Quality Control

By

V.Bhanu Chander

Basic Definitions

1.Statistics : It is a process of collection, grouping

and analysis of a group of data, making it useful for some

future applications.

2.Control : Process by means of which we observe

the actual performance and compare it with some

standard. If there is any deviation, then it is necessary to

make corrective action.

3. Quality : Quality can be defined in a number of ways. Major definitions are based on the following concepts

Fitness for purpose

Conformance to requirements

Grade

Degree of performance

Degree of excellence

Measure of fulfillment of promises

Meeting customer needs

About Quality : Quality is generally used with reference to the end use of the product. The quality depends on the perception of a person in a given situation. A product can be said to possess good quality if the following requirements are properly balanced while designing and manufacturing it

1.Suitability

2.Reliability

3.Durability

4.Safe and foolproof workability

5. Affordability

6. Maintainability

7. Aesthetic look

8. Satisfaction to customers

9. Economical

10. VersatilityFactors affecting quality : Quality can be asserted if we answer to the five questions: what, why, when, where and whom, combining with how. This are termed as 5W-H factors.

Whom factors (W5)1.Responsibility2.Management

Why factors (W1)1.Market compellations2.Product complexities

How factors (H) 1.Information system

Where factors (W4)1.Shop floor2. Point of delivery

What factors (W2)1.Money2.Men3.machines

When factors (W3)1. All the time

5W-H factor description

Product Quality cycle is shown below

Customer

Marketing

Product Engg.

Purchasing

Manufacturing Engg.

Manufacture

Inspection and Testing

Package and shipping

Product service

Quality Product

Quality Control (QC):

Quality control is the process through which we measure the

actual quality performance, compare it with the standards and take

corrective action if there is a deviations.

It is a system, plan or method of approach to the solution of

quality problems.

It is also the tools, devices or skills through which quality

functions

A QC system performs inspection, testing and analysis to

ensure that the quality of the products produced is as per the laid

down quality standards

Inspection should not be confused with quality

control. Inspection means checking of material, product or

components of product at various stages, with reference to

certain pre-determined factors and detecting and sorting out

the faulty or defective items.

Quality control involves inspection at particular

stage. In QC activity, the emphasis is placed on the quality of

the past production.

Objectives of Quality Control : To

1.Improve the company’s income

2.Reduce company’s cost

3.Achieve interchangeability of manufacturing

4.Produce optimum quality at minimum time

5.Ensure satisfaction of customers

6.Make inspection prompt to ensure quality control at proper

stages to ensure production of non-defective products.

7.Judging the conformity of the process to the established

standards and taking suitable action when there are deviations

8. To improve quality and productivity by process control,

experimentation and customers feedback

9. Develop procedure for good vendor-vendee relations

10.Develop quality consciousness in the organization

Statistical Quality Control (SQC) :

A QC system is said to be SQC when statistical

techniques are employed to control, improve and maintain quality

or to solve quality problems. SQC is Systematic as compared to

guess-work of haphazard process inspection.

SQC consists of three general activities :

1.Systematic collection and graphic recording of accurate data

2.Analyzing the data

3.Practical Engg. or management action, if the information

obtained indicates significant deviations from the specified

limits.The following are the tools of SQC1.Frequency distribution2.Control chart3.Acceptance sampling4.Analysis of the data

Benefits of SQC :

Efficiency- SQC ensures rapid and efficient inspection at a

minimum cost

Reduction of scrap, Easy detection of faults

Adherence to specifications

Increases output, reduces wasted machine and man hour

Efficient utilization of personnel, machines and materials

resulting in higher productivity

Better customer relations

Elimination of bottlenecks in the process of manufacturing

Creating quality awareness in employees

Sources of quality variation

• Raw materials

• In-process

• Packaging material

• labeling

• Finished product variables

Steps of QC :• Material qc• In process qc• Product qc• Specifications and tests for – active ingredients – Excipients – Product itself – Stability procedures – Freedom from microbial contamination – Storage and labeling – Containers• Provision for cross referencing

Control of quality variation

• Can be done by

– Raw material control

– In-process items control

– Packaging materials control

– Label control

– Finished product control

Quality Costs :

1.Cost of prevention

2.Cost of appraisal

3.Cost of material failure

4.Cost of external failures

Control Charts

Definition :

A control chart is a graphical representation of the

collected information. The information may pertain to measured

quality characteristics or judged quality characteristics of

samples. Thus it is an important aid or statistical device used for

the study and control of the repetitive processes.

It detects the variations in processing and warns if

there is any departure from the specified tolerance limits. With the

help of CC it is possible to find out the natural capability of a

production process, which permits better decisions on engg.

Tolerances and other fields.

In other words CC is a device which specifies

the state of statistical control, second a device for attaining

statistical control, and third, a device to judge whether statistical

control has been attained.

The CC which are most commonly used are:

1.CC for measurable quality characteristics (CC for Variables). This

includes X bar and R charts and charts for X bar and σ

2.CC for fraction defective (P-chart)

3.CC for number of defects per units (C-chart)

SQC Charts1.Variables2.Attributes--Variables 1. X bar chart 2. R bar chart 3. X bar and S chart 4. X bar and μ chart--Attributes 1. P chart a. Fraction rejected as non conforming units 2. np chart a. No. of non conforming units 3. C chart a. No. of nonconformities 4. V chart a. No. of non conformities per unit

X bar shows the centering of the process, i.e. it shows the

variations in the averages of samples. It is most commonly

used variable chart.

