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Furthermore, there are other considerations that can be useful to the analyst. One of the most important is the reminder that, even with processes that are in statistical control, the probability of getting a false signal of a special cause on any individual subgroup increases as more data are reviewed.
While it is wise to investigate all signals as possible evidence of special causes, it should be recognized that they may have been caused by the system and that there may be no underlying local process problem.
If no clear evidence of a special cause is found, any "corrective" action will probably serve to increase, rather than decrease, the total variability in the process output. It might be desirable here to adjust the process to the target if the process center is off target. These limits would be used for ongoing monitoring of the process, with the operator and local supervision responding to signs of out-of-control conditions on either the location and variation X or R chart with prompt action see Figure A change in the subgroup sample size would affect the expected average range and the control limits for both ranges and averages.
This situation could occur, for instance, if it were decided to take smaller samples more frequently, so as to detect large process shifts more quickly without increasing the total number of pieces sampled per day. As long as the process remains in control for both averages and ranges, the ongoing limits can be extended for additional periods. If, however, there is evidence that the process average or range has changed in either direction , the cause should be determined and, if the change is justifiable, control limits should be recalculated based on current performance.
The goal of the process control charts is not perfection, but a reasonable and economical state of control. For practical purposes, therefore, a coiltrolled process is not one where the chart never goes out of control. Obviously, there are different levels or degrees of statistical control.
The definition of control used can range from mere outliers beyond the control limits , through runs, trends and stratification, to fidl zone analysis. As the definition of control used advances to fill1 zone analysis, the liltelihood of finding lack of control increases for example, a process with no outliers may demonstrate lack of control though an obvious run still within the control limits. For this reason, the definition of control used should be consistent with your ability to detect this at the point of control and should remain the same within one time period, within one process.
Some suppliers may not be able to apply the hller definitions of conti on the floor on a real-time basis due to immature stages of operator training or lack of sophistication in the operator's ability. The ability to detect lack of control at the point of control on a real-time basis is an advantage of the control chart.
Over-intespretation of the data can be a danger in maintaining a true state of economical control. The presence of one or more points beyond either control limit is primary evidence of special cause variation at that point. This special cause could have occurred prior to this point. Since points beyond the control limits would be rare if only variation from comrnon causes were present, the presumption is that a special cause has accounted for the extreme value.
Therefore, any point beyond a control limit is a signal for analysis of the operation for the special cause. Mark any data points that are beyond the control limits for investigation and corrective action based on when that special cause actually started. A point outside a control limit is generally a sign of one or more of the following: The control limit or plot point has been miscalculated or misplotted. The piece-to-piece variability or the spread of the distribution has increased i.
The measurement system has changed e. For charts dealing with the spread, a point below the lower control limit is generally a sign of one or more of the following: The control limit or plot point is in error. The spread of the distribution has decreased i. A point beyond either control limit is generally a sign that the process has shifted either at that one point or as part of a trend see Figure When the ranges are in statistical control, the process spread - the within-subgroup variation - is considered to be stable.
The averages can then be analyzed to see if the process location is changing over time. If the averages are not in control, some special causes of variation are malting the process location unstable. This could give the first warning of an unfavorable condition which should be corrected. Conversely, certain patterns or trends could be favorable and should be studied for possible permanent improvement of the process. Comparison of patterns between the range and average charts may give added insight.
There are situations where an "out-of-control pattern" may be a bad event for one process and a good event for another process. An example of this is that in an X and R chart a series of 7 or more points on one side of the centerline may indicate an out-of-control situation.
If this happened in a p chart, the process may actually be improving if the series is below the average line less nonconformances are being produced. So in this case the series is a good thing - if we identify and retain the cause. Mark the point that prompts the decision; it may be helpful to extend a reference line back to the beginning of the run. Analysis should consider the approximate time at which it appears that the trend or shift first began.
J A change in the measurement system e. J A change in the measurement system, which could mask real performance changes. OTE: As the subgroup size n becomes smaller 5 or less , the likelihood of runs below R increases, so a run length of 8 or more could be necessary to signal a decrease in process variability.
