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Quality Control

Definition:

Quality is a measure of how closely a good or service confirms

to specified standard.

Extra quality means extra cost. So, the level of quality shouldbe suitably mixed with other factors such that the product is well

absorbed in the market.

Quality standards may be any one or a combination ofattributes/variables of the product being manufactured. Theattributes will include performance, reliability, appearance,

commitment to delivery time etc.

Variables may be some measurement variables like, length,width, height, diameter, surface finish etc.

Quality assurance is the system of polices, procedures and

guidelines which help in building specified standards ofproduct/service quality.

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NEED FOR CONTROLLING QUALITY

In the absence of quality, the following will result.

- No yardstick for comparing the quality of goods/services.

- Difficulty in maintaining consistency in quality.

- Dissatisfied customers due to increased maintenance and

operating costs of product/services.

- Increased rework cost while manufacturing products/providingservices.

- Reduced life time of the products/services.

- Reduced flexibility with respect to usage of standard spare parts.

Hence, controlling quality is an essential activity.

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DEFINITION OF A QUALITY SYSTEM

A quality system is a process that combines with manufacturing

process to ensure that a manufacturing process produces quality-

perfect products.

The scope of a quality system is more than a manufacturingprocess.

A quality system covers areas related to the suppliers whoproduce parts for the product. It also covers other departments

in the company to ensure that customers are properly

informed, trained and serviced whenever problems arepresented.

Finally, it covers the design department to ensure that productsare designed to specifications and perform as intended.

Strategic areas of quality control program in manufacturing are as

listed below.

- Supplier quality.

- Incoming raw materials quality.

- Process quality.

- Final inspection.

- Customer quality.

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CLASSIFICATION OF QUALITY CONTROL TECHNIQUES

The quality control techniques can be classified as shown below.

Quality Control Techniques

||+----------------------------------------+| || |

Control Charts Acceptance Sampling| |

+-------------------+ +------------------+| | | |

For Variables For Attributes For Variables For Attributes| | | |

_X Chart P chart Plan with a. Single sampling Plan

R Chart C Chart Plan with Double sampling plana & B. Multiple sampling plan

Control charts are used to control in-process quality. Acceptance sampling plans are aimed to control the

quality of incoming raw materials, semi-finished

products and finished products.

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CONTROL CHARTS

Control charts show the performance of a process fromtwo points of view.

First, they show a snap-shot of the process at the momentthe data are collected.

Second, they show the process trend as time progresses. Process trends are important because they help in

identifying the out of control status if actually exists.

Also it helps to detect variations outside the normaloperational limits. They also help to identify the causes of

variations.

||| Upper Control Limit|---------------------------------------------------------|| Central Line

Variable |---------------------------------------------------------|| Lower Control Limit|---------------------------------------------------------||+----------------------------------------------------------

Time (Sample Number)

Generalized Representation of Control Chart

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CONTROL CHARTS FOR VARIABLE

As the name indicates, these chart will use variable dataof a process._

X chart gives an idea of the central tendency of theobservations.

These charts will reveal the variations between sampleobservations.

R chart gives an idea about the spread (dispersion) of theobservations. This chart shows the variations within the

samples._X Chart & R Chart:

The formulas used to establish various

control limits are as follows:_

CONTROL LIMITS FOR X CHART--------------------------

= =Upper control limit, UCL _ = X + 3 _ = X + 3/n0.5

X X

= =Lower control limit, LCL _ = X - 3 _ = X - 3/n0.5

X X_

Where, X = Mean of a sample.

=X = Mean of the sample means.

_ = Sample standard error = /n0.5

X

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CONTROL LIMITS FOR R CHART--------------------------

Upper control limit, UCL = R + 3 RR

Lower control limit, LCL = R - 3 RR

Where, R = Range of a sample observations

= Standard deviation of RR

In practice, the calculations of control limits based onstandard deviation are a cumbersome process.

Hence, they are established using table values (A,B andC) which are used as factors in the formulas to establish

control limits._

Control Limits for X

= _UCL_ = X + A R

X

= _LCL_ = X - A R

X

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Control Limits for R_

UCL = B R

R _LCL = C R

R

Factors of Control Charts---------------------------------------------------------------

Sample Mean Upper Range Lower Rangesize Factor Factor Factorn A B C

---------------------------------------------------------------2 1.88 3.27 0.003 1.02 2.57 0.004 0.73 2.28 0.005 0.58 2.11 0.006 0.48 2.00 0.007 0.42 1.92 0.088 0.37 1.86 0.149 0.34 1.82 0.1810 0.31 1.78 0.2211 0.29 1.74 0.2612 0.27 1.72 0.2813 0.25 1.69 0.3114 0.24 1.67 0.3315 0.22 1.65 0.3516 0.21 1.64 0.3617 0.20 1.62 0.3818 0.19 1.61 0.3919 0.19 1.60 0.4020 0.18 1.59 0.41

--------------------------------------------------------------

SEE EXAMPLE

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CONTROL CHARTS FOR ATTRIBUTES

In many situations, quality measurements are expressed asattributes (good or bad etc. ).

