Statistical Process Capability SPC used to control process in the industries. This include Cp, Cpk, Control charts, p chart, np chart, u chart, C chart. X-Bar & R-Bar used to detect process under control.
Statistical Process Capability ( S P C )
This statistical
process Capability is used in all industries. The purpose of this is to
controlling the quality and reduces the variation. Every process takes input
& generates output. We have to collect this data to interpret the output in
the systematic manner to streamline our process.
History
SPC was pioneered by
Walter A. Shewhart at Bell Laboratories in the early 1920s. Shewhart developed
the control chart in 1924 and the concept of a state of statistical control. We
are using same charts & formulae’s as pioneered by A. Shewhart in 1920s.
How do you answer to customer if parts get rejected?
- We will do 100% inspection
- We shall take care in future
- We shall see that the problem does not occur again
- We shall inform our Quality Control ( Q C ) Manager
So, this is not the
right way to answer the customer. At the end of this SPC you will well aware
about how to answer & satisfy customer even if there is customer complaint.
S P C
S = Statistical techniques used to examine process
variation
P = Process, ANY Process
C = Controlling the process through active management
AIAG
Manual
This reference manual
was developed by the statistical process control SPC work Group, sanctioned by
the Daimler Chrysler / Ford / General Motors supplier quality requirements task
force, and under the auspices of the American Society for Quality (ASQ) and the Automotive Industry Action group (AIAG).
AIAG Manual - First
issue 1992
AIAG Manual - Second
Edition, Issued July 2005
Process
As we know every
process has input & output. We have to collect this data to interpret the
output in the systematic manner to streamline our process.
Definition:
-
A series of
actions or steps taken in order to achieve a particular end.
OR The actions which
take input & convert into output.
Defect
What is a defect?
Defect is traditionally deviation from the engineering specifications.
In reality defect is deviation from the targeted value of a
characteristics.
The closer we go to the target, more is the customer satisfied and
farther we go, we have dissatisfied customer.
Defect
Detection Vs Prevention
In every process there is rejection or rework. There are two methods of
control to avoid bad parts supplies to customer. One is defect detection and
other is defect prevention.
Defect
Detection
- It uses customer as final inspector
- Is reactionary
- Tolerates waste such as scrap/rework
- Relies on inspection, audits, or checks of large samples of output
- Treats all defects the same
- Focuses on specification
- Involves action only on output
- Provides late feedback for defect
- Detection is not cost effective
Thus by
detection
- Wait until the customer uses the product
- Wait until the customer reacts to it.
- This method of feedback we use today
- It uses
- Warranty
- Lot rejection
- Vendor rating
The feedback is not only delayed, but cannot be used for products already
in the field.
Then how can we avoid
using the customer as the final Inspector?
What should be done that will make it possible to improve the product
before it gets to the customer?
What to do?
- First identify customer’s input requirements and make sure that they are translated into appropriate targets, goals & objectives.
- Then use voice of customer to make sure that the above meet expectations.
Defect Prevention
- Is pro-active
- Avoids waste
- Uses small samples of product and process information
- Is analytically based
- Discriminates between potential defects based on causes
- Involves action on the process or process parameters
- Provides timely feedback
- It is cost effective
- Focuses on target value
Voice
of Customer Vs Process
Voice of process
Every process generates information that can be used
to measure it. The most effective way to take advantage of this is to:
- Determine the process quality characteristics & respective target value
- Collect data about process.
- Compare process characteristics to pre-established target values.
- Act based on results of comparison.
F Test
This is the f test conducted to interpret as 100% inspection is never
reliable.
Method for this test
Give papers to all participants (min. 8 nos required)
Inform to find out f in the first paragraph. Give 2 min to find.
After, inform to find out f in second paragraph. Give 2 min to find.
Outcome as given below ( Your result may be different)
Record nos. for both test.
Here in first test we will get big variation & also some many f not
found.
In second test we will get very less variation & find exact numbers.
Conclusion
If there is more problem (para 1) in the process / parts then we cannot
find all the problems, some skip from us to customer which leads to customer
complaints. Besides if fewer defects present (para 2) in the process / part
then it can easily identified.
So 100% inspection is not reliable.
What is
statistics?
- What are the first thoughts come in your mind when you hear the word statistics?
- Do you use statistics anytime?
- Many people hate statistics.
- Some believe that it is very difficult to understand.
- Some of you are ready to quit the class.
But Wait
……..