A run relative to the process average is generally a sign of one or both of the following: J The process average has changed - and may still be changing. J The measurement system has changed drift, bias, sensitivity, etc. Care should be taken not to over-interpret the data, since even random i. Examples of nom-andom patterns could be obvious trends even though they did not satisfy the runs tests , cycles, the overall spread of data points within the control limits, or even relationships among values within subgroups e.
One test for the overall spread of subgroup data points is described below. If several process streams are present, they should be identified and tracked separately see also Appendix A.
Figure The most commonly used are discussed above. Determination of which of the additional criteria to use depends on the specific process characteristics and special causes which are dominant within the process. Note 2: Care should be given not to apply multiple criteria except in those cases where it makes sense. The application of each additional criterion increases the sensitivity of finding a special cause but also increases the chance of a Type I error. In reviewing the above, it should be noted that not all these considerations for interpretation of control can be applied on the production floor.
There is simply too much for the appraiser to remember and utilizing the advantages of a computer is often not feasible on the production floor. So, much of this more detailed analysis may need to be done offline rather than in real time. This supports the need for the process event log and for appropriate thoughtfill analysis to be done after the fact. Another consideration is in the training of operators. Application of the additional control criteria should be used on the production floor when applicable, but not until the operator is ready for it; both with the appropriate training and tools.
With time and experience the operator will recognize these patterns in real time. The Average Run Length is the number of sample subgroups expected between out-of-control signals.
The in-control Average Run Length A X , is the expected number of subgroup samples between false alai-ins. The ARL is dependent on how out-of-control signals are defined, the true target value's deviation from the estimate, and the tme variation relative to the estimate.
This table indicates that a mean shift of 1. A shift of 4 standard deviations would be identified within 2 subgroups.
Larger-subgroups reduce the size of o, and tighten the control limits around X. Alternatively, the ARL ' s can be reduced by adding more out-of-control criteria. Other signals such as runs tests and patterns analysis along with the control limits will reduce the size of the ARL ' s.
The following table is approximate ARL's for the same chart adding - the runs test of 7-points in a row one side o f 2. As can be seen, adding the one extra out-of-control criterion significantly reduces the ARLs for small shifts in the mean, a decrease in the risk of a Type I1 error. Note that the zero-shift the in-control ARL is also reduced significantly. This is an increase in the risk of a Type I error or false alarm.
This balance between wanting a long ARL when the process is in control versus a short ARL when there is a process change has led to the development of other charting methods. Some of those methods are briefly described in Chapter There are other approaches in the literature which do not use averages. Therefore, valid signals occur only in the ; form of points beyond the control limits.
Other rules used to evaluate the j data for non-random patterns see Chapter II, Section B are not reliable indicators of out-of-control conditions. These control charts use categorical data and the probabilities related to the categories to identify the presences of special causes. The analysis of categorical data by these charts generally utilizes the binomial, or poisson distribution approximated by the normal form. Traditionally attributes charts are used to track unacceptable parts by identifying nonconfoi-ming items and nonconforrnities within an item.
There is nothing intrinsic in attributes charts that restricts them to be solely used in charting nonconforming items.
They can also be used for tracking positive events. However, we will follow tradition and refer to these as nonconformances and nonconformities. Guideline: Since the control limits are based on a normal approximation, the sample size used should be such that np 2 5. Most of these charts were developed to address specific process situations or conditions which can affect the optimal use of the standard control charts.
A brief description of the more common charts will follow below. This description will define the charts, discuss when they should be used and list the formulas associated with the chart, as appropriate.
If more information is desired regarding these charts or others, please consult a reference text that deals specifically with these types of control charts. Probability based charts belong to a class of control charts that uses categorical data and the probabilities related to the categories. The analysis of categorical data generally uses the binomial, multinomial or poisson distribution. Examples of these charts are the attributes charts discussed in Chapter I1 Section C.
