chapter 9 attribute control charts

5/19/2018 Chapter 9 Attribute Control Charts

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Quality

Improvement

PowerPoint presentation to accompany

Besterfield, Quality Improvement, 9e

Chapter 9- ControlCharts for Attributes


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Quality Improvement, 9eDale H. Besterfield

2013, 2008 by Pearson Higher Education, Inc

Upper Saddle River, New Jersey 07458 All Rights Reserved

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Outline

Attribute Control Charts for Nonconforming Units

Control Charts for Count of Nonconformities

A Quality Rating System


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Learning Objectives

When you have completed this chapter you should: Know limitations of variable control charts and the different

types of attibute charts.

Know the objectives of the p chart group and the applicable

distribution.

Be able to construct a:

Fraction defective chart- fixed subgroup size

Fraction defective chart-variable subgroup size Percent defective chart

Number defective chart


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Learning Objectives contd.

When you have completed this chapter you should: Know how to minimize the effect of variable

subgroup size.

Know the applications of the c chart group, theapplicable distribution and two conditions.

Be able to construct a c chart and a u chart and

know the difference between them. Know the three classes of defect severity


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The term Attribute refers to those qualitycharacteristics that conform to specifications

or do not conform to specifications.

Attribute are used:1. Where measurements are not possible.

2. Where measurements can be made but are

not made because of time, cost, or need.

Attribute


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A nonconformity is a departure of a qualitycharacteristic from its intended level or state

that occurs with a severity sufficient to cause

an associated product or service not to meet

a specification requirement.

Defect is concerned with satisfying intended

normal, or reasonably foreseeable, usage

requirement.

Attribute


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Defect is appropriate for use when evaluationis in terms of usage.

Nonconformity is appropriate for conformance

to specifications. The term Nonconforming Unitis used to

describe a unit of product or service

containing at least one nonconformity.

Attribute


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Defective is analogous to defect and isappropriate for use when unit of product

or service is evaluated in terms of usage

rather than conformance to specifications.

Limitations of variable control charts:

These charts cannot be used for quality

characteristics which are attributes.

Attribute


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Types of Attribute Charts:1. Nonconforming Units (based on the

Binomial distribution): pchart, npchart.

2. Nonconformities (based on the Poissondistribution): cchart, uchart.

Attribute


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The PChart is used for data that consist of theproportion of the number of occurrences of an

event to the total number of occurrences.

It is used in quality to report the fraction orpercent nonconforming in a product, quality

characteristic, or group of quality characteristics.

The P Chart


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Formula:

The fraction nonconforming, p, is usually small,

say, 0.10 or less.

Because the fraction nonconforming is very

small, the subgroup sizes must be quite largeto produce a meaningful chart.

npp

n

The P Chart


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2013, 2008 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 All Rights Reserved

12

It can be used to control one qualitycharacteristic, as is done with X bar and R chart,

Or to control a group of quality characteristics of

the same type or of the same part, Or to control the entire product.

It can be established to measure the quality

produced by a work center, by a department, by ashift, or by an entire plant.

The P Chart


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It is frequently used to report theperformance of an operator, group of

operators, or management as a means of

evaluating their quality performance.

The subgroup size of the Pchart can be

either variable or constant.

The P Chart


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Objectives of the PChart:1. Determine the average quality level: This

information provides the process

capability in terms of attributes.2. Bring to the attention of management

any changes in the average.

3. Improve the product quality: Ideas forquality improvement.

The P Chart


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Objectives of the PChart contd:4. Evaluate the quality performance of

operating and management personnel.

5. Suggest places to use Xbar and R chart:They are more sensitive to variation.

6. Determine acceptance criteria of a

product before shipment to the customer.

The P Chart


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P-Chart Construction for ConstantSubgroup Size1. Select the quality characteristic(s):

a) Single quality characteristic.

b) Group of quality characteristics.c) A part.

d) An entire product.

e) A number of products.

f) It can be established for performance control of anoperator, work center, department, shift, plant, or

corporation

The P Chart


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PChart Construction for Constant Subgroup Sizecontd.

2. Determine the subgroup size and method:

The size of the subgroup is a function of theproportion nonconforming.

