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PPT – Introduction to Statistical Quality Control, 5th edition PowerPoint presentation | free to download - id: 679f73-YTMzY

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Learning Objectives

P Control Chart

- The most versatile and widely used attributes

control chart - -- used when the subgroup size is not constant
- Used to evaluate fraction defective
- Control limits are based on Binomial Distribution

P Control Chart

P CONTROL CHART ALCAS PEFLOW SOLDER MACHINE

90 80 70 60 50 40 30 20 10 0

PERCENT DEFECTIVE

UCL PERCENT

2 4 6 8

10 12 14 16 18 20

22 24 26

SUBGROUP NUMBER

P Chart

- Compute the control limits
- The UCL and LCL are not straight lines, they rise

and fall with respect to the subgroup size

The P Chart

- When to use
- Only when variable data cannot be obtained.
- When charting fraction rejected as nonconforming

from a varying sample size. - When screening multiple characteristics for

potential monitoring on variable control charts. - When tracking the quality level of a process

before any rework is performed.

The P Chart

- How
- By counting the number of defective items from a

sample and then plotting the percent that are

defective. - Conditions
- In order to be of help, there should be some

rejects in each observed sample. - The higher the quality level, the larger the

sample size must be to contain rejects. For

example, if 20 of a product is rejectable, a

sample size of 5 will be needed. However, a

sample of 1,000 will give an average of only one

reject per sample if 0.1 of the product is

rejectable.

The P Chart

Table 1 Formulas for the P Chart

Chart Control limits Centerline Plot point Sample size

p Varying

The P Chart

- To calculate Plot Points
- The p plot point is the fraction defective in a

sample. The centerline is the average fraction

defective in series of samples. Figure 1 is a

cross section showing countersunk holes for rivet

installation.

The P Chart

- To calculate Plot Points
- In a sheet metal assembly shop a common process

is bucking rivets. Because of the combined

variation in the rivets, the drilled holes, and

the bucking process, there are quality problems.

After the rivets in an assembly have been bucked

into place they are checked for nonconformity. A

P chart is used to track the first-time-through

fraction defective.

Figure 1

- Cross section of sheet metal plates with

countersunk holes for rivet installation

P Chart

P Chart

TOTALS

X Relay

Fluorocarbon Leak Test

NP Control Chart

- Number of defectives
- Used when subgroup size is constant (n)
- The actual number of defects is represented by pn

(or np)

NP Control Chart

- NP Control Chart plating defects of assembled

parts

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

UCL

2 4 6 8 10 12 14 16 18 20

22 24 26 28 30

LOT NUMBER

NP Control Charts

- Computations
- Control limits are based on the Binomial

Distribution - 1) Central line
- 2)
- 3)

NP Charts

4 Steps in control chat for Fraction Rejected

- I Preparatory Decisions
- II Starting the control chart
- III Continuing the control chart
- IV Reports and Action based on control chart

I. Preparatory Decisions

- Purpose
- Select Quality Characteristic
- Selection of subgroup
- P or NP chart
- Control limit calculated

II. Starting the control chart

- Recording data
- , Calculation
- Trial limits
- Plotting points

III Continuing the control chart

- Selection of P0
- Calculation of control limits
- Plotting the points/limits
- Interpretation of lack of control
- Periodic Review/Revision of Pi

IV Reports and Action based on control chart

- Action to bring process into control-Pareto, high

spot/low spot. - Review of Design and specification
- Information to Management(Quality level)
- Sensitivity of p chart 0.1 requires 1000s

Example of Attribute control chart

LOT Number inspecting Number of defectives P

1 500 27 0.054

2 50 12 0.240

3 800 12 0.015

4 100 14 0.140

5 150 15 0.100

Total 1600 80

Example of Attribute Control Chart

Subgroup Subgroup Size n of Defectives Percent Defective P () UCL() LCL

1 115 15 13.0 17.7 1.

2 220 18 8.2 15.4 3.

3 210 23 10.9 15.6 3.

4 220 22 10.0 15.4 3.

