SPC Training (1)

23-04-17 ©SKF Slide 1 [Code] SKF [Organisation]

SKF ED

Statistical Process Control



•Statistical Process Control

•Variation & Causes of Variation

•Process : Control, Capability

•Process Capability Indices

•Control Charts



A process is unique combination of machines, tools, methods, materials, environment and people that attains an output in goods, software or services.

Generally we are interested in the output of a process e.g. Certain characteristics of interest like Groove Dia, Bore, Outer Diameter of rings.

In order to have the desired output we need to utilize a combination of all the inputs and also need to ensure this control continually.

Use of statistical techniques for controlling the process is called Statistical Process Control.



Variation & its causes

Variation: It is a well known fact that there can not be two products / things having exactly identical characteristic values.This is nothing but Variation.

In manufacturing / processing industry, we come across two different types of variations viz. Random variation and Non random variation

Random variation is due to common causes (chance causes) only where as nonrandom variation is the effect of special causes (assignable causes) and common causes (chance causes).



Random Variation Non random Variation

Due to common causes only

Due to common and special causes

Variation is fairly consistent; predictable

Variation is in consistent ; un predictable

Always a part of the process

Visitor to the process

Statistics apply Statistics do not apply

Controllable by management

Controllable by operating personnel

e.g. M/C Vibration, Power fluctuation

e.g. Wrong setting of tools, mix up of incoming materials,



Statistical Process Control :

A process is said to be in a state of statistical control if it is free of special causes of variation.

If a process remains to be in a state of statistical control over a period of time, it is called as a stable process.

A process under statistical control also needs to be

acceptable. (Remember – every process under statistical control may or may not be acceptable to the customer.)



Under Statistical

Control

Not under statistical

control

Acceptable – meeting

specifications

Case I Case III

Not Acceptable - not meeting

specifications

Case II Case IV

Types of processes

Case III processes may be accepted by customers under certain conditions as due to – the nature of process, root cause of the process is known and is uneconomical to control



How to see whether Process is in statistical control or not?

- Histogram : should demonstrate normal distribution (bell shape)

- Control charts (see out of control conditions on the chart)



What can go wrong with a process and which tools can detect it?

Process average shift – Monitor Control charts (e.g. averages chart)

Process spread change – Monitor Control chart (e.g. Ranges chart)

Distribution change – Plot Histogram and monitor

Either or combination of Process average, Process Spread, Distribution can change with respect to time

Time



Process capability:

Total variation ( 6 ) of process when process is under statistical control is called process capability.



USL LSL

6 > TOL

6 = TOL

6 < TOL



Process capability:

It is not possible for the customer to specify the total variation acceptable to him for each parameter; hence there was a need for developing indices for relating tolerances and the total variation

Cp = Tolerance / Total Variation = Potential Process Capability Index

Process capability , as measured by Cp refers to variation in the process about the average value. Hence Cp index measures the potential capability assuming average at the target value or midpoint of specification limits and the process is operating under statistical control.



Process capability:

Very often it is observed that the process average is not at the target or midpoint of the specifications and hence the need to have a useful indicator for both variation and process average location i.e. Cpk.

Cpk = Min {((USL-X Bar)/ 3 ) or ((X bar – LSL) / 3 ) }

· Higher the value of Cpk , the lower will be the amount of product which is outside the specification limits.

· If actual average is equal to the midpoint of the specification range , then Cpk = Cp

· Cpk cannot exceed Cp

A capability index can also be calculated around the target value rather than the actual



Pp, Ppk Cp, Cpk

Index is process performance index This is used during PPAP / short process capability study Used for stable & chronically unstable processes Captures variation due to both common causes & special causes

Standard deviation = Calculated considering all individual reading using calculator or PC Customer requirements are: Ppk > 1.67

These are process capability index This is used during ongoing process capability study Used only for stable processes Captures variation due to only common causes. Standard deviation = R bar/ d2 Customer requirements are : Cpk > 1.33



Srno 1 2 3 4 5

1 1.440 1.420 1.410 1.410 1.440

2 1.440 1.420 1.420 1.430 1.410

3 1.440 1.420 1.430 1.430 1.430

4 1.440 1.420 1.430 1.420 1.410

5 1.420 1.430 1.430 1.420 1.410

6 1.440 1.430 1.410 1.420 1.420

7 1.430 1.440 1.440 1.430 1.430

8 1.440 1.440 1.440 1.430 1.450

9 1.440 1.430 1.420 1.430 1.440

10 1.420 1.440 1.440 1.430 1.410

11 1.440 1.440 1.410 1.440 1.440

12 1.430 1.430 1.420 1.420 1.420

13 1.420 1.430 1.410 1.410 1.420

14 1.420 1.400 1.410 1.420 1.410

15 1.430 1.430 1.420 1.410 1.420

16 1.420 1.430 1.420 1.410 1.430

0 0 01

14

2322

19

10 0 0 0 0 0

0

5

10

15

20

25

1.370 1.380 1.390 1.400 1.410 1.420 1.430 1.440 1.450 1.460 1.470 1.480 1.490 1.500 1.510