A minimum size of 50 is suggested as a

starting point.

The P Chart


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PChart Construction for Constant Subgroup Sizecontd.

3. Collect the data:

At least 25 subgroups. Different sources (Check sheet).

For each subgroup the proportion

nonconforming is calculated by the formulaP= np/n

The P Chart


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PChart Construction for Constant Subgroup Size4. Calculate the trial central line and the control

limits:

(1 )3

(1 )3

nppn

p pUCL p

n

p pLCL p

n

The P Chart


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FIGURE 9-2 A p Chart to Illustrate the Trial Central Line and

Control Limits Using the Data from Table 9-1


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P Chart Construction for Constant Subgroup Sizecontd.

5. Establish the revised central line and control limits.

0

0 00

0 00

(13

(1 )3

d

new

d

np npp p

n n

p pUCL p

np p

LCL pn

The P Chart


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FIGURE 9-3 Continuing Use of the p Chart for Representative

Values of the Proportion Nonconforming, p


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The PChart is most effective if it is postedwhere operating and quality personnel can

view it.

The control limits are usually three standarddeviations from the central value. Therefore,

approximately 99% of the plotted points, P,

will fall between the upper and lower control

limits.

The P Chart


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A PChart will also indicate long-rangetrends in quality, which will help to

evaluate changes in personnel, methods,

equipment, tooling, materials, and

inspection techniques.

P-chart is based on the binomial

distribution.

The P Chart


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FIGURE 9-4 Various Techniques for Presenting p -Chart Information


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PChart Construction for Variable Subgroup Size1. Collect the data.

2. Determine the trial central line and control

limits: Since the subgroup size changes eachday, limits must be calculated for each day.

The P Chart


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FIGURE 9-5 Preliminary Data, CentralLine, and Trial Control Limits

FIGURE 9-5 Preliminary Data, Central Line, and Trial Control Limits


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PChart Construction for Variable Subgroup Sizecontd.

2. As the subgroup size gets larger, the control

limits are closer together.3. Establish revised central line and control limits:

The P Chart


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If Pois known, the process of data collection

and trial control limits is not necessary. Pis the proportion (fraction) nonconforming

in a single subgroup.

Pbar is the average proportion (fraction)nonconforming of many subgroups.

The P Chart


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Pois the standard or reference value of the

proportion (fraction) nonconforming based

on the best estimate of PBar.

is the population proportion (fraction)

nonconforming.

The P Chart


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Minimizing the Effect of Variable Subgroup Size1. Control limits for an average subgroup size: By

using an average subgroup size, one limit can

be calculated and placed on the control chart.

0 00

0 00

(13

(1 )3

av

av

av

nn

g

p pUCL pn

p pLCL p

n

The P Chart


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FIGURE 9-7 Chart for May Data Illustrating Use of an

Average Subgroup Size


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Minimizing the Effect of Variable Subgroup Size contd.Case I:This case occurs when a point (subgroup

fraction nonconforming) falls inside the limits and

its subgroup size is smaller than the average

subgroup size.

Case II: This case occurs when a point (subgroup

fraction nonconforming) falls inside the average

limits and its subgroup size is larger than the

average subgroup size.

The P Chart


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Minimizing the Effect of Variable Subgroup Size contd.Case III:This case occurs when a point (subgroup

fraction nonconforming) falls outside the limits and

its subgroup size is larger than the average

subgroup size.

Case IV: This case occurs when a point (subgroup

fraction nonconforming) falls outside limits and its

subgroup size is less than the average subgroup

size.

The P Chart


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FIGURE 9-8 p Chart Illustrating Central Line and Control

Limits for Different Subgroup Sizes


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Number Nonconforming Chart (np): The np chart is easier for operating personnel

to understand than the pchart.

The limitation that this chart has is that thesubgroup size needs to be constant.

The np Chart


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0

0 0 0

Central Line =

Control Limits = 3 (1 )

np

np np p

The np Chart


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Number Nonconforming Chart (np): If the fraction nonconforming pois unknown,

then it must be determine by collecting data,

calculating trial control limits, and obtaining

the best estimate of po.

