The document discusses statistical process control and data collection. It covers topics such as measuring performance, collecting and representing data, process control, process capability analysis, and calculating process capability indices. Control charts for variables and attributes are also mentioned. The key points are that statistical process control uses statistical methods to analyze processes and identify abnormal variations, and process capability analysis determines the inherent variability of a process.

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STATISTICAL PROCESS CONTROL

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MEASURING PERFORMANCE
PROCESS
EVERY ACTIVITY IS A
A SEQUENCE OF OPERATIONS
& ANALYSING DATA
COLLECTING,REPRESENTING
CONTROL
PROCESS
STATISTICAL
SPC & DATA COLLECTION
STATISTICAL PROCESS
CONTROL

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NOT ACCEPTABLE,GO GAUGE
& NO GAUGE
OK NOT OK ,ACCEPTABLE
e.g
IT IS A QUALITATIVE
OR NOT ACCEPTABLE &
AS OK NOT OK,ACCEPTABLE
(ANY DATA IS EXPRESSED
e.g
DIM.,TEMP.,ANY VALUE)
UNITS OF MEASUREMENT AS
QUANTITATIVELY IN SPECIFIC
BE MEASURED & EXPRESSED
R/O , LINEAR DIMENSIONS
MOT,PCD R/O,FACE
(ANY DATA THAT CAN
ATTRIBUTE VARIABLE
INDUSTRIAL AREA
INDUSTRIAL DATA CATEGORIES

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DATA ; DATA IS A COLLECTION OF
NUMERICAL FACTS & FIGURES WE NEED FOR:-
 UNDERSTANDING THE CURRENT STATUS & PERFORMANCE
EVALUATION
 ANALYSIS OF PROBLEM
 CONTROL OF PROCESS
 MAKING IMPROVEMENTS
 FINDING VARIATION & TRENDS
 JUDGEMENT OF ACCEPTANCE OR REJECTION

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IMPORTANCE OF DATA
 FACTS ARE BETTER THAN OPINION
 KNOW WHAT FACTS ARE
 EXPRESS FACTS THROUGH DATA
 CLARIFY THE PURPOSE OF COLLECTING DATA
 COLLECT DATA IN A SUITABLE MANNER
 FIND THE RIGHT WAY TO RECORD DATA
 ALL RELEVANT INFORMATION WHICH COULD BE OF VALUE
SHOULD BE RECORDED
 PROVIDE QUICK FEEDBACK ON ANALYSIS OF DATA
 PREVENT FALSIFICATION OF DATA
 ENSURE THE SAMPLE IS REPRESENTATIVE

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A PROCESS CONTROL SYSTEM
IT IS A FEEDBACK SYSTEM .SPC IS ONE TYPE OF
FEEDBACK SYSTEM , FOUR ELEMENTS ARE:-
1.THE PROCESS:- MEANS COMBINATION OF SUPPLIERS , SUBCONTRATORS,
PEOPLE , EQUIPMENT , INPUT MATERIAL , METHODS & ENVIRONMENT
THAT WORK TOGETHER TO PRODUCE OUTPUT & CUSTOMER WHO
USES THAT OUTPUT.
2.INFORMATION ABOUT PERFORMANCE:- UNDERSTANDING OF THE PROCESS
& ITS INTERNAL VARIABILITY GIVES INFORMATION ABOUT PROCESS
3.ACTION ON PROCESS:- ACTION TAKEN TO PREVENT IS ECONOMICAL. THIS
MAINTAINS THE STABILITY & THE VARIATION OF PROCESS OUTPUT.
4.ACTION OF THE OUTPUT:-LEAST ECONOMICAL WHEN RESTRICTED TO
DETECTING AND CORRECTING OUT OF SPECS PRODUCTS W/O
ADDRESSING PROCESS PROBLEM. IT SHOULD BE INTERIM MEASURE ONLY.

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VARIATION
A NATURAL PHENOMENON INHERENT TO EVERY
PROCESS
1. NO TWO THINGS ARE EXACTLY ALIKE AND WILL
ALWAYS VARY.
2. A) PANDIT RAVISHANKAR CAN NOT PLAY ‘RAG
BHAIRAVI’WITH HIS SITAR, TWICE IN EXACTLY
THE SAME DAY.
B) WE DO NOT KNOW WHICH WAY PANDIT RAVI
SHANKAR’S NEXT SITAR RECITAL ON BHAIRAVI
WILL DIFFER FROM THE LAST ONE.
C) THERE IS SOMETHING IN HIS BHAIRAVI’S THAT MAKE
THEM RECCOGNIZELY DIFFERENT FROM OTHERS.

