Stastical Process Capability SPC

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.