Statistical tools for quality control

Fisher and others. Jerzy Neyman and E. Pearson developed a more complete mathematical framework for hypothesis testing in the s. This included now-familiar concepts to statisticians, such as:. ANOVA has proven to be a very helpful tool to address how variation may be attributed to certain factors under consideration. Edwards Deming and others have criticized the indiscriminate use of statistical inference procedures, noting that erroneous conclusions may be drawn unless one is sampling from a stable system.

Consideration of the type of statistical study being performed should be a key concern when reviewing data. You can also search articles , case studies , and publications for statistics resources. Continuous Improvement, Probability, And Statistics.

Statistical Learning Methods Applied to Process Monitoring: An Overview and Perspective Journal of Quality Technology While the research on multivariate statistical process monitoring tools is vast, the application of these tools for big data sets has received less attention. These graphics procedures offer extensive flexibility to get your graph to look just as you want it, while still maintaining ease-of-use and intuitiveness.

Videos providing details of individual aspects of graphing in NCSS are available for free at our website. The utility, precision, documentation, output and ease-of-use of your products are the best in the business. With all the procedures that you need for research or to make a good, informative presentation, it can be used for teaching in a university. Here in Idesem-Chile we have found it to be the best tool to support our measurement activities. I recommend this tool to make your job more enjoyable!

The design means the selection of the sample size, control limits, and frequency of sampling. For example, it can be specified a sample size of five measurements, three-sigma control limits, and the sampling frequency to be every hour.

In most quality control problems, it is customary to design the control chart using primarily statistical considerations. The use of statistical criteria along with industrial experience has led to general guidelines and procedures for designing control charts.

These procedures normally consider cost factors only in an implicit manner. Recently, however, control chart design have begun to be examined from an economic point of view, considering explicitly the cost of sampling, losses from allowing defective product to be produced, and the costs of investigating out-of-control signals which are really false alarms. Another important consideration in control chart usage is the type of variability.

This is the type of behaviour which Shewhart implied, was produced by an in-control process. Time-series analysis is a field of statistics devoted exclusively to study and modelling time-oriented data. In this type of process, the order in which the data occur does not tell much that is useful to analyze the process.

In other words, the past values of the data are of no help in predicting any of the future values. There can be stationary but auto-correlated process data. These data are dependent, that is, a value above the mean tends to be followed by another value above the mean, whereas a value below the mean is normally followed by another such value. There can be non-stationary variation. This type of process data occurs frequently in the process industries. In several industrial settings, this type of behaviour is stabilized by using engineering process control, such as feedback control.

This approach to process control is needed when there are factors which affect the process that cannot be stabilized, such as environmental variables or properties of raw materials. Specifying of the control limits is one of the critical decisions which are to be made in designing a control chart.

By moving the control limits farther from the centre line, the risk of a error is decreased, that is, the risk of a point falling beyond the control limits, indicating an out-of-control condition when no assignable cause is present. However, widening the control limits also increase the risk of an error, that is, the risk of a point falling between the control limits when the process is really out of control. If we move the control limits closer to the centre line, the opposite effect is achieved.

The use of three-sigma control limits is normally justified on the basis that they give good results in practice. Some analysts suggest using two sets of limits on control charts.

The outer limits, say, at three-sigma, are the usual action limits, that is, when a point plots outside of this limit, a search for an assignable cause is made and corrective action is taken if necessary. The inner limits, usually at two-sigma, are called warning limits. If one or more points fall between the warning limits and the control limits, or very close to the warning limit, then there is suspicion that the process is not operating properly.

The use of warning limits can increase the sensitivity of the control chart; that is, it can allow the control chart to signal a shift in the process more quickly. One of their disadvantages is that they can be confusing to operating personnel. This is not normally a serious objection, however, and many practitioners use warning limits routinely on control charts. A more serious objection is that although the use of warning limits can improve the sensitivity of the chart, they can also result in an increased risk of false alarms.

In designing a control chart, it is necessary to specify both the sample size and the frequency of sampling. In general, larger samples make it easier to detect small shifts in the process. When choosing the sample size, the size of the shift which is being tried to detect is to be kept in mind. If the process shift is relatively large, then smaller sample sizes are used than those which are to be employed if the shift of interest is relatively small. Also, the frequency of sampling is to be determined.

The most desirable situation from the point of view of detecting shifts is to take large samples very frequently; however, this is normally not economically feasible. The general problem is one of allocating sampling effort. That is, either small sample is taken at short intervals or larger samples taken at longer intervals.

Present industry practice tends to favour smaller, more frequent samples, particularly in high-volume manufacturing processes, or where a great many types of assignable causes can occur. Essentially, the ARL is the average number of points which is to be plotted before a point indicates an out-of-control condition.

The use of ARLs to describe the performance of control charts has been subjected to criticism in recent years. The reasons for this arise since the distribution of run length for a Shewhart control chart is a geometric distribution. As a result, there are two concerns with ARL namely i the standard deviation of the run length is very large, and ii the geometric distribution is very skewed, so the mean of the distribution the ARL is not necessarily a very typical value of the run length.

It is also occasionally convenient to express the performance of the control chart in terms of its average time to signal ATS. Patterns on control charts are to be assessed.

A control chart can indicate an out-of-control condition when one or more points fall beyond the control limits or when the plotted points show some non-random pattern of behaviour. In general, a run is a sequence of observations of the same type.

In addition to runs up and runs down, the types of observations can be defined as those above and below the centre line, respectively, so that two points in a row above the centre line have a run of length 2. A run of length 8 or more points has a very low probability of occurrence in a random sample of points.