And think about
- Do you understand the theory of Television or telecommunication?
- Do you watch TV?
- Do you talk on the telephone?
- Do you understand aerospace Engg.?
- Do you ride on airplane?
- Do you understand Theory of statistics?
- Do you use statistics?
So what is statistics?
Even though theory behind statistics is hard to understand, we use it every
day extensively.
To talk about sport.
To shops intelligently.
To complete tasks at home or at work.
Whatever way we use data, there must be a way to
collect & organize the data.
Definition
of Statistic
The practice or science of collecting and analyzing numerical data in
large quantities, especially for the purpose of inferring proportions in a whole
from those in a representative sample.
A branch of mathematics dealing with the collection, analysis,
interpretation, and presentation of masses of numerical data.
Few
fundamentals of Descriptive Statistics
- Mean - It is arithmetic average of all observations.
- Mid-range - It is mid-point between the highest & lowest observations.
- Mode -It is most commonly occurring observations.
- Median - It is the middle observation when all observations are arranged in order of magnitude
Example
15, 12, 14, 20, 16, 18, 18, 16, 15, 17, 14, 15, 16, 18, 15, 15, 17, 20
From the above values fundamentals descriptive statistics are
Mean :-16.17 Mid-Range :- 16
Mode :- 15 Median :- 16
Means, medians & Mode are useful when
- We talk about bowling average.
- Average income of India is up.
- Average age of our team.
But they don’t tell the whole story.
But,
They give some reference of centering but we need to
determine how the numbers are spread.
- Are same runs scored in every over?
- Are all incomes higher?
- Is age of every player same?
- Statistics help us describe understand variability.
Spread
Spread is how far apart the ends of the group are.
Bowling average
Observations :- 4, 2 , 6 , 0 , 3 , 5 , 2 , 1 , 3 , 4
Average / mean = 3 Spread = 6
Income Rs.
Observations :- 400, 200, 660, 90,
300, 250, 100, 300, 480, 180
Average / Mean = 296
Spread = 570
Another term that relates spread is S.D. (Standard Deviation)
Sigma Measure
Sigma as a measure of process variation
Sigma is a measure of process variation for a
population – Known as population standard deviation, which is given by
Root of mean square of deviations (RMS) of
individual data points from its mean
Standard
Deviation
Sigma is a measure of process variation for a population – Known as
population standard deviation, Which is given byRoot of mean of squares of deviations ( RMS) of individual data points
from its mean
Here if we consider all jobs (Population) than our SD is sigma (Latin
Letter)
Or
If we are taking samples then out SD is ( Small s letter)
Standard Deviation is a statistical measure of spread or variation that
is present in the group data.
Standard Formula is given by.
To
calculate SD there are six steps
1. Calculate the average of all the observations.
2. Subtract this average from each observation.
3. Square each number obtained in step 2.
4. Find the sum of all numbers obtained in step 3.
5. Divide the number obtained instep 4 by number of
observations minus one.
6. Take the square root of the number obtained in 5.
These steps are very important to understand
Standard Deviation.
Let’s take an example & we will calculate
Standard Deviation of the process
One process has specification 15±5. 10 nos
observation reading are
13, 16, 12, 14, 15, 18, 13, 16, 15, 18.
Find the
Standard Deviation, Cp, Cpk Values of this process
Step 1
Find the average
13, 16, 12, 14, 15, 18, 13, 16, 15, 18
= Sum of 10nos reading / Numbers of observations
= 150/10 = 15
Step 2
Subtract Average from each observation
13 – 15 = -2
16 – 15 = 1
12 – 15 = -3
14 – 15 = -1
15 – 15 = 0
18 – 15 = 3
13 – 15 = -2
16 – 15 = 1
15 – 15 =0
18 - 15 = 3
Step 3
Square all the numbers that came out from step 2
-2 x -2 = 4
1 x 1 = 1
-3 x -3 = 9
-1 x -1 = 1
0 x 0 = 0
3 x 3 = 9
-2 x -2 = 4
1 x 1 = 1
0 x 0 = 0
3
x 3 = 9
Step 4
Add the outcomes of step 3
4 + 1 + 9 + 1 + 0 + 9 + 4 +1 + 0 + 9 = 38
Step 5
Normalize
Divide the result of step 4 by number of
observations minus one
38 / (10-1) =
4.22
Step 6
Take
square root
Square root of 4.22 = 2.05
It is denoted by
s & called as sigma
The calculations can also be done by using MS Excel.
