# Tools for SQC

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We already know SQC = Statistical Quality Control.
The following four techniques are the most important statistical tools for data analysis in quality control of the manufactured products.
1. Shewhart's control chart for variables
2. Shewhart's control chart for function defective or p-chart
3. Shewhart's control chart for the number of Defectives per unit or C-chart.
4. The portion of the sampling theory which deals with the quality of protection given by any specified sampling acceptance procedure.
First 3 involve process control while the last involves product control.

Details are given below and on following posts.
1. Shewhart's control chart for variables:
It is used for the variables which can be measured quantitatively. Many quality characteristics of a product are measurable and can be expressed in specific units of measurement such as diameter of a screw, specific resistance of a wire, life of an electric bulb etc.
Such variables are of continuous type & regarded to follow normal probability law. For quality control of such data, two types of control charts are used-
a) Chart for X̄ (mean) & Range R.
b) Chart for X̄ (mean) & σ (Standard Deviation, SD)

2. Shewhart's control chart for function defective or p-chart
This chart is used if we are dealing with attributes in which case the quality characteristics of the product are not amenable measurement but can be identified by their absence or presence from the product or by classifying the product as defective or nondefective.

3. Shewhart's control chart for the number of Defectives per unit or C-chart:
This is usually used with the advantage when the characteristic representing the quality of a product is a discrete variable e.g., the number of surface defects observed in a roll of coated paper on a sheet of photographic film.

4. [See the point above]
The portion of the sampling theory which deals with the quality protection given by any specified sampling acceptance procedure.
Control Charts:

UCL = E (t) + 3 SE(t)
LCL = E (t) - 3 SE(t)
CL = E (t)
Important Points:
If ranges goes out of UCL (Upper Control Line) or LCL (Lower Control Line), then there are assignable causes. Otherwise, reasons are random.
Probability of being outside is .0027
n → ∞, Normal Distribution
If μ & σ are known, using Chebyshev's inequality it can be known how many values fall within range.