Normal distribution:
An important continuous probability distribution is the normal distribution or the Gaussian distribution. The most important distribution in statistics is the Normal Distribution. This distribution has a symmetric bell-shaped form and tends to infinity in both directions. The normal distribution occupies an important part due to
- It has properties that make it applicable to a number of situations in which decision¬ makers have to make inferences by drawing samples.
- The normal distribution comes quite close to fitting the actual observed distribution of many phenomena, including output from physical processes.
Normal distribution having same mean but different spreads:
- The curve has a single peak.
- It is bell shaped.
- The mean (average) lies at the centre of the distribution or symmetrical around a vertical line erected at the mean.
- The two tails of the normal distribution extend indefinitely and never touch the horizontal axis.
Any normal distribution is defined by two measures:
- The mean (x) which locates the centre.
- The standard deviation, which measures the spread around the centre
In probability theory, the normal or Gaussian distribution is a very common continuous probability distribution. A normal distribution is a very important statistical data distribution pattern occurring in many types in cement quality control. The spread of a normal distribution is controlled by the standard deviation ‘σ’. The concentrated data will be available if the standard deviation is small.
The formula for normal probability distribution is given by:
Distribution Pattern of SQC:
Statistical quality control relies upon theory and concept of probability, and probability basically accepts the possibility of variation in all things.
Generally, the variations occurring in (industrial processes or) products manufactured by an industry are classified as:
- Variations due to assignable causes
- Random or change variations.
The variations which occur due to assignable causes possess greater magnitude as compared to those due to chance causes and can be easily traced. Various assignable causes leading to variations may be, differences amongst the skills of the operators, poor raw material and machine conditions, changing working conditions, mistake on the part of a worker.
When the measured quality of all the products are plotted against the frequency of occurrence of each quality, in the form of a graph and the curve is smoothened, it resembles bell shape and approximates Normal Distribution curve.