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VARIATION
EXPECTED
(THIS WE MUST LIVE WITH)
UNEXPECTED
(THIS WE DO NOT HAVE TO LIVE WITH)
TOTAL PROCESS
VARIATION
+
=
WHEN THE UNEXPECTED VARIATION IS ELIMINATED ,
WE HAVE THE TRUE PROCESS CAPABILITY.

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CONCEPT OF PRECISION & ACCURACY
NOT
ACCURATE
A P A P
ACCURATE
A P A P

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COMMON VS. ASSIGNABLE CAUSES
COMMON CAUSES
(CHANCE CAUSES)
(RANDOM CAUSES)
ASSIGNABLE CAUSES
(SPECIAL CAUSES)
- CONSISTENT OF MANY INDIVIDUAL CAUSES.
- ANY ONE CAUSES RESULTS IN ONLY A MINUTE
AMOUNT OF VARIATION
EXAMPLE :
- SLIGHT VARIATION IN RAW MATERIAL
- LACK OF HUMAN PERFECTION IN READING
INSTRUMENTS & SETTING CONTROL
- CANNOT BE ECONOMICALLY ELIMINATED
- PROCESS FOLLOWS A PREDICTABLE
(STATISTICAL) PATTERN
- CONSISTENT OF JUST ONE OR TWO INDIVIDUAL
CASES.
- ANY CAUSE CAN RESULT IN LARGE VARIATION
EXAMPLE :
- BATCH OF DEFECTIVE MATERIAL
- UNTRAINED OPERATOR
- FAULTY SET UP
- EASY TO DETECT & GENERALLY ECONOMICAL
TO ELIMINATE
- NO SPECIFIC PATTERN
GOD ONLY KNOWS HUMAN ONLY KNOWS

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WHAT IS PROCESS ?
- IT IS A SEQUENCE THROUGH WHICH INPUTS ARE CONVERTED OR TRANSFORMED INTO
DESIRED OUTPUT.
- IT IS A COMBINATION OF PEOPLE, M/Cs, MATERIALS, METHODS, ENVIRONMENTS,
PLANNING AND ASSOCIATE SYSTEM.
WHAT IS PROCESS CONTROL ?
A PROCESS IS CONTROLLED WHEN IT IS OPERATING UNDER CHANCE (COMMON) CAUSES
ONLY (FREE FROM ASSIGNABLE CAUSES) AND IS CENTRED AROUND THE TARGET.
ADVANTAGES OF CONTROLLED PROCESS
1. PROCESS OPERATES AT ITS BEST WHEN UNDER COMMON CAUSES ALONE ( PREDICTABLE
CAUSES).
2. IT EXHIBITS MINIMUM VARIATION.
3. LOWER LEVEL OF NON -CONFORMANCE.
4. SAMPLING INSPECTION POSSIBLE.
STATISTICAL PROCESS CONTROL IS STATISTICAL METHOD OF SPOTLIGHT ABNORMAL
PROCESS VARIATION LEADING TO THE SEARCH AND REMOVAL OF ASSIGNABLE OR
SPECIAL CAUSESOF PROCESS VARIATION.

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CONTROLLED PROCESS V/S CAPABLE PROCESS
(SPECIAL CAUSE V/S CHANCE CAUSE)
- PROCESS OPERATING UNDER CHANCE & SPECIAL CAUSES
- PROCESS OPERATING UNDER CHANCE CAUSES ONLY
- PROCESS IN CONTROL BUT NOT CAPABLE
- PROCESS IN CONTROL & CAPABLE

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MEASURES OF DISPERSION
RANGE ( R ) - DIFFERENCE BETWEEN LARGEST & SMALLEST.
STANDARD DEVIATION (S)
NORMAL DISTRIBUTION -
-IT IS A CONTINUOUS DISTRIBUTION
- BELL SHAPED, SYMMETRICAL CURVE
- AREA COVERAGE
WITHIN ONE SIGMA - 68. 26%
WITHIN TWO SIGMA- 95. 44%
WITHIN THREE SIGMA- 99.73%
WITHIN FOUR SIGMA - 99. 994%

