate on the process in conjunction with one another.
Figure 13. Instability. In the latter case, the unstable pattern can become very complex, and the causes may be more difficult to identify than those of simpler patterns. The underlying distribution of any unstable pattern is wide and it is frequently irregular in shape; it may also exhibit several peaks. It is helpful to remember that the ultimate causes of even complex patterns are likely to be very simple - they appear to be complicated only because they exist in complex combinations. The common causes of instability include over adjustment of a machine, different lots of materials mixed in the storeroom, piece parts mixed on the line, erratic behavior of automatic controls, and differences in test sets or gages. Conclusion Trend analysis provides a means to monitor manufacturing processes and to improve product quality. As with any problem-solving method, manufacturers must develop a simple but effective action plan in order to successfully apply this technique, as follows:
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