In such situations, the percent defective chart (P-chart) or thenumber of defective per sample area (C-chart) are considered to

be more suitable control charts to control the quality.

Both charts convey a similar type of information but P chart isbased on a normal distribution and the C chart is based on

the poisson distribution.

P Chart

The other name for P-chart is percent defective chart. The purposes of this

chart are summarized below.

To discover the average proportion of non conforming articles or partssubmitted for inspection over a period of time.

To bring to the management attention, if there is any change in averagequality level.

The formulas for control limits are as follows:

_ _ _ 0.5 _UCLp = p + 3 p(1-p)/n = p + 3 rp

_ _ _ 0.5 _LCLp = p - 3 p(1-p)/n = p - 3 rp

where, p = process percent defective of a sample.

= (Number of defective items in a sample)/n

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_

p = Process mean percent defective.

n = Sample size.

k = Number of samples.

p = Standard deviation of percent defectives.

C-CHART

This chart applies to the number of nonconformities in samples ofconstant size.

C is a variable representing the number of nonconformities(defects) in each sample.

Usually, the sample size is considered to be one. The controllimits of this chart are based on poisson distribution.

Some applications of C-chart are listed below.

To control the number of nonconforming rivets in an aircraftwing.

To control the number of imperfections observed in agalvanized sheet.

To control the number of surface imperfections on a largecasting like gear blank which is used to rotate kiln in cement

plants.

To control the number of defects in final assemblies (like, TV,radio, computer, I.C. engines etc).

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The formulas for control limits are given below.

_ _ 0.5

UCLc = c + 3 C

_ _ 0.5LCLc = c 3 C

_where c is the mean number of nonconformities.

Also, this is the central line in the control chart.

ACCEPTANCE SAMPLING

The objective of acceptance sampling is to take decision whether to acceptor reject a lot based on sample's characteristics.

The lot may be incoming raw materials or finished parts. An accurate method to check the quality of lots is to do 100% inspection.

But, 100% inspection will have the following limitations.

The cost of inspection is costly. Destructive testing will result in 100% spoilage of the parts. Time taken for inspection will be too long. When the population is large or infinite, then it would be impossible

or impracticable to inspect each unit.

Hence, acceptance sampling procedure has lot of scope in practical

application.

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Acceptance sampling can be used for attributes as well as variables.

Specifications of a single sampling plan will contain a sample size (n) and

an acceptance number C.

As an example, if we assume the sample size as 50 and the acceptancenumber as 3, the interpretation of the plan is explained as follows: Select a

sample of size 50 from a lot and obtain the number of defective pieces in

the sample.

If the number of defective pieces is less than or equal to 3, then accept thewhole lot from which the sample is drawn.

Otherwise, reject the whole lot. This is called single sampling plan. There are several variations of this

plan.

In this process, one will commit two types of error, namely, type-I error

and type-II error.

If the lot is really good, but based on the sample information, if it isrejected, then the supplier/producer will be penalized. This is called

producer risk or type-I error. The notation for this error is a.

On the other hand, if the lot is really bad, but it is accepted based onthe sample information, then the customer will be at loss. This iscalled consumer's risk or type II error. The notation for this error is B.

So, both parties should jointly decide about the levels of producer's risk (a)and consumer's risk (B) based on mutual agreement.

OPERATING CHARACTERISTIC CURVE (O.C. CURVE)

The concepts of the two types of risk are well explained using an operatingcharacteristic curve.

This curve will provide a basis for selecting alternate sample plans. For a given value of sample size (n), acceptance number (C), the O.C.

curve is shown in figure.

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In the OC curve, percent defective is shown on x-axis. The probability of accepting the lot for a given percent defective is

shown on y-axis.

The value for percent defective indicates the quality level of the lotinspected.

AQL means acceptable quality level. LTPD means lot tolerance percent defectives. These represent quality levels of the lot submitted for inspection. If the quality level of the lot inspected is at AQL or less than AQL,

then the customers are satisfied with the quality of the lot. The

corresponding probability of acceptance is called 1-.

On the other hand, if the quality level is more than or equal to LTPD, thequality of the lot is considered to be inferior from consumer's view

point. The corresponding probability of acceptance of the lot is called .

The quality level in-between AQL and LTPD is called indifferent zone.

So, we require a, B, AQL and LTPD to design a sample plan. Based

on these, one can determine n and C for implementation purpose of the

plan.