5 255 18 7.0 15.0 4.

6 365 15 4.1 4.

7 255 44 15.0 4.

8 300 13 4.3 4.

9 280 33 11.7 14.8

10 330 42 12.7 14..3

Total 2550 243

- Purpose of maintaining attribute charts is to

continuously improve the processes for defect

free production by highlighting the key problems. - How to work on getting desirable pattern
- Recommend working on 3 top problems for the day

or week of month as the time permits and solve by

a systematic problem solving method namely - Define problems
- Find key causes
- Solution to cure the key causes demonstrated by

statistics

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Design of the Fraction Nonconforming Chart

- Three parameters must be specified
- The sample size
- The frequency of sampling
- The width of the control limits
- Common to base chart on 100 inspection of all

process output over time - Rational subgroups may also play role in

determining sampling frequency

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Average sample size approach

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Charts for Nonconformities

C cart and U chart

- Often times there is interest in knowing how many

defects an item has - -- C charts total number of nonconformities

in subgroups of fixed size (defects per square

yard of cloth) - -- U charts average number of nonconformities

per unit (defects per TV set)

Charts for Nonconformities

- Used during inspection of complex assemblies
- Control limits based on Poisson Distribution

C Control Chart

- UCL and LCL are straight lines because of fixed

sample sizes - CL
- UCL
- LCL
- Where is the central line and equal to

The data in table 2 represent the types of

defects found on the first two boxes. Box 1 has

nine defects and box 2 has twelve. Notice that

the types and quantity of defects are different

for the two boxes nevertheless, the total number

of defects is plotted on the C chart.

Note A C chart (as well as any other attribute

chart) should only be used when there is

absolutely no way to obtain variable data from

the characteristic in which measurable data is

available. To get started, this data can be

analyzed on an attribute chart to get ideas

(using the Pareto analysis) on the

characteristics.

U Control Chart

- As the subgroup size varies, UCL and LCL varies
- CL
- UCL
- LCL
- where is the central line and equal to

The U Chart

- When to use
- Only when variable data cannot be obtained.
- When plotting the average number of defects found

per unit. - When screening multiple characteristics for

potential monitoring on variable control charts. - How
- Each unit is examined and the average number of

defects found are plotted.

The U Chart

- Conditions
- Constant unit size, but any convenient number of

units per plot point. Unit size is different from

samples size. For example, one unit could be

defined as 1 square-foot of material. - On a particular day, 12.3 square-feet of material

is inspected. The plot point would represent the

average number of defects per unit, but the - sample size would be 12.3.

The U Chart

- There are potentially several different types of

defects per unit, but none of which would

necessarily render the part a defective. - For example paint blemishes on a skin panel, or

various electrical faults on a circuit board. A

unit can be single part, an assembly of several

parts, an area of material, or any rational

grouping in which the likelihood of defect(s) is

constant from - unit to unit.

- In order for this type of analysis to be of help,

there should be some defects in each observed

unit.

The U Chart

- To Calculate Plot Points
- The u plot point is the average number of defects

per unit in a sample of n units. The centerline

is the average of all the plot points on the

chart. Figure 6-17 shows a roll of composite

material/dyed cloth with potential multiple - defects.

The U Chart

- Composite materials are generally made up of

several layers of materials that are bonded to

form the desired characteristics. - Prior to lay up, are used each day, the number of

rolls inspected for defects. Since different

amounts of the material are used each day, the

number of rolls inspected also changes - daily.

Attribute Control Charts

Chart type Names/remarks Central line Control Limits

Fraction defective

Number defectives

Number of defects per subgroup

Number of defects per inspection unit

Attribute data

Variable data

Ngt50 N not constant Fraction defective

X-bar chart R chart

P chart

nlt6

Ngt50 N is constant Fraction defective

X-bar chart S chart

ngt6

np chart

ngt25

n?1 n not constant Defects per unit

X-bar chart S2 chart

u chart

n1

n?1 Is constant Defects per unit

Individual chart

c chart

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Low Defect Levels

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Actions taken to improve a process

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Learning Objectives