The np Chart


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FIGURE 9-9 Number Nonconforming Chart ( np Chart)


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For an attribute this process is much simpler. The process capability is the central line of

the control chart.

Management is responsible for the capability. When the plotted point is outside the control

limit, operating personnel are usually

responsible.

Process Capability


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FIGURE 9-10 Process Capability Explanation and Responsibility


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The nonconformities chart controls the count

of nonconformities within the product or

service. An item is classified as a nonconforming unit

whether it has one or many nonconformities.

Count of nonconformities (c) chart. Count of nonconformities per unit (u) chart.

Control Charts for Count of Non-conformities

l h f f


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Since these charts are based on the Poisson

distribution, two conditions must be met:

1. The average count of nonconformitiesmust be much less than the total possible

count of nonconformities.

2. The occurrences are independent.


C l Ch f C f


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Objectives:

1. Determine the average quality level: This

information gives the initial process capability.2. Bring to the attention of management any

changes in the average.

3. Improve the product quality: Ideas for qualityimprovement.


C l Ch f C f


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Objectives contd.:

4. Evaluate the quality performance of

operating and management personnel.5. Suggest places to use Xbar and R chart.

6. Determine acceptance criteria of a

product before shipment to the customer.


C t l Ch t f C t f N


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C Chart construction:

1. Select the quality characteristic(s):

a) Single quality characteristic.

b) Group of quality characteristics.c) A part.

d) An entire product.

e)

A number of products.f) It can be established for performance control of

an: operator, work center, department, shift, plant,

or corporation




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C Chart construction contd:

2. Determine the subgroup size and method:

3. Collect the data: At least 25 subgroups.

Different sources.




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c-Chart Construction contd:

4. Calculate the trial central line and the control

limits:

3

3

cc

g

UCL c c

LCL c c



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FIGURE 9-11 Control Chart for Count of Nonconformities ( c Chart), Using

Preliminary Data



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5. Establish the revised central line and control

limits

dnew 0

d

0 0

0 0

c - cc = c =

g - g

UCL = c + 3 c

LCL = c - 3 c



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6.Achieve the objectives: The reason for thecontrol chart is to achieve one or more of the

previously stated objectives.


C chart construction contd:



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Chart for Count of Nonconformities/Unit (uChart)

3

3

ccu u

n n

uUCL u

n

uLCL u

n

Control Charts for Count of Non-conformities/Unit


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FIGURE 9-13 u Chart for Errors on Waybills

Cont ol Cha ts fo Co nt of Non


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Chart for Count of Nonconformities/Unit

(uChart)

Scale selected is continuous for the uchart.

For the cchart is discrete.

Subgroup size for the uchart can vary. For

the cchart is 1.

The uchart is limited in that we do not

know the location of the nonconformities.


A Q lit R ti S t


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Nonconformity Classification:

1. Critical nonconformities: Unsafe conditions for

individuals using, maintaining, or depending upon the

product.

2. Major nonconformities: Result in failure or reducematerially the usability of the product for its intended

purpose.

3. Minor nonconformities: Reduce materially the usability

of the product for its intended purpose.

A Quality Rating System

Control Charts for Demerits/Unit


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0 0 0 0

2 2 20 0 0 0

0 0

0 0

, 9, 3 1

9 3 1

9 3 1

9 3 1

3

3

c c ma ma mi mi

c ma mi

c ma mi

c ma mi

u c ma mi

u

u

D w u w u w u

when w w and w are and

D u u u

D u u u

u u u

UCL D

LCL D

Control Charts for Demerits/Unit


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FIGURE 9-16 Demerit-Per-Unit Chart ( D Chart)

Control Chart Selection


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Quality Characteristic

Variable Attribute

n>1?

n>=10?

x and MRno

yes

x and s

x and Rno

yes

Defective Defect

constantsample

size?

p-chart withvariable sample

size

no

p or

np

yes SamplingUnit one

c u

yes no

Control Chart Selection

Comp te P og am


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Computer Program

EXCEL program files on the website willsolve for:

p chart

np chart

c chart U chart

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chapter 9 attribute control charts

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