According to the sixth principle of SPC a frequency distribution will be deviating from normal distribution, only in the presence of any assignable cause.
A frequency distribution is a tally of measurements that shows the number of times the measurement is included int he tally. From this frequency distribution we can see if there are only chance causes present in the process of any assignable causes are acting.
If there is a distortion from the normal curve, we can say that there is presence of assignable causes. This finding can actually help us to find the causes and address them.
Various effects of the presence of assignable causes, will tend to distort the shape in center, or the spread as sees earlier. This indication forms the basis of various techniques used in Statistical Process Control.
The Fifth Principle of SPC states that it is possible to determine the shape of the distribution form the measurements of any process. We can learn abut what the process is doing, against what we want the process to do. For this we need to measure the output of the process with the design specifications.the process can be altered if we donot like the comparison, especially if we see a variation.
We need to address eh variation so that it falls in the required pattern. The variation is due to mainly of 2 types. Common Cause variation and Special Cause Variation.
If the variation in output is caused only by common causes, the output will vary in a normal and predictable manner. In such cases, the process is said to be “stable” or “in a state of Statistical Control”. While the individual measurements may differ from each other, they tend to follow a Normal Distribution.
The normal distribution is characterized by the following
Location (Typical Value)
Spread – Amount by which the smaller values differ from the center.
The shape of the distribution will deviate from the normal curve in case of any un usual occourances. These changes can be called as Assignable causes.
The presence of assignable causes will result in difference from the usual normal curve, either in Shape, or in spread or a combination of both.
some changes are given below.
The above findings will lead us to the sixth principle of SPC – Variation due to assignable causes tend to distort the normal distribution curve.
Fourth Principle of SPC is logical extension of the third principle which is covered in my last post. In which it was said that most measurements will be clustered around the middle. In Fact it was proved by statisticians that we can make failry accurate predictions of the percentage measurements in the various sections of the frequency distribution curve.
Frequency curve with normal distribution
You can see this graph Most measurements fall clso to the middle. This is applicable in general. You will find about 68.2% (34.1%+34.1%)of the measurements will be in the two middle sections of this graph.
28%(14%+14%) of the measurements will fall within the next two sections after the middle sections.
About 4.2%(2.1%+2.1%) will fall in the two outside sections.
A very minute percentage of the measurements will fall outside these sections. This seems to be a bit odd, bu this is a proven fact. However, absense of external conditions is mandatory.
This Curve shown above will be called as a normal distribution. In fact many statsistical theories are centered around the theme of Normal distibution.
The above example will lead to our fifth principle of Statistical Process Control (SPC)- It is possible ot determine the shape of the distribution curve for parts/output produced by any process.
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The Third Principle of SPC is extension of the second one. In the last post on Second Principle of SPC, I mentioned that we notice a Feature if the measurements of the output are analysed.
If we want to see the pattern, all we need to do is plot the individual data points or the measures taken onto a tally form. we will see definite pattern begin to form after several measurements are plotted.
An easy way to demonstrate this is to roll a pair of dice about 50 times or more and record them on a tally sheet. the pattern we see is a frequency distribution.
We can make a frequency distribution curve by enclosing the tally marks in a curved line. The curve you see will have more measurements at the middle and fewer as we go away from middle. It can be seen that the curve looks like a bell.
Whenver one takes a group of measurements, a frequency distribution curve appears.
This would be explaind by the fourth basic principle of Statistical Process Control (SPC)
We have already discussed about the same thing done by us giving different output in the first principle of SPC. The second principle is based on the first principle and states that the variation in the process can be measured.
Some Variation is always inherent to our job and this is acceptable to some extent so far as the variation is within the Tolerance. However, the Variation tends to increase over a period of time. We need to measure and monitor our job to see that the variation is well within the normal expectations. If we donot make an effort to do so, we land up in trouble and the consequences add to the costs.
Even though it is always desirable to Measure the output of a process, it becomes necessary to measure the output of the process or operation to know when the trouble is brewing.
The measurements can be on the characteristics of the output. It can be the Continuous Variables dimensions, or attribute Variables like colour, shape, finish etc.
After collecting the information as described above, we must analyse to see if things are OK. When we check the output of the feature, we will quickly notice a Feature. This feature noticed is the basis of third principle of Statistical Process control – Things Vary according to a definite pattern
Control Charts is a running record of the process performance. It is a recod of results of periodic sampling inspections.
A chart becomes a control chart when it has control limits based on inherent process variation. Process control limits are boundaries on a control chart within which the process can operate to a standard. These limits are based on natural variation of the process without the influence of assignable causes. each time the job is checked, the results are compared with the control limits. If the results are within the control limits, then the process is to be left alone. But if a point on a control chart falls outside the control limits, or any other indications of an out of control process, it indicates that there is some change which is happened and the process in no lnger operating normally.
In other words, Control Limits are warning singnals that tell us
1. When to take action
2. When to leave the process alone.
Taking action on a process operating within control limits is not only eneconomcal but may also increase the variation.
There are two general types of Control Charts
1. Variables Chart – This type of chart is used where a dimentsion of a charecteristin is meaeasured and the result is a value.
Popularly used Variables charts are
X-Bar – R Charts
X-Bar – S – Charts
2. Attributes Chart. – This type of chart is used where a product quality is assessed by sensory means or the data is in terms of count of defectives of count of defects.
Teh popularly used Attributes Charts are
In addition to above there are some adapations to the control charts which are a combination of the above. These are called Special Contorl Charts which will be discussed later.