BS 7785:1994 download free.Shewhart controll charts.
The traditional approach to manufacturing is to depend on production to make the product and on quality control to inspect the final product and screen out items not meeting specifications. This strategy of detection is often wasteful and uneconomical because it involves after-the-event inspection when the wasteful production has already occurred. Instead, it is much more effective to institute a strategy of prevention to avoid waste by not producing unusable output in the first place. This can be accomplished by gathering process information and analysing it so that action can be taken on the process itself.
The control chart as a graphical means of applying the statistical principles of significance to the control of a production process was first proposed by Dr. Walter Shewhart in 1924111. Control chart theory recognizes two kinds of variability. The first kind is random variability due to “chance causes” (also known as commnn causes”). This is due to the wide variety of causes that are consistently present and not readily identifiable. each of which constitutes a very small component of the total variability but none of which contributes any significant amount. Nevertheless, the sum of the contributions of all of these unidentifiable random causes is measurable and is assumed to be inherent to the process. The elimination or correction of common causes requires a management decision to allocate resources to improve the process and system.
The second kind of variability represents a real change in the process. Such a change can be attributed to wine identifiable causes that are not an inherent part of the process and which can, at least theoretically, be eliminated. These identifiable causes are referred to as “assignable causes” or “special causes” of
variation. They may be attributable to the lack of uniformity in material, a broken tool, workmanship or procedures or to the irregular performance of manufacturing or testing equipment.
Control charts aid in the detection of unnatural patterns of variation in data resulting from repetitive
processes and provide criteria for detecting a lack of statistical control. A process is in statistical control when the variability results only from random causes. Once this acceptable level of variation is determined. any deviation from that level is assumed to be the result of assignable causes which should be identified and eliminated or reduced.
The object of statistical process control is to serve to establish and maintain a process at an acceptable and stable level so as to ensure conformity of products and services to specified requirements. The major
statistical tool used to do this is the control chart, which is a graphical method of presenting and comparing information based on a sequence of samples representing the current state of a process against limits
established after consideration of inherent process variability. The control chart method helps first to
evaluate whether or not a process has attained, or continues in, a state of statistical control at the proper specified level and then to obtain and maintain control and a high degree of uniformity in important
product or service characteristics by keeping a continuous record of quality of the product while production is in progress. The use of a control chart and its careful analysis leads to a better understanding and improvement of the process.
The control limits on the Shewhart charts are at a distance of 30 on each side of the central line, where 7 is the population within-subgroup standard deviation of the statistic being plotted. The within-subgroup variability is used as a measure of the random variation. Sample standard deviations or appropriate multiples of sample ranges are computed to give an estimate of a. This measure of does not include subgroup-to-subgroup variation but only the within-subgroup components. The 30 limits indicate that approximately 99.7 % of the subgroup values will be included within the control limits, provided the process is in statistical control. Interpreted another way, there is approximately a 0,3 % risk, or an average of three times in a thousand, of a plotted point being outside of either the upper or lower control limit when the process is in control. The word “approximately” is used because deviations from underlying assumptions such as the distributional form of the data will affect the probability values.
It should he noted that some practitioners prefer to use the factor 3,09 instead of 3 to provide a nominal probability value of 0,2 % or an average of one spurious observation per thousand, but Shewbart selected 3 so as not to lead to attempts to consider exact probabilities. Similarly, some practitioners use actual probability values for the charts based on non-normal distributions such as for ranges and fraction nonconforming. Again, the Shewhart control chart used ± 30 limits, instead of the probabilistic limits, in view of the emphasis on empirical interpretation.
The possibility that a violation of the limits is really a chance event rather than a real signal is considered so small that when a point appears outside of the limits, action should be taken. Since action is required at this point, the 3a control limits are sometimes called the ‘action limits”.
Many times, it is advantageous to mark 2c limits on the chart also. Then, any sample value falling beyond the 2o limits can serve as a warning of an impending out-of-control situation. As such, the 2c control limits are sometimes called “warning limits”.
Two types of error are possible when control charts are applied. The first is referred to as a type I error, which occurs when the process involved remains in control but a point falls outside the control limits due to chance. As a result, it is incorrectly concluded that the process is out of control, and a cost is then incurred in an attempt to find the cause of a non-existent problem.
A PCI value of less than 1 indicates that the process is not capable, while PCI = 1 implies that the process is only just capable. In practice, a PCI value of 1,33 is generally taken as the minimum acceptable value because there is always some sampling variation and no process is ever fully in statistical control.
It must, however, he noted that the PCI measures only the relationship of the limits to the process spread; the location or the centring of the process is not considered. It would be possible to have any percentage of values outside the specification limits with a high PCI value. For this reason, it is important to consider the scaled distance between the process average and the closest specification limit. Further discussion of this topic is beyond the scope of this International Standard.
In view of the above discussion, a procedure. as schematically presented in Figure 3, can he used as a guide to illustrate key steps leading towards process control and improvement.
9 Attributes control charts
Attributes data represent observations obtained by noting the presence or absence of some characteristic (or attribute) in each of the units in the subgroup under consideration, then counting how many units do or do not possess the attribute, or how many such events occur in the unit, group or area. Attributes data are generally rapid and inexpensive to obtain and often do not require specialized collection skills. Table 5 gives control limit formulae for attributes control charts.
In the case of control charts for variables, it is common practice to maintain a pafr of control charts, one for the control of the average and the other for the control of the dispersion. This is necessary because the underlying distribution in the control charts for variables is the normal distribution, which depends on these two parameters. However, in the case of control charts for attributes, a single chart will suffice since the assumed distribution has only one independent parameter, the average level. The p and np charts are based on the binomial distribution, while the c and U charts are based on the Poisson distribution.
Computations for these charts are similar except in cases where the variability in subgroup size affects the situation. When the subgroup size is constant, the same set of control limits can be used for each subgroup. However, if the number of items inspected in each subgroup varies, separate control limits have to be computed for each subgroup. np and c charts may thus be reasonably used with a constant sample size, whereas p and u charts could be Use(l in either situation.
Where the sample size varies from sample to sample, separate control limits are calculated for each sample.