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
When talking of statistics, we come across many simple terms. These Basics are called as basic statistics. we come across them day in and day out, when ever we are working on any statistics. Without these basic statistics terms, we cannot understand anything with respect to our statistical problem. Most of them are also used in our daily life, but may be with a different name in statistics
Average – Also called the mean, it is the arithmetic average of all of the sample values. It is calculated by adding all of the sample values together and dividing by the number of elements (n) in the sample.
Central Tendency – A measure of the point about which a group of values is clustered; two measures of central tendency are the mean, and the median.
Characteristic – A process input or output which can be measured and monitored.
Cycle Time – The total amount of elapsed time expended from the time a task, product or service is started until it is completed.
Long-term Variation – The observed variation of an input or output characteristic which has had the opportunity to experience the majority of the variation effects that influence it.
Median – The middle value of a data set when the values are arranged in either ascending or descending order.
Mode : The data point which occurs at maximum frequency
Lower Control Limit (LCL) – for control charts: the limit above which the subgroup statistics must remain for the process to be in control. Typically, 3 standard deviations below the central tendency.
Lower Specification Limit (LSL) – The lowest value of a characteristic which is acceptable.Range – A measure of the variability in a data set. It is the difference between the largest and smallest values in a data set.
Specification Limits – The bounds of acceptable performance for a characteristic.
Standard Deviation – One of the most common measures of variability in a data set or in a population. It is the square root of the variance.
Trend – A gradual, systematic change over time or some other variable.
Upper Control Limit (UCL) for Control Charts – The upper limit below which a process statistic must remain to be in control. Typically this value is 3 standard deviations above the central tendency.
Upper Specification Limit (USL) – The highest value of a characteristic which is acceptable.
Variability – A generic term that refers to the property of a characteristic, process or system to take on different values when it is repeated.
Variables – Quantities which are subject to change or variability.
Variable Data – Data which is continuous, which can be meaningfully subdivided, i.e. can have decimal subdivisions.
Variance – A specifically defined mathematical measure of variability in a data set or population. It is the square of the standard deviation.
Statistics can be described as a quantitative method of scientific investigations.
If used as plural noun ‘Statistics’ means the numerical data arising out of any sphere of human experience.
Used as singular ‘Statistics’ is the name for the body of scientific methods used for collection, analysis, Organizing, and interpretation of Numerical data.
According to American Statistical Association “Statistics” is the scientific application of mathematical principles to the collection, analysis, and presentation of numerical data’
Also, There is a different meaning for the word ‘Statistic’ in the field of Statistics(subject). In this sense A ‘Statistic’ is a numerical item which are produced by the some calculations using the data. Standard Deviation, Mean etc are called as ‘Statistic’ in this sense.
This is one arm of Mathematics, which is extensively used in all most every field. It has become an important tool in the work of many academic disciplines such as medicine, psychology, education, sociology, engineering and physics, just to name a few. It is also important in many aspects of society such as business, industry and government. Because of the increasing use of statistics in so many areas of our lives, it has become very desirable to understand and practice statistical thinking. This is important even if you do not use statistical methods directly.
Even with so many uses, there is some mistrust in public about the subject. This is because of the misuse of the figures by the people for their convenience. During the introduction to the course i joined on, this statement is used. There are 3 types of lies. 1 – Lies, 2- damned Lies 3-Statistics. We will teach you the 3rd part here.
Used properly statistics is a panacea for all the problems faced by the world. it can be a tremendous tool for the growth of any organization. Visit the next post Data Collection – Types of Data