However, there is nothing inherent in any of these forms or any other forms that requires one or more categories to be "bad. This is as much the fault of professionals and teachers, as it is the student's. There is a tendency to take the easy way out, using traditional and stereotypical examples. This leads to a failure to realize that quality practitioners once had or were constrained to the tolerance philosophy; i. With stoplight control charts, the process location and variation are controlled using one chart.
The chart tracks the number of data points in the sample in each of the designated categories. The decision criteria are based on the expected probabilities for these categories. A typical scenario will divide the process variation into three parts: warning low, target, warning high.
One simple but effective control procedure of this type is stoplight control which is a semi- variables more than two categories technique using double sampling. In this approach the target area is designated green, the warning areas as yellow, and the stop zones as red. The use of these colors gives rise to the "stoplight" designation.
Of course, this allows process control only if the process distribution is known. The quantification and analysis of the process requires variables data. The focus of this tool is to detect changes special causes of variation in the process.
That is, this is an appropriate tool for stage 2 activities27 only. At its basic implementation, stoplight control requires no computations and no plotting, thereby making it easier to implement than control charts. Since it splits the total sample e. Although, the development of this technique is thoroughly founded in statistical theory, it can be implemented and taught at the operator level without involving mathematics.
Process performance including measurement variability is acceptable. The process is on target. Once the assumptions have been verified by a process performance study using variables data techniques, the process distribution can be divided such that the average i 1.
Any area outside the process distribution the If the process distribution follows the normal form, approximately Similar conditions can be established if the distribution is found to be non-normal. Check 2 pieces; if both pieces are in the green area, continue to run.
If one or both are in the red zone, stop the process, notify the designated person for corrective action and sort material. When setup Select 2 or other corrections are made, repeat step 1. Samples 3. If one or both are in a yellow zone, check three more pieces.
If any I pieces fall in a red zone, stop the process, notify the designated person for corrective action and sort material. When setup or other Green? J If no pieces fall in a red zone, but three or more are in a yellow zone out of 5 pieces stop the process, notify the designated 1 J person for corrective action.
When setup or other corrections are made, repeat step I. If three pieces fall in the green zone and the rest are yellow, continue to run. Select 3 Additional Samples Measurements can be made with variables as well as attributes gaging.
I Certain variables gaging such as dial indicators or air-electronic columns are better suited for this type of program since the indicator background Any Red? Although no charts or graphs are required, charting is Yes I recommended, especially if subtle trends shifts over a relatively long period of time are possible in the process. In any decision-making situation there is a risk of making a wrong decision.
With sampling, the two types of errors are: Probability of calling the process bad when it is actually good false alarm rate. Probability of calling the process good when it is actually bad miss rate. Sensitivity refers to the ability of the sampling plan to detect out-of-control conditions due to increased variation or shifts from the process average.
The disadvantage of stoplight control is that it has a higher false alarm rate than an X and R chart of the same total sample size. The advantage of stoplight control is that it is as sensitive as an X and R chart of the same total sample size. Users tend to accept control mechanisms based on these types of data due to the ease of data collection and analysis.
Focus is on the target not specification limits - thus it is compatible with the target philosophy and continuous improvement.
An application of the stoplight control approach for the purpose of nonconformance control instead of process control is called Pre- control. It is based on the specifications not the process variation. The first assumption means that all special sources of variation in the process are being controlled. The second assumption states that The area outside the specifications is labeled red.
For a process that is normal with C , Cpk equal to 1. Similar calculations could be done if the distribution was found to be non-normal or highly capable. The pre-control sampling uses a sample size of two. However, before the sampling can start, the process must produce 5 consecutive parts in the green zone.
Each of the two data points are plotted on the chart and reviewed against a set of rules. Every time the process is adjusted, before the sampling can start the process must produce 5 consecutive parts in the green zone.
Pre-control is not a process control chart but a lionconformance control chart so great care must be taken as to how this chart is used and interpreted. Pre-control charts should be not used when you have a C,, Cpk greater than one or a loss function that is not flat within the specifications see Chapter IV. The disadvantage of pre- control is that potential diagnostics that are available with normal process control methods are not available.