R-chart shows the uniformity or consistency of the

process, i.e. it shows the variations in the ranges of the

samples. It is a chart for measure of spread.

σ –chart shows the variation of the process.

P- chart is an attribute control chart.

Need for Control of Both Mean and Variability

The number of nonconforming product is dependent on both mean

shift and larger variation

Normal mean and variance

Larger mean and normal variance

normal mean and larger variance

Mean is monitored by X bar chart• Variability is monitored by either S chart (standard deviation) or R chart (range)

Review of the Basic Model of Control Charts

Let w be a sample statistic that measures some quality

characteristic of interest, and suppose that the mean of w is μw

and the standard deviation of w is σw. Then the center line, the

upper control limit, and the lower control limit become

UCL = μw + k σw

Center line = μw

LCL = μw - k σw

where k is the "distance" of the control limits from the center line,

expressed in standard deviation units

Control Chart for X bar and R— Known μ,σ- Statistical Basis of the Charts

1. suppose {xij, i=1,…,m, j=1,…,n} are normally distributed with

xij,~N(μ,σ2), thus,

2. X bar chart monitors between-sample variability (variability

over

time) and R chart measures within-sample variability

(instantaneous variability at a given time)

3. If μ and σ are known, X bar chart is

μ+3σx‾ => μ+3σ/sqrt(n) => μ+Aσ

X ~ N(μ,(σ / n )2 )

UCL = μ + Aσ Center line = μ LCL = μ - Aσ

A = 3/sqrt(n)

Control Chart for X bar and R — Known μ, σ ( Cont’s)

Range Ri=max(xij)-min(xij) for j=1,..n

If μ and σ are known, the statistical basis of R charts is as

follows:

Define the relative range W=R/σ. The parameters of the

distribution of W are a function of the sample size

Denote μW =E(W)=d2, σW =d3,

a. (d2 and d3, are given in Tables)

μR =d2σ, σR=d3 σ, which are obtained based on R=W σ

R chart control limits

Contd…

μ ± 3σ ⇒ d2 σ ± 3d3 σ ⇒ (d2 ± 3d3 )σ

UCL = D1 σ

Center line = d2 μ

LCL = D2σD1 = d2 – 3d3D2 = d2 + 3d3

Interpretation of X bar and R Chart

First check the R chart and eliminate the assignable causes

from R chart, and then check the X bar chart

Check non-random pattern

1. Cyclic pattern due to temperature, regular rotation of

operators or machines, maintenance schedules, tool wear

2. Mixture pattern when the plotted points tend to fall near or

slightly outside the control limits. Two overlapping

distributions are resulted from too often process adjustment.

.

3. Shift in process level due to introduction of new workers,

methods, materials, or inspection standard.

4. Trend pattern due to gradual tool wear.

5. Stratification pattern for the points to cluster around the

center line due to incorrect calculation of Control limits or

inappropriate reasonable sampling group

Application Conditions of X bar and R chart

1.Underlying distribution of the quality characteristics is normal

a. X bar chart is more robust to non normality than R chart

b. samples of 4 or 5 are sufficient to ensure reasonable

robustness to the normality assumption for X bar chart

2. Calculation accuracy of Type I error is dependent on the

distribution

3. X bar chart (n=4, 5, 6) is not effective to detect a small mean

shift (less than 1.5 σ) on the first sample following the shift

4. R chart is insensitive to small or moderate shifts (σ1/σ0 <2.5) for

the sample size of n=4, 5, or 6. If n>10, a s chart should be used

instead of a R chart

Revisit Example: Sample Thread Pitch Diameter DataAircraft Fittings (Thread Pitch Diameter)5 items sampled each hourValues in .0001 inches excess of 0.4000 in.Sample Avg. R 1 36 35 34 33 32 34.0 4 2 31 31 34 32 30 31.6 4 3 30 30 32 30 32 30.8 2 4 32 33 33 32 35 33.0 3 5 32 34 37 37 35 35.0 5 6 32 32 31 33 33 32.2 2 7 33 33 36 32 31 33.0 5 8 23 33 36 35 36 32.6 13 9 43 36 35 24 31 33.8 19

10 36 35 36 41 41 37.8 6 11 34 38 35 34 38 35.8 4 12 36 38 39 39 40 38.4 4 13 36 40 35 26 33 34.0 14 14 36 35 37 34 33 35.0 4 15 30 37 33 34 35 33.8 7 16 28 31 33 33 33 31.6 5 17 33 30 34 33 35 33.0 5 18 27 28 29 27 30 28.2 3 19 35 36 29 27 32 31.8 9 20 33 35 35 39 36 35.6 6 33.6 6.2

Out of control

Out of control

CL

UCL

LCL

X bar chart

Out of control

CL

UCL

LCL

R BAR CHART

CL

UCL

LCL

Revised X bar chart

CL

UCL

LCL

Revised R BAR CHART

References :

1.Quality control- A practical approach- Basterfield H.Dale2.Statistical Quality Control- M.Mahajan3.SQC – Grant E.L4.SQC – R.C.Gupta5.Fundamentals of QC and improvement- Amitava Mitra