SPC leads to the right mix for investment casters.
Since the value of investment cast parts increases substantially from the wax room to finishing, investment casters may benefit from using SPC even more than other casting operations.
Companies usually begin Statistical Process Control (SPC) with processes directly affecting their end product, such as raw materials or in-process operating conditions. Indeed, this approach is well-taken since difficulties in product quality often are traced back to these processes.
As improvements are made in these primary processes, however, it soon becomes apparent that secondary processes also influence system performance. As a logical next step, companies often expand their SPC programs to include secondary processes, such as dip room slurry controls and environmental controls.
By the time the quality program encompasses virtually all operations at a given site, most personnel recognize that the suppliers of equipment, services and chemicals for these secondary processes must also impact their final quality of parts and services. This leads to a supplier qualification program.
Investment Casting SPC
Investment casters may benefit even more than other industries from SPC since there is a substantial progressive cost as the product proceeds from the wax department through to finishing. Solutions to problems discovered in earlier stages of production provide a substantial savings in minimizing costly casting defects.
Improper dip room humidity control can lead to cracked shells, breakouts, increased rework and scrap. Fluctuating humidity can result in all of these problems and also make troubleshooting difficult.
Consistent and precise dip room environmental control, however, results in a stronger shell with limited cracks or leakers. System efficiency is maintained, productivity and quality improve and costs are kept at the lowest practical level. When dip room environmental control is operated more consistently and efficiently, there are fewer shell-related production problems. Additionally, production personnel are able to concentrate more of their efforts on factors more closely related to product quality.
Consider an example where the specified limits for a shell drying area are 45-55%, with a target of 50%. Three readings are taken daily, one each eight-hour shift.
Readings are recorded on a log sheet, compared to the specification limits and, if within those limits, promptly forgotten. Some facilities go a step further and plot these values against time to look for trends.
SPC considers two types of process variability causes: special and common. Special causes are defined as fluctuations, upsets and breakdowns in the process resulting from the process not operating as designed. (The "design" was
made by the choice of personnel, equipment, material, methods and environment.) Examples are power failures, equipment breakdowns and human errors. SPC monitoring quickly spots and eliminates special causes of variation. Special causes are attacked first because they produce unpredictable and unstable fluctuations in the process.
Once these special causes all are identified and eliminated, the process is said to be in a state of statistical control. The only remaining variability would then be the predictable and stable inherent variation resulting from the process operating as designed. This type of variability is said to result from common causes of variation.
Examples are fluctuations in analytical measurement techniques and the fluctuations of job sizes, alloy characteristics and equipment performance parameters. The second goal of SPC monitoring is to measure the size of this variation once the process is in statistical control, then determine if the variation is small enough to produce acceptable results almost all of the time.
The inherent process variability resulting from these common causes is measured by the standard deviation--[Sigma] (sigma). Since [Sigma] can only be estimated from a finite amount of data, it is best to label this value as [Sigma Prime] (sigma prime) to signify that it is just an estimate. Historical data from our example produces an overall average of 51% and a [Sigma] of 1.4%. These values were calculated following formulas presented in Table 1.
Sigma plays an important role in describing the normal (or bell-shaped) distribution curve of responses. In simplified terms, a distribution curve can be thought of as a smooth curve drawn through a bar chart (or histogram) of the data. Sigma is the distance from the center of the curve to the inflection point, the point where the curve stops sloping downward and starts sloping outward. Also, 68, 95 and 99.73% of all readings will, on the average, fall within one, two or three standard deviations of the true process average.
These facts can be used to determine where the readings of a statistically controlled process are likely to fall. In Fig. 1, 95% of the readings should fall between 48.2% and 53.8%, and 99.73% of them should fall between 46.8% and 55.2%. This, in fact, is good news since the specified limits for humidity are 45% and 55%.
The [X-bar] Chart
In the example, the three daily humidity readings make up one statistical sample. There is nothing magical about the selection of three samples per day. Samples can be taken more or less frequently depending on several factors: the importance of the response or process, cost and consequences of loss of control, difficulty and cost of measurement, desired control frequency and cycle times.
The sample size of three does provide a better idea of the average level and variability of the humidity during the day than just one or two readings. To gauge the average and variability, [X-bar] (X-bar), which is the average of the readings, and R, which is the range (highest minus lowest), are calculated for each sample or grouping.
SPC uses [X-bar] and R charts as the primary control tools. In this example, the [X-bar] chart (Fig. 2) contains daily averages ([X-bar]) for humidity, plotted over time. This chart also includes three horizontal lines: the average, the upper control limit (UCL) and the lower control limit (LCL). The solid average line represents the average of the daily averages, [X double-bar] (X double-bar).
