statistical process control introduction. statistical process control what is spc ? what is vsc ?...

Statistical Process Control

INTRODUCTION


What is SPC ?

What is VSC ?

Why we use control charts ?

Plotting of control chart ...


The Arithmetic mean :

Most of the time when we refer to the average of something we are talking about arithmetic mean only. To find out the arithmetic mean , we sum the values and divide by the number of observation.

Advantages : it's a good measure of central tendency.It easily understood by most people

Disadvantages :- Although the mean is reliable in that it reflects all the values in the data set, it may also be affected by extreme values that are not representative of the rest of the data.


The Median :

The median is a single value from the data set that measures the central item in the set of numbers.Half of the item lie above this point and the other half lie below it.

We can find median even when our data are qualitative descriptions.

For example we have five runs of the printing press the results of which must be rated according to the sharpness of the image.Extremely sharp, very sharp, sharp slightly blurred, and very blurred.


Mode :-The mode is a value that is repeated most often in the data set. Infect it is the value with highest frequency.


Average Income

Country X Country Y

10,000 Rs/Month 11000 Rs/Month

Which country is ECONOMICALLY more stable ???


Country X Country Y

8000 4600012000 300010000 10009000 300011000 2000

Avg. 10000 11000

Std dev. 1414 17516


Measure of SPREAD

sigma

Standard Deviation is the


(sigma)=√(x-x ) + (x-x ) + … (x-x )

(n - 1)

_ _ _

1 2 n2 2 2


4.2 12.4 65.2 14.8 7.85.4 18 112.1 17 11.89 19 9.4

9.6 15.5 10.813 2 1014 5 1115 7 10.19.6 10.1 8.8

Data

Plot HISTOGRAM for following DATA

Normal Distribution Curve



• It is symmetrical , unimodel and bell shaped.• The values of mean , median and mode are identical.• It is uniquely determined by the two parameters , namely mean

and standard deviation.• In the family of normal curves smaller the standard deviation ,

higher will be the peak.• If the original observations follow a normal model with mean mu

and std dev sigma then the averages of random sample of size n drawn from this distribution will also follow a normal distribution. The mean of the new model is same as the original model I.e mu but the standard deviation gets reduced to (sigma)/root "n"

Properties of a normal model curve :-


34.13%34.13% 13.6%13.6%2.14% 2.14%

+/- 1 sigma

+/- 2 sigma

+/-3 sigma

68.26%

95.45%

99.73%


LOCATION:

The central tendency it is usually expressed as the AVERAGE

SPREAD:The dispersionit is usually expressed as SIGMA

Description of a NORMAL DISTRIBUTION LOCATION

SPREAD


A Process Control System

• THE PROCESS

• INFORMATION ABOUT PROCESS

• ACTION ON THE PROCESS• Local Action - Special cause• Action on the System - Common cause

• ACTION ON THE OUTPUT


DEMING’s Funnel Experiment


Variation :- Common cause and Special Cause

In order to effectively use of process control measurement data, it is important to understand the concept of variation.

No two characteristic or products are exactly alike, because any process contain many source of variability.

Some source of variation in the process cause short-term, piece to piece difference's - e.g., backlash and clearance with in a machine and its fixturing. Other sources of variation end to cause changes in the output only over along period of time, either gradually as with tool or machine wear, step with procedural changes, or irregularly, as with environmental changes such as power surge. Therefore the time period and condition over a which measure are made will effect the amount of the total variation that will be present.

Common cause refer to the many sources of variation within a process that has a stable and repeatable

distribution over a time. This is called “STATE of STATISTICAL CONTROL” .Common cause behave like a stable system of chance cause. If only common cause of variation are present and do not change, the output of a process is predictable.

The change in the process due to the SPECIAL cause can either be detrimental or beneficial. When detrimental, they need to be identified and removed. When beneficial, they should be identified and made a permanent part of the process.


LOCAL ACTION

COMON CAUSE

SPECIAL CAUSE

ACTION on SYSTEM


CONTROL CHART

Variable DataAttribute

DataX bar - R chartX-s ChartX- Mr Chart

p Chartnp Chartc Chartu chart

When you need to discover how much variability in a process is due to unique events/individual actions in order to determine whether a PROCESS IS IN STATISTICAL CONTROL


X =X+X+X+…X1 2 3 n

nR =

R+R+R+…R1 2 3 n

n

Upper Control Limit

UCL = X + A R2

Lower Control Limit

LCL = X - A R2

Center Line for Average Chart is X double barand

Center line for Range chart is R bar


The p Chart = Proportion Defective

p =Number of rejects in a subgroup

Number inspected in subgroup

p =Total Number of rejects

Total Number inspected

_


INTERPRETING CONTROL CHARTS


COMMON QUESTION TO ASK

WHEN INVESTIGATING AN

OUT OF CONTROL PROCESS


Process Capability

(USL-X d bar), (X d bar - LSL)

Tolerance band

6 * Cp =

Cpk =3* 3* Min of

statistical process control introduction. statistical process control what is spc ? what is vsc ?...

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