As a result, any type of run of length 8 or more is frequently taken as a signal of an out-of-control condition. For example, eight consecutive points on one side of the centre line can indicate that the process is out of control. Although runs are an important measure of non-random behaviour on a control chart, other types of patterns can also indicate an out-of-control condition. For example, the plotted sample averages can show a cyclic behaviour, yet they all fall within the control limits.

Such a pattern can indicate a problem with the process such as operator fatigue, raw material deliveries, heat or stress build-up, and so forth. Although the process is not really out of control, the yield can be improved by elimination or reduction of the sources of variability causing this cyclic behaviour.

The problem is one of pattern recognition, which is, recognizing systematic or non-random patterns on the control chart and identifying the reason for this behaviour.

The ability to interpret a particular pattern in terms of assignable causes needs experience and knowledge of the process. That is, not only the statistical principles of control charts are to be known, but a good understanding of the process is also necessary.

The process is normally out of control if either i one point plots outside the three-sigma control limits, ii two out of three consecutive points plot beyond the two-sigma warning limits, iii four out of five consecutive points plot at a distance of one-sigma or beyond from the centre line, or iv eight consecutive points plot on one side of the centre line.

These rules apply to one side of the centre line at a time. Hence, a point above the upper warning limit followed immediately by a point below the lower warning limit does not signal an out-of-control alarm. These are frequently used in practice for enhancing the sensitivity of control charts. That is, the use of these rules can allow smaller process shifts to be detected more quickly than the case where only criterion is the normal three-sigma control limit violation.

Several criteria can be applied simultaneously to a control chart to determine whether the process is out of control. The basic criterion is one or more points outside of the control limits. The supplementary criteria are sometimes used to increase the sensitivity of the control charts to a small process shift so that people can respond more quickly to the assignable cause.

Some of the sensitizing rules for control charts which are widely used in practice are i one or more points outside of the control limits, ii two of three consecutive points outside the two-sigma warning limits but still inside the control limits, iii four of five consecutive points beyond the one-sigma limits, iv a run of eight consecutive points on one side of the centre line, v six points in a row steadily increasing or decreasing, vi fifteen points in a row zone close to centre line both above and below the centre line , vii fourteen points in a row alternating up and down, viii eight points in a row on both sides of the centre line with none in zone close to centre line, ix an unusual or non-random pattern in the data, and x one or more points near a warning or control limit.

When several of these sensitizing rules are applied simultaneously, a graduated response to out-of-control signals is frequently used. In general, care is to be exercised when using several decision rules simultaneously. Control charts are one of the most commonly used tools. They can be used to measure any characteristics of a product.

These characteristics can be divided into two groups namely variables and attributes. A control chart is used for monitoring a variable which can be measured and has a continuum of values. On the other hand, a control chart for attributes is used to monitor characteristics which have discreet values and can be counted.

Frequently attributes are evaluated with a simple yes or no decision. Control chart gives signal before the process starts deteriorating. It aids the process to perform consistently and predictably. It gives a good indication of whether problems are due to operation faults or system faults. Typical control chats are given in Fig 4. Various types of control charts are i mean or x-bar chart which is the control chart used to monitor changes in the mean value or shift in the central tendency of a process ii range chart which is the control chart used to monitor the changes in the dispersion or variability of the process, and iii c-chart which is used to monitor the number of defects per unit and which is used when one can compute only the number of defects but cannot compute the proportion which is defective, and iv p-chart which is a control chart used to measure the proportion which is defective in a sample.

The centre line in the p-chart is computed as the average proportion defective in the population p. A p-chart is used when both the total size and the number of defects can be computed. Various advantages of using the control charts are given below. Control charts are among the most important management control techniques. They are as important as cost controls and material controls. Modern computer technology has made it easy to implement control charts in any type of process, as data collection and analysis can be performed on a micro-computer or a local area network terminal in real-time, on-line at the work centre.

When people are able to relate different causes to the effect, namely the quality characteristics, then they can use this logical thinking of cause and effect for further investigations to improve and control the quality. This type of linking is done through cause and effect diagrams. Cause and effect analysis was devised by Professor Kaoru Ishikawa, a pioneer of quality management, in Cause and effect analysis diagram is also known as Ishikawa diagram, Herringbone diagram, or Fishbone diagram since a completed diagram can look like the skeleton of a fish.

Cause and effect analysis diagram technique combines brain-storming with a type of mind map. It pushes people to consider all possible causes of a problem, rather than just the ones which are most obvious. Cause and effect analysis diagrams are casual diagrams which show the causes of a specific event.

Common uses of these diagrams are i product design and quality defect prevention, and ii to identify potential factors causing an overall effect. Rethinking Statistics For Quality Control Quality Engineering As methods used for statistical process control become more sophisticated, it becomes apparent that the required tools have not been included in courses that teach statistics in quality control. A basic description of these tools and their applications is provided, based on the ideas of Box and Jenkins and referenced publications.

Clearing SPC Hurdles Quality Progress Statistical process control has provided significant cost savings for companies that are fortunate enough to implement it fully.

However, these six obstacles can waylay the best of intentions. SPC: From Chaos to Wiping the Floor Quality Progress A history of statistical process control shows how it has gone from taming manufacturing processes to enabling all organizations to maintain their competitive edge.

Using Control Charts In A Healthcare Setting PDF This teaching case study features characters, hospitals, and healthcare data to help readers create a control chart, interpret its results, and identify situations that would be appropriate for control chart analysis. Cart Total: Checkout.

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