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RATIONAL SUB GROUPING
- ALL THE UNITS IN THE SAMPLE SHOULD HAVE BEEN PRODUCED UNDER HOMOGENEOUS
SET OF CONDITION SO THAT VARIATION WITHIN THE UNITS IN THE SAMPLE MAY BE
IRREDUCIBLE MINIMUM.
- THE SUB GROUP SHOULD BE CHOSEN SO THAT OPPURTINITES FOR VARIATION AMONG
THE UNITS WITHIN A SUBGROUPARE SMALL. IF THE VARIATION WITHIN A SUBGROUP
REPRESENTS PIECE TO PIECE VARIABILITY OVER A VERY SHORT PERIOD OF TIME, THEN
ANY UNUSUAL VARIATION BETWEEN SUBGROUPS WOULD REFLECT CHANGE IN PROCESS
THAT SHOULD BE INVESTIGATED FOR EXISTENCE OFASSIGNABLE CAUSES AND TO TAKE
APPROPRIATE ACTION.
- SUB GROUP SHOULD TYPICALLY CONSIST OF 4 TO 5 CONSECUTIVELY PRODUCED PIECES.
THE INTENTION IS IS THAT PIECES WITHIN EACH SUBGROUP WOULD ALL BE PRODUCED
UNDER VERY SIMILAR PRODUCTION CONDITIONS OVER A VERYU SHORT TIME INTERVAL
WITH NO OTHER SYSTEMATIC RELATIONSHIP TO EACH OTHER; HENCE VARIATION
WITHIN EACH SUB GROUP WOULD PRIMARILY REFLECT COMMON CAUSES.
- DURING INITIAL STUDY SUBGROUPS ARE OFTEN TAKEN CONSECUTIVELY / IN SHORT
INTERVAL , TO DETECT WHETHER THE PROCESS CAN SHIFT TO SHOW OTHER INSTABILITY,
TIME GROUP BETWEEN SUB GROUP CAN BE INCREASED.

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CONTROL LIMIT V/S SPECIFICATION LIMIT
CONTROL LIMIT SPECIFICATION LIMIT
- INHERENT TO THE PROCESS
- CALCULATED FROM DATA GATHERED
DURING THE PROCESS
- USE TO JUDGE WHETHER A PROCESS
IS IN “ STATISTICAL PROCESS CONTROL
VOICE OF THE PROCESS
- EXTERNAL TO THE PROCESS
- GIVEN BY CUSTOMER (MAY BE INTERVAL
CUSTOMER) ON DRAWING, OPERATION
SHEET OR OTHER SPECIFICATION
- TO JUDGE ACCEPTABILITY OF INDIVIDUAL
PRODUCT.
VOICE OF THE CUSTOMER

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WHAT IS PROCESS CAPABILITY
 PROCESS CAPABILITY IS SIMPLE THE VARIATION
EXHIBITED BY A PROCESS UNDER COMMON INFLUENCE
ONLY.
 IT IS THE VARIATION THAT WOULD BE SEEN IF ALL
ELIMINABLE (SPECIAL CAUSES) SOURCES OF VARIATION
WERE ELIMINATED.
 IT IS ALSO CALLED THE NATURAL TOLERANCE OF THE
PROCESS.
 IT REFLECTS THE INHERENT VARIABILITY OF THE PROCESS
AND TELLS THAT CAN BE EXPECTED FROM THE PROCESS
IN FUTURE.

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WHAT IS
PROCESS CAPABILITY STUDY
 A SCINTEFIC SYSTEMATIC PROCEDURE FOR DETERMINING THE
CAPABILITY OF A PROCESS , AND IF NECESSARY , CHANGING/
MODIFYING THE PROCESS TO OBTAIN A BETTER CAPABILITY.
 A PROCESS CAPABILITY STUDY SHOULD :-
1. IMPLY SOLUTION TO THE PROBLEM.
2. FIND & ELIMINATE THE SPECIAL CAUSES THAT UPSET
THE PROCESS.
 ROUTINE DATA COLLECTION & Cp ,Cpk REPORTS ARE
MEANINGLESS , IF THE PROCESS IS NOT UNDER ‘STATISTICAL
CONTROL’.