Further, pre-control does not evaluate nor monitor process stability. Pre-control is a compliance based tool not a process control tool. However there are processes that only produce a small number of products during a single run e. Further, the increasing focus on just-in-time JIT inventory and lean manufacturing methods is driving production runs to become shorter.
From a business perspective, producing large batches of product several times per month and holding it in inventory for later distribution, can lead to avoidable, unnecessary costs.
Manufacturers now are moving toward JIT - producing much smaller quantities on a more frequent basis to avoid the costs of holding "work in process" and inventory. For example, in the past, it may have been satisfactory to make 10, parts per month in batches of 2, per week. Now, customer demand, flexible manufacturing methods and JIT requirements might lead to malting and shipping only parts per day.
To realize the efficiencies of short-run processes it is essential that SPC methods be able to verifL that the process is truly in statistical control, i. The process must be operated in a stable and consistent manner. The process aim must be set and maintained at the proper level. The Natural Process Limits must fall within the specification limits.
Short-run oriented charts allow a single chart to be used for the control of multiple products. There are a number of variations on this theme. Among the more widely described short-run charts are: 29 a. Production processes for short runs of different products can be characterized easily on a single chart by plotting the differences between the product measurement and its target value. These charts can be applied both to individual measurements and to grouped data. The DNOM approach assumes a common, constant variance among the products being tracked on a single chart.
When there are substantial differences in the variances of these products, using the deviation from the process target becomes problematic. In such cases the data may be standardized to compensate for the different product means and variability using a transformation of the form: This class of charts sometimes is referred to as Z or Zed charts.
In some short-run processes, the total production volume may be too small to utilize subgrouping effectively. In these cases subgrouping measurements may work counter to the concept of controlling the process and reduce the control chart to a report card function. But when subgrouping is possible, the measurements can be standardized to accommodate this case.
Standardized Attributes Control Charts. Attributes data samples, including those of variable size, can be standardized so that multiple part types can be plotted on a single chart. The standardized statistic has the form: z. There are situations where small changes in the process mean can cause problems.
Shewhart control charts may not be sensitive enough to efficiently detect these changes, e. The two alternative charts discussed here were developed to improve sensitivity for detecting small excursions in the process mean.
See Montgomery , Wheeler and Grant and Leavenworth for in-depth discussions of these methods and comparisons with the supplemental detection rules for enhancing the sensitivity of the Shewhart chart to small process shifts A CUSUM chart plots the cumulative sum of deviations of successive sample means from a target specification so that even minor permanent shifts 0.
For larger shifts, Shewhart control charts are just as effective and take less effort. These charts are most often used to monitor continuous processes, such as in the chemical industry, where small shifts can have significant effects. A graphical tool V-mask is laid over the chart with a vertical reference line offset from origin of the V passing through the last plotted point see Figure The offset and angle of the arms are functions of the desired level of-sensitivity to process shifts. An out-of-control I Vmask Chart for Coating Thickness condition e g , a significant process shift is indicated when previously plotted points fall outside of the V-mask arms.
These arms take the place of the upper and lower control limits. The chart in Figure When the V-mask was positioned on prior data points, all samples fell within the control limits, so there was no indication of an out-of-control situation. See Montgomery for a discussion of this procedure. An initial value, zo must be estimated to start the process with the first sample. The manual covers the majority of situations that occur in early planning, design, or process analysis phases.
Program Management: Quality Team - Loading Changes. Please wait. There are two phases in statistical process control studies. Cpkand PpkComparison Comparison between a Predictable and Immature Process Loss Function Comparison of Loss Function and Specifications Comparison of Loss Functions Process Alignment to Requirements We must constantly seek more efficient ways to produce products and services.
These products and services must continue to improve in value. We must focus upon our customers, both internal and external, and make customer satisfaction a primary business goal. To accomplish this, eveiyone in our organizations must be committed to improvement and to the use of effective methods.
