Statistical Process ControlStatistical Process ControlStatistical Process ControlStatistical Process Control

Statistical : Collection, Analysis & Implementation of Numerical data (Facts & Figures).

Process : A Combination of man, machine, material, method & equipments for producing the desired product & Service

CControlontrol : Performance comparison with standard and taking necessary action for achieving the end result.

is to influence and to control the quality at the time of control the quality at the time of manufacturingmanufacturing..

Statistical Process Control (SPC) focuses on controlling the manufacturing process to prevent defects rather than detect prevent defects rather than detect them.them.

Purpose and Application of SPCPurpose and Application of SPCPurpose and Application of SPCPurpose and Application of SPC

BENEFITS OF SPCBENEFITS OF SPC

Less downtimeFewer production interruptionsLess trouble at next operationImproved performanceMore involved operatorsFewer complaintsFewer complaintsFewer DefectivesSavings in timeIncreased CapacityLess Scrap.

Sources of variation which are built into the process and will be caused by such problems as

Types of variationTypes of variation

Inherent variation (chance cause) :Inherent variation (chance cause) :

These are the source of random variation , the extent of which can be measured and monitored. The level of variation will continue unless something special occurs.

EnvironmentEnvironment power power Slight variation in raw-material / machine, Slight variation in raw-material / machine, lack of human perfection in reducing instruments etc.,lack of human perfection in reducing instruments etc.,

Sources of variation which will be due to specific identifiable causes such as variation in

Raw material Raw material

Tool wearTool wear

SettingSetting

State of maintenance State of maintenance

Batch of defective raw materialBatch of defective raw material

Untrained operator & Untrained operator &

faulty setup etc.,faulty setup etc.,

Special cause variation (assignable cause)Special cause variation (assignable cause)

CHANCE CAUSES ASSIGNABLE CAUSES

Man1)Normal errors in handling material and machine slides

1)Carelessness

2)Mood

3)Untrained operator

Machine 1)Normal play in Machine slides 1)Excessive play (old machine)

2)Poor maintenance

Material 1)Hardness within Tolerance 1)Defective material

2)Hard spots

3)Blow holes

4)Mix-up of material

Method 1)Small variation in job clamping 1)Wrong speed and feed

2)Bush oversize

3)Clamps broken

4)Wrong drawings

Environment1)Temperature change 1)Checking of Hot components

with cold instruments

Defect Any non-conformance of an item with respect to the

specification for a characteristic or dimension

Defective: Any item containing one or more defects.

The basic element of SPC is data analysisdata analysis, and the primary document is control charts.

SPC involves control followed by improvement. Processes are initially brought under control by identifying and eliminating the ASSIGNABLE CAUSES of Variation.

A controlled situation is one when the process is operating only under the influence of CHANCE CAUSE(Inherent).

Statistics is the art of making decisions about a process based on an analysis of information obtained from a process.

Statistical methods provide means by which the output is studied and evaluated.

Statistics is quite simply the collection, collation and use of data.

StatisticsStatisticsStatisticsStatistics

Average ( ) or Mean :Average ( ) or Mean :

It simply means sum of all the individual observed data divided by the no. of observations.

X1 + X2 + X3 + - - - - + Xn n

n = no. of Observations.

Example : Observations = 20, 24, 26, 28, 43, 18

n = 6 20+24+26+28+43+18

X =

X

X = 6

= 26.5

Range (R) :Range (R) :

Range is measure of the variation in a set of data. It is calculated by subtracting the lowest value in the data set from the highest value in that same set.

R = X max – X min

X max = 43, X min = 18

R = 43 – 18 = 25

Observations = 20, 24, 26, 28, 43, 18

Assuming Normal distribution as the pattern of variation for measured characteristics, we know that Average + 3 / - 3 comprises almost all (99.73%) of the observations.

Hence 6 sigma is used as a measure of process capability. Lack of statistical control results in a variability larger than 6 sigma.

Thus 6 Sigma is valid for statistically stable process and sigma is estimated as

= / d2 R

Standard Deviation (Standard Deviation () :) :

Standard deviation is measure of the of the process output or the of a sampling statistic from the process (eg. Of subgroup averages) denoted by the greek letter (Sigma).

n 2 (Xi – ) i = 1

n

Where,

= Standard deviation, Xi = Observed value

= Average , n = No. of ObservationsX

=

X

spreadspread

IndicesIndices

Tolerance

Process Capability = =

USL - LSL

6 / d2 R

Cp = Potential Capability

The Capability Index is defined as the ratio of the Specification spread or Tolerance to the Process Variation

The capability index is defined as: The capability index is defined as:

The capability index show how well a process is able to meet specifications. The higher the value of the index, the more capable is the process:

•Cp < 1 (process is unsatisfactory)

•1 < Cp < 1.6 ( process is of medium relative capability)

Cp > 1.6 (process shows high relative capability)

Cpk = Achieved CapabilityCpk = Achieved Capability

3 Min of Or

- LSL

3 Cpk =

USL – X X

Where, = / d2 and the actual average is R X

Chart Factor 2 3 4 5 6 7 8 9 10

A2 1.881 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308

F2 1.88 1.187 0.769 0.691 0.549 0.509 0.432 0.412 0.363

d3 0 0 0 0 0 0.076 0.136 0.184 0.223

d4 3.267 2.575 2.282 2.115 2.004 1.924 1.864 1.816 1.777

B3 0 0 0 0 0.03 0.118 0.185 0.239 0.284

B4 3.267 2.568 2.266 2.089 1.97 1.882 1.815 1.761 1.716

d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.97 3.078

Table of factors for computing control chart limitsSubgroup Size

X

X median

R

S

CONSTANT

Inferences based on Cpk :Inferences based on Cpk :

1. Cpk = 2.00 represents a very capable process. Such an index is achieved only when you are able to produce within 50% of tolerance.

2. Cpk = 1.33 is considered to be a minimum capability requirement and most industries demand a Cpk of 1.33 as minimum criterion. This is achieved if you are able to produce 75% of the tolerance.

Inferences based on Cpk :Inferences based on Cpk :

3. Cpk = 1.00 represents a just capable process and the process can give good results only if it is perfectly centered. Even a small deviation from the mid of specification will result in non conformance. Here 100% of the tolerance is used. Not a very desirable solution.

4. Cpk < 1.00 means that the process not capable of meeting the specified tolerance. In this case, rework and rejection will be inevitable.

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