Initially, this average is calculated using the average of the available sample averages; subsequently, it is calculated using the average of the last 100 or so individual readings (in this case, the last 33 or so averages). The exception to this rule is that sample averages, which are affected by already identified (and eliminated) problems, should not be included.
The UCL and LCL are action limits. Any sample average that falls outside these limits requires immediate attention to identify the cause, correct it and, if possible, prevent it from happening again. These limits are easily calculated using the formulas and constants provided in Table 1.
These formulas require three values from the data: [X double-bar] (X double-bar), [R bar] (R bar) and n. [X double-bar] is the average of the sample averages; [R bar] is the average of the sample ranges; and n is the number of readings per sample.
The [X-bar] chart (Fig. 2) shows that the last two points both fall below LCL, indicating the need for immediate attention. The cause of the problem was quickly found to be an open outside panel in the air recirculation system. After the panel was replaced, the humidity soon returned to its proper range, varying as expected about the center of the control range.
With the assistance of the [X-bar] chart, an otherwise unseen problem was detected and eliminated. Had it not been detected, this problem could have initiated shell cracking leading to increased scrap.
SPC can also provide an early indication of trouble. In Fig. 2, the presence of five or more consecutive sample averages all below [X double-bar] is considered a warning sign.
It is important to note that a process in statistical control does not imply that process output will consistently fall within specification limits, which have not yet been discussed. This is determined by the capability of the process. Achieving process capability is the second major goal of an SPC program. Ford Motor Co's manual contains an excellent discussion of process capability.
The R Chart
A sample R (range) chart, shown in Fig. 3, also provides useful information about process control. The R chart shows the daily range of values compared to the UCL and average lines.
The solid average line in the R chart is positioned at [R bar], the average of the sample range values. The dashed UCL line for range values is calculated using the formula given in Table 1. This formula requires the values for R and n. The same rules apply to the revision of the R and UCL values as those given above for the [X-bar] chart. Range values measure the amount of variability within a sample. Large range values (above UCL) indicate an increase in process variability, an erroneous measurement or a miscalculated control limit.
The R chart shows that one range was above the UCL on August 2. This was an early indication of trouble since the large range value was caused largely by the rapid decline in humidity when the outside panel opened. Once the humidity level stabilized at the new lower level, the range values also returned to more typical levels.
The [X-bar] and R charts are best used in tandem. The [X-bar] chart shows when the average level of the process has shifted upward or downward, compared with past performance. The R chart shows, after checking for erroneous measurements, when the variability in the process has increased or decreased, again, relative to previous levels. Together these charts provide a powerful tool for detecting system upsets before they result in negative consequences.
X and Moving Range Charts
In many cases, readings cannot be taken as frequently or as regularly as in the aforementioned example. In these cases the individual readings are plotted over time. This chart is called the X chart. The average, UCL and LCL values are calculated as before, by considering each reading a sample size of one. However, since each sample is of size one, the ranges plotted within the moving range chart are the positive differences between each consecutive pair of readings.
For example, the first moving range is the difference between the first and second reading, the second moving range is the difference between the second and third reading, and so on. All formulas given in Table 1 apply to the X and moving range charts using the constants for a sample size of one (n = 1).
X and moving range charts, also known as individuals charts, are for situations where less frequent readings are taken on the process output. Actually, these charts have been used for situations ranging from multiple readings per shift to one reading per week. The question then arises, in cases where the [X-bar] and R charts and the X and moving range charts both apply, which set of charts is preferable?
The general rule is, whenever possible, use the [X-bar] and R charts, either singly or in conjunction with the individuals charts. One reason for this rule is that the [X-bar] and R charts are more sensitive to changes in the process than the individuals charts. This means that the former charts will generally detect smaller process changes more quickly than the latter. Also, the [X-bar] and R charts will generally better fulfill the statistical assumptions behind the action and warning rules than the individuals charts. This means, among other things, that fewer "false alarms" will result with the former than with the latter.
Thus, [X-bar] and R charts are generally better to use than X and moving range charts. Why, then, are the individuals charts used?
The individuals charts are used when the data are infrequently or irregularly spaced over time, and/or when quicker control is desired than is possible with the use of the [X-bar] and R charts.
When readings are not taken on a regular or frequent basis, use of the [X-bar] and R charts becomes less valid and more difficult. Readings from points, remote in time, could be grouped together to form a sample. Variability within a sample is assumed to represent primarily the inherent process variability--common cause variation.
Blindly grouping readings in samples of size two or more also could add special cause variation and/or variation due to planned process changes to [Sigma Prime], the estimate of [Sigma]. This inflated [Sigma Prime] will miss more of the medium-sized process changes (and, therefore, miss identification of the corresponding special causes of variation) than a proper estimate of [Sigma].