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CALCULATING THE
PROCESS CAPABILITY INDEX
Cp = PROCESS CAPABILITY
Cpk = PROCESS CAPABILITY INDEX
Cp = SPECIFICATION WIDTH
PROCESS WIDTH
= USL - LSL
6 s

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C p k = USL - X
s3
( WHEN ONLY USL EXISTS )
C p k = X - LSL
s3
( WHEN ONLY LSL EXISTS )
X & ARE USUALLY UNKNOWN & ARE ESTIMATED USING
THE PROCESS DATA .
s
CALCULATING THE
PROCESS CAPABILITY INDEX
Cpk 1 = USL – X
s3
Cpk 2 = X - LSL
s3

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USES OF PROCESS CAPABILITIES
 CHOOSING FROM AMONG COMPETING PROCESSES THAT WHICH IS
MOST APPROPRIATE FOR THE TOLERANCES TO BE MET .
 PLANNING THE INTERRELATIONSHIP OF SEQUENTIAL PROCESSES.
FOR EXAMPLE , ONE PROCESS MAY DISTORT THE PRECISION
ACHIEVED BY A PREDECESSOR PROCESS, AS IN HARDENING OF
GEAR TEETH . QUANTIFYING THE RESPECTIVE PROCESS
CAPABILITIES OFTEN POINTS THE WAY TO A SOLUTION .
 PROVIDING A QUANTIFIED BASIS FOR ESTABLISHING A SCHEDULE
OF PERIODIC PROCESS CONTROL CHECKS AND ADJUSTEMENT.
 ASSIGNMENT MACHINES TO CLASSES OF WORK FOR WHICH THEY
ARE BEST SUITED.
 SERVING AS A BASIS FOR SPECIFYING THE QUALITY
PERFORMANCE REQUIREMENTS AT MACHINE’S STAGE.

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USLLSL
INCAPABLE PROCESSCAPABLE PROCESS
USLLSL
66
PROCESS CAPABILITY INDEX Vs PERFORMANCE
Cp CONFORMING OUTPUT(%) NONCONFORMING OUTPUT(%)
.5 86.66 13.5
.6 92.80 7.2
.7 96.40 3.6
.8 98.40 1.6
.9 99.30 0.7
.10 99.70 0.3
1.1 99.90 0.1
1.2 99.97 0.03
1.3 99.99 0.01
1.33 99.994 0.006

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PROCESS CAPABILITY
CAPABLE BUT NOT PERFORMING PROCESS
USLTXLSL
PROCESS CAPABILITY INDEX Vs PERFORMANCE
Cpk CONFORMING OUTPUT(%) NON CONFORMING OUTPUT(%)
0.5 93.3 6.7
0.6 96.4 3.6
0.7 98.2 1.8
0.8 99.2 0.8
0.9 99.65 0.35
1.0 99.86 0.14

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NORMAL DISTRIBUTION

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Cp - a measure of variation
(Upper spec. limit= 40;Lower spec. limit =20;
Process width Defined as ± 3 sigma limits)
Cp = 20/30 = 0.67
-2
U.S. in
1970s
20
+2
A
40
40
1980s
U.S. in
+3
B
20
Cp = 20/20 = 1.0
-3
Cp = SPEC.WIDTH (S)
PROCESS WIDTH (P)

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Cp - a measure of variation
(Upper spec. limit= 40;Lower spec. limit =20;
Process width Defined as ± 3 sigma limits)
Cp = SPEC.WIDTH (S)
PROCESS WIDTH (P)

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OUT OF CONTROL SITUATIONS
When the actual variation exceeds the control limits, or when there is
a pattern or a trend, or when all points are too close to the central line,
or all points are too close to control limits, or there is run of 7 or
more points. All such cases are abnormal (probability of such thing
happening is very remote) and are signals of assignable causes.
(A) Unusual Patterns
1. Trend
2. Points on same side
3. Stratification (all points lying within 1 *)
4. Mixture (All points close to control limits)
5. Cyclic Pattern (Time related assignable cause)
s

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CONTROL CHARTS FOR VARIABLES
A) Plot of X
B) Plot of R

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CONTROL CHARTS FOR ATTRIBUTES
A) np Charts (Number of defective - charts)
B) c Charts (Number of defects - charts)
A) np Charts It follows binomial distribution
UCL, LCL = np + 3 np (1-p)
B) c Charts It follows poisson distribution
UCL, LCL = C + 3 C

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