This manual describes several basic statistical methods that can be used to make our efforts at improvement more effective. Different levels of understanding are needed to perfom different tasks. This manual is aimed at practitioners and managers beginning the application of statistical methods.
It will also serve as a refresher on these basic methods for those who are now using more advanced techniques. Not all basic methods are included here.
Coverage of other basic methods such as check sheets, flowcharts, Pareto charts, cause and effect diagrams and some advanced methods such as other control charts, designed experiments, quality fiinction deployment, etc. The basic statistical methods addressed in this manual include those associated with statistical process control and process capability analysis. Chapter I provides background for process control, explains several important concepts such as special and common causes of variation.
It also introduces the control chart, which can be a very effective tool for analyzing and monitoring processes. Chapter I1 describes the construction and use of control charts for both variables1 data and attributes data.
Chapter I11 describes other types of control charts that can be used for specialized situations - probability based charts, short-sun charts, chasts for detecting small changes, non-normal, multivariate and other charts. Chapter IV addresses process capability analysis.
The Appendices address sampling, over-adjustment, a process for selecting control charts, table of constants and formulae, the normal table, a glossary of terms and symbols, and references.
The overall aim should be increased understanding of the reader's processes. It is very easy to become technique experts without realizing any improvements. Increased knowledge should become a basis for action. Measurement systems are critical to proper data analysis and they should be well understood before process data are collected.
When such systems lack statistical control or their variation accounts for a substantial portion of the total variation in process data, inappropriate decisions may be made. For the purposes of this manual, it will be assumed that this system is under control and is not a significant contributor to total variation in the data.
The basic concept of studying variation and using statistical signals to improve performance can be applied to any area. Such areas can be on the shop floor or in the office. Some examples are machines performance characteristics , bookkeeping error rates , gross sales, waste analysis scrap rates , computer systems performance characteristics and materials management transit times.
This manual focuses upon shop floor applications. The reader is encouraged to consult the references in Appendix H for administrative and service applications. Historically, statistical methods have been routinely applied to parts, rather than processes. Application of statistical techniques to control output such as parts should be only the first step. Until the processes that generate the output become the focus of our efforts, the fhll power of these methods to improve quality, increase productivity and reduce cost may not be fully realized.
Although each point in the text is illustrated with a worked-out example, real understanding of the subject involves deeper contact with process control situations. The study of actual cases from the reader's own job location or from similar activities would be an important supplement to the text.
There is no substitute for hands-on experience. This manual should be considered a first step toward the use of statistical methods. It provides generally accepted approaches, which work in many instances. However, there exist exceptions where it is improper to blindly use these approaches. This manual does not replace the need for practitioners to increase their knowledge of statistical methods and theory. Readers are encouraged to pursue formal statistical education.
Where the reader's processes and application of statistical methods have CHAPTER I Continual Improvement and Statistical Process Control advanced beyond the material covered here, the reader is also encouraged to consult with persons who have the proper knowledge and practice in statistical theory as to the appropriateness of other techniques.
In any event, the procedures used must satisfy the customer's requirements. In administrative situations, work is often checked and rechecked in efforts to catch errors. Both cases involve a strategy of detection, which is wasteful, because it allows time and materials to be invested in products or services that are not always usable. It is much more effective to avoid waste by not producing unusable output in the first place - a strategy of prevention.
A prevention strategy sounds sensible - even obvious - to most people. It is easily captured in such slogans as, "Do it right the first time". However, slogans are not enough. What is required is an understanding of the elements of a statistical process control system. The remaining seven subsections of this introduction cover these elements and can be viewed as answers to the following questions: What is meant by a process control system?
How does variation affect process output? How can statistical techniques tell whether a problem is local in nature or involves broader systems? What is meant by a process being in statistical control?
What is meant by a process being capable? What is a continual improvement cycle, and what part can process control play in it? What are control charts, and how are they used? What benefits can be expected from using control charts?
As this material is being studied, the reader may wish to refer to the Glossary in Appendix G for brief definitions of key terms and symbols.
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