6 Sigma - Chapter3

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Chapter 3: Data and Variation and Process Capability
Aim
This chapter is a detailed discussion of the basics of data, variation and Statistical
Control. You will learn here how to understand a distribution graph, Understand what
process capability is and to enumerate the various methods and indices used to
calculate the process capability.
Data Facts – Basic nature of data
Two kinds of data are normally found in any organization:
1. Continuous Data
Data which can be measured and which characterizes a product or some process
features in terms of its size, weight and volts. This type of data is said to be
continuous by nature. In other words, the measurement scale can be meaningfully
divided into finer and finer increments using the concept of least count.
2. Discrete Data
When data cannot be measured but only observed and when it occurs in the form of
frequency of occurrences; e.g., the number of times some events happen or fail to
happen. For example, the number of typing errors or number of days an employee is
absent cannot be measured but can be counted.
The validity of inferences made from discrete data depends a lot upon the number of
observations. The more the number of observations the more would be the accuracy
of inference. Thus, a sample size required to characterize discrete data would be
typically much larger than that required when continuous data is used.
Data Facts - Location and Variation Estimates
Location and variation quantify essential information about output of the process.
Location is the most central part of the process. For example, bolts manufactured
may vary in their thickness. Location refers to that value which represents the
setting of the process. It could be the mean of all the values; could be the median or
the mode.
Of these, mean is the most commonly used measure.
Variability is the spread or range of the process where most values occur. Measures
of variation can be either Standard Deviation or Range.

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Variation
The need for quality control arises from the fact that even after the quality standards
have been specified, variation in quality is unavoidable due to process variation.
For example,
A machine is producing 100,000 bolts per day of 2 inch lengths each. It is very
unlikely that all bolts measure exactly 2 inches. If the measuring instrument is
sufficiently good, we can detect some bolts that are slightly less than 2 inches and
some that are slightly more than 2 inches. This leads to a search for the possible
causes of variation in the product.
A measure of variation or dispersion is one that measures the extent to which there
are differences between individual observations and some central or average value.
Note that in measure of variation we would be interested in the amount of variation
or its degree and not in the direction. For example, a measure of 4 inches below the
mean has just as much variation as a measure of six inches above the mean.
Types of variation
The variation of a quality characteristic can be divided under two heads:
1. Chance variation
2. Assignable variation
Chance variation
These are variations that result from many minor causes. These causes behave in a
random manner. This variation follows statistical property like Normal distribution,
and hence, we say it is predictable variation.
This type of variation is permissible and actually inevitable in a practical
manufacturing environment. There is no way in which it can completely be
eliminated - when the variability present in a production process is confined to
chance variation only, the process is said to be in a state of statistical control.
Assignable variation
These variations may be attributed to special non-random causes. This variation
does not follow any statistical law and hence, we can say it is unpredictable.
Such variations can be a result of several factors such as a change in the raw
material, a new operation, an improper machine setting, broken or worn-out parts,
mechanical faults in plants etc.

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The value of Quality control lies in the ability to detect these variations in a process.
In fact, these variations can be discovered before the product becomes defective.
Understanding Distribution curve
Distribution can differ in:
1. Spread: The distribution curve 1 represents two distributions with same mean
but with different dispersions.
2. Location: The distribution Curve 2 has two distributions that have the same
dispersion but with unequal means X1 and X2.
3. Shape: The two distributions have unequal dispersion.
Process Capability
Process Capability represents the best performance (i.e. minimum spread) of the
process, when the process is operating in a state of Statistical control due to no
assignable causes.
It indicates only the natural fluctuations that take place in Key characteristic of a
process. When a process is in a state of statistical control the only variations in the
process are due to the chance causes. Thus Capability is determined by the variation
that comes from chance causes.
Mathematically, Capability = Six Sigma calculated from a set of individual
measurements.
Potential capability (Cp).
This is the simplest and most straightforward indicator of process capability.
It is defined as the ratio of the specification range to the process range; using ± 3
sigma limits we can express this index as:
Cp = (USL-LSL)/(6*Sigma)
Put into words, this ratio expresses the proportion of the range of the normal curve
that falls within the engineering specification limits.

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Capability ratio (Cr)
This index is equivalent to Cp; specifically, it is computed as 1/Cp
A drawback of the Cp index is that it really evaluates only process spread and
ignores the process average. If the system is not centered at the middle of the
specifications, the Cp index may be misleading.
Assuming the system is centered, a Cp value of 1 indicates that the system is
producing 99.73% of output within specification limits.
Lower/upper potential capability (Cpl, Cpu.)
A major shortcoming of the Cp (and Cr) index is that it may yield erroneous
information if the process is not on target, that is, if it is not centered or if the
process shows one-sided specifications such as minimum length, etc.
For non-centered distribution (such as in the diagram shown) upper and lower
potential capability indices can be computed which would aptly reflect the deviation
of the observed process mean from the LSL and USL.
Demonstrated Excellence
It is denoted by Cpk and takes the value of either Cpl or Cpu based on which value is
lower.
Cpk = Smaller value of [(USL - Mean)/ 3 Sigma, (Mean - LSL)/3 Sigma]
Unlike potential capability, demonstrative excellence takes into account the centering
of the key characteristics of the process.
While Cp is a function of the range, Cpk is the function of the average i.e. the mean.
The Cpk tells how well a system can meet specification limits while accounting for
the location of the average. The Cpk index modifies the Cp index to account for the
location of the average (or center). A Cpk of 1 indicates that the system is producing
at least 99.73% within the specification limits.

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Summary
1. Data can be continuous or discrete.
2. A set of data can be measured for its location and spread.
3. Location is measured using mean, median or mode.
4. Spread of a data is determined using either Standard deviation or range.
5. Measure of dispersion measures the extent to which there are differences
between individual observations and some central or average value.
6. Variations can be chance or assignable.
7. Chance variations are caused by random causes that cannot be completely
removed form the process.
8. Assignable variations may be attributed to special non-random causes and
these should be corrected.
9. When process shows only chance variation, it is under statistical control.
10. Process Capability represents the best performance (i.e. minimum
spread) of operating in a state of Statistical control.
11. Potential capability is the ratio that expresses the proportion of the
range of the normal curve that falls within the engineering
specification limits.
12. For non-centered distribution, upper and lower potential capability indices
are computed.