Histogram



Short Term Capability StudyMachine : SHG Channel : 05 Time of data collection : 10.05 to 11.05 Hrs

Type : QJ 209 IR Characteristic: Bore Specification: Φ 45.00 +0/-0.01

Total No of samples selected for study: 100

All the dimensions are deviations from 45.00 in microns

Min Max Average 1 Min Max Average 2

1 -4 -5 -4.5 -6 -7 -6.5 2 -5.52 -5 -7 -6 -6 -8 -7 1 -6.53 -5 -6 -5.5 -6 -8 -7 1.5 -6.254 -3 -4 -3.5 -4 -6 -5 1.5 -4.255 -4 -5 -4.5 -5 -6 -5.5 1 -56 -4 -5 -4.5 -6 -7 -6.5 2 -5.57 -3 -4 -3.5 -5 -6 -5.5 2 -4.58 -4 -6 -5 -6 -7 -6.5 1.5 -5.759 -4 -6 -5 -5 -6 -5.5 0.5 -5.2510 -4 -5 -4.5 -6 -7 -6.5 2 -5.5

Average ID Side 1 Side 2

TaperRdng . No Calculations :

Maximum ID -4

Minimum ID -10.25

Range 6.25

Average Bore -5.58

Standard Deviation - Bore 0.938

Upper Specification Limit 0Lower Specification Limit -10

Pp= (USL-LSL)/ 6 σ = 1.777Ppk= Min (( USL-Average)/ 3*σ, (Average- LSL)/ 3 * σ)

PPk1 3.6424

PPk2 1.5707

Ppk 1.5707



On Going Process Capability Study

Machine : SHG Channel : 05 Upper Specification Limit 0Date of Study : 10.04.2006 Lower Specification Limit -10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0830 0900 0930 1000 1030 1100 1130 1230 0100 0130 0200 0230 0300 0400 0430 0500 0530 0600 0630

1 -4.5 -4.5 -5 -5.5 -5.5 -6.5 -5.5 -4.5 -5.5 -4.5 -6.5 -3.5 -6.5 -3.5 -4.5 -4 -4.5 -4.5 -4.5

2 -5.5 -5 -5.5 -4.5 -6.5 -6.5 -5 -4.5 -3.5 -4.5 -5.5 -4.5 -5.5 -2.5 -4.5 -4.5 -4.5 -5 -4.5

3 -5.5 -5 -5.5 -5.5 -6.5 -5.5 -4.5 -5 -6 -4.5 -6.5 -3.5 -5.5 -3.5 -4.5 -5 -4.5 -5 -4

4 -5.5 -4.5 -5 -5 -5.5 -4.5 -5.5 -5.5 -4.5 -5.5 -4.5 -3.5 -6 -2.5 -3.5 -4 -4 -5.5 -5.5

5 -4.5 -5.5 -5.5 -5.5 -5.5 -4.5 -5 -5.5 -4.5 -4.5 -4.5 -3.5 -4.5 -4.5 -5.5 -4.5 -5 -5.5 -5.5

Avg -5.1 -4.9 -5.3 -5.2 -5.9 -5.5 -5.1 -5 -4.8 -4.7 -5.5 -3.7 -5.6 -3.3 -4.5 -4.4 -4.5 -5.1 -4.8

Range 1 1 0.5 1 1 2 1 1 2.5 1 2 1 2 2 2 1 1 1 1.5Avg of Avg -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69 -4.69Avg of Ranges1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84 1.84UCL X bar -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63 -3.63LCL Xbar -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75UCL R bar 3.8942 3.8942 3.8942 3.8942 3.8942 3.8942 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894 3.894LCL R bar 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Average of averages - 4.89Average of Ranges 1.342

Std Dev= Average of Ranges / d2 0.577 σ ind 0.838Upper Specification Limit 0

Lower Specification Limit -10

2.888 Pp 1.99

2.825 Ppk 1.94Cpk= Min (( USL-Average)/ 3* Std dev, (Average- LSL)/ 3 * Std dev)

Cp= (USL-LSL)/ 6 Std Dev



Average - Range Chart

-8

-6

-4

-2

0

2

4

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Sample #

Avera

ge /

Range (

µ)

Avg

Range

Avg of Avg

Avg of Ranges

UCL X bar

LCL Xbar

UCL R bar

LCL R bar

Range Chart



Interpret Control Charts

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