Another option in this case is to group the readings into more valid samples without forcing the sample size to remain constant. This option provides a more valid estimate of [Sigma], but calculations and control chart interpretation become more difficult. In this setting, the control limits move in and out for each sample to reflect the variability expected in the [X-bar] and R values for its sample size. The X and moving range charts provide a simpler, more valid alternative to these two options.
The individuals charts also are useful in cases where more frequent checks of process control are desired than is possible in [X-bar] and R charts. In [X-bar] and R charts, checks of process control occur only after all readings for a sample are obtained and the new [X-bar] and R values are calculated.
Depending on the sample size used and the amount of time between readings, the process control may not be checked often enough to identify problems before they become painfully obvious. Using individuals charts, process control is checked every time a new reading is obtained, thus reducing the time between checks.
In both of these situations, it is best, whenever possible, to use individuals charts for quick detection of bigger problems and then use the appropriate [X-bar] and R charts (possibly with varying sample sizes) for detection of smaller problems. Together, these four charts will provide a sensitive and timely signal for out-of-control situations and the presence of special causes of variation.
In cases where readings are readily available (digital temperature, humidity and pH readings), care must be taken to allow sufficient time between readings for the inherent process variability to show itself. This is especially true when monitoring, say, the pH of a large dip tank.
In such a process, measurements taken at five minute intervals and averaged to form a sample every 15 minutes would likely produce a [Sigma Prime] value substantially smaller than the inherent variability of the process. This would lead to values of UCL and LCL that are inappropriately close to [X double-bar] and would yield too many false indications of out-of-control situations.
Once a control chart is completed, how is it used to determine whether a process is out of control? Several rules are available to help make this decision. In each case warning and action rules will be presented. A warning situation is a yellow caution flag indicating that the process probably is not in statistical control. A warning may initiate additional monitoring of the process. An action situation is a red flag indicating that the process is almost certainly out of control: immediate attention is needed to identify the cause of the change in the process.
It has already been mentioned that action is needed if any single point falls above the UCL or below the LCL. A warning situation exists when any point falls above the upper warning limit (UWL) or below the lower warning limit (LWL). UWL is the value two-thirds of the way from [X double-bar] to UCL, and LWL is the value two-thirds of the way from [X double-bar] to LCL. Table 1 provides formulas for calculating UWL and LWL.
Two consecutive points outside the warning limits demand action. Five or six consecutive points all above or all below the average constitute a warning, while seven or more such points require action. Similarly, five or six consecutive increases or consecutive decreases in the sample averages indicate a warning; seven or more consecutive internals call for action.
An SPC program may seem more complicated than it really is. The problem has always been to develop the interest and commitment of management and workers needed to make it work. The most frequent objections are that it would require additional staff (thus actually decreasing profitability and productivity) and that it would just mean more work on the floor.
But most organizations can now initiate SPC programs with no increase in manpower by using a personal computer. Many software programs are available which can provide the necessary data management and/or SPC charts.
The better programs provide both data management and SPC graphics in a versatile and easy to use environment. Good SPC software keeps SPC in production areas where it needs to be and meets the following requirements:
Simple Data Entry--Workers should be able to enter process data on a quick and easy to use electronic log.
Simple Data Recall--Workers should be able to easily and quickly produce log sheets and/or up-to-date sets of control charts, either on the screen or on paper.
Data Security--The data base should be protected against accidental or malicious deletion.
Versatility--The software should be able to, among other things, produce the appropriate control charts even if the sample size, n, does not remain constant (e.g., when a reading is missed).
Minimal Training--Workers should be able to quickly learn (in about an hour) how to use the software.
Note that effective interpretation and use of control charts by workers will require time, practice, encouragement and training. Altogether, computer-assisted SPC helps the user respond quickly to out of control situations before they lead to disastrous results. This also aids greatly efforts to identify and eliminate their causes.
Inexpensive hardware and flexible SPC software permits most shops, with minimal effort, to take full advantage of SPC, and thereby gain and maintain process control. [Tabular Data Omitted] [Figures 1, 2, 3 Omitted]
References Deming, W. Edwards, "Quality, Productivity and Competitive Position,"
Massachusetts Institute of Technology, Center for Advanced
Engineering Study (1982). "Continuing Process Control and Process Capability Improvement,"
Ford Motor Co, Statistical Methods Office (1985). Burr, Irving W., "Statistical Quality Control Methods," pp 169-172,
Marcel Dekker, Inc (1976).
S. J. Armitage, J. R. Gassen Nalco Chemical Co Naperville, IL
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|Title Annotation:||statistical process control|
|Date:||Aug 1, 1989|
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