Lesson 7.1

Quality Control

Today we will learn to…> use quality control charts to determine if a manufacturing process is out of control

A business hires someone to be in charge of “quality control”to ensure that they produce a

quality product.

X Charts

The X Chart is used to analyze the means

of measured values to determine if a quality product

is being produced.

R chartsThe R Chart is used to

analyze the ranges of measured values to

determine if the manufacturing process is consistent.

Step 1 – compute the mean and range of each sample

Step 3 – compute upper and lower control limits

Step 2 – compute the Grand Mean ( XGM ) and the mean of the ranges (R)

Step 4 – plot control charts

Step 5 – analyze the charts

LCLx

UCLx

XGM

control chart for a process that is in control

LCLx

UCLx

XGM

control chart for a process that is out of control

Two types of variation that can occur in manufacturing process:

1) chance variation – random problem & cannot be eliminated entirely2) assignable-cause variation – not random & must be eliminated to maintain quality of product

Why is a process out of control?

A manufacturer of rope tests the breaking strength of 6 samples of 5 ropes.

Sample Breaking Strength (pounds)

1 46 47 45 46 47

2 50 51 52 53 49

3 48 51 50 50 49

4 52 50 49 50 51

5 51 47 46 48 47

6 49 51 50 51 52

51

50

50

4851

243

3

5

3

Step 1 –

46

X R

mean & range of samples n = 5

XGM = 49.3 3.33 R =

49

3

Step 2 – the mean of the means

the mean of the ranges

Step 3 –

A is a constant obtained from the Quality Control Table where n is the

number of items in one sample.

UCLx = XGM + A R

LCLx = XGM – A R

compute the upper control limit and the lower control limit

Step 3 – compute the upper control limit and the lower control limit

49 + (0.577)(3) = 50.7

49 - (0.577)(3) = 47.3

Step 4 –

51

47

UCLx = XGM + A R

LCLx = XGM – A R

draw the chart

the quality is out of control

=49XGM

=51 UCLx

=47LCLx

1 2 3 4 5 6

52515049484746

X Chart

Step 3 –

D4 and D3 are constants obtained from the Quality Control Table where n is the

number of items in one sample.

UCLR = D4R

LCLR = D3R

compute the upper control limit and the lower control limit

UCLR = D4R

LCLR = D3R

n = D4 =

R = D3 =

(2.115)(3) =

(0)(3) =

5

3

2.115

0

6.345

0

Step 4 – draw the chart

6

The process is consistent!

= 3R

=6.3UCLR

=0LCLR 1 2 3 4 5 6

76543210

R chart

A battery is designed to last for 200 hours. Ten samples of six

batteries each were selected and tested. Construct and analyze a

quality control X chart for the data.

n = 6

Sample X R1 200.2 3.1

2 198.9 0.8

3 199.3 2.24 201.1 1.0

5 200.8 3.6

6 201.3 2.3

7 202.6 1.4

8 203.7 2.2

9 205.6 2.3

10 206.1 2.4

Battery Tests

XGM = 201.96

2.1R =

202.0

How is this chart different from the first

chart?

Step 3 – compute the upper control limit and the lower

control limit

UCLx = XGM + A R

LCLx = XGM – A R

202 + (0.483)(2.1) = 203

201202 - (0.483)(2.1) =

n = 6A = 0.483

XGM =

2.1R =

202.0

The battery performance is

=202XGM

=203UCLx

=201LCLx

1 2 3 4 5 6 7 8 9 10

206 205204203202201200199198

out of control (not consistent)

R chart

X charts

R charts

In control

Out of control

In control

Out of control

quality is consistent

quality is NOT consistent

quality of product is acceptable

quality of product is NOT acceptable

Lesson 7.2

Quality Control

Today we will learn to…> use quality control charts to determine if a manufacturing process is out of control

X chart R chart Analysis?

In control In control

In controlOut of control

Out of control

In control

Out of control

Out of control

Product quality acceptable, manufacturing process

consistent

Product quality acceptable, manufacturing process

not consistentProduct quality not

acceptable, manufacturing process consistentProduct quality not

acceptable, manufacturing process not consistent

Lesson 7.3Attribute Charts

Today we will learn to…> use attribute charts to determine if

a manufacturing process is out of control

Attribute Charts are used to determine if manufactured items

are within the acceptable limits of defects.

When manufacturing items, there is always some level of “acceptable” defects.

Two types of charts are used to measure attributes.

p charts and c charts

The c chart is used to analyze the quality of and item by counting the

number of defects per item

The p chart is used to analyze the percent of defects per sample.

A company manufactures ball point pens. Five samples of 50 pens each are selected, and the number of defective pens in each sample is recorded.

n = 50

Sample Size# of

defective pens

%1 50 32 50 13 50 44 50 25 50 5

0.060.02

0.040.08

0.10

Step 1 – find proportion of defective parts for each sample

Step 2 – find the mean for the proportions of defective parts

p = 0.06 + 0.02 + 0.08 + 0.04 + 0.10

5

p = 0.06

n = 50

Step 3 – find the UCLp and LCLp

UCLp = p + 3

p (1 – p )

n

p (1 – p )

n LCLp = p – 3

♪♫ Memories ♪♫

-3σ -2σ -1σ +1σ +2σ +3σ

Step 3 – find the UCLp and LCLp

UCLp =0.06 (1 – 0.06 )

50 0.06 + 3

LCLp =0.06 (1 – 0.06 )

50 0.06 – 3

UCLp =

LCLp =

0.16

– 0.042

Since proportions cannot be negative, we use zero.

= 0

=0.16

= 0.06

=0

p

UCLp

LCLp 1 2 3 4 5

0.160.140.120.100.080.060.040.020

The number of defects per sample is acceptable.

Step 4 – Draw the p chart

Calculators are manufactured and checked for defects. Twelve of the defective calculators are checked for the number of defects per calculator. The defects might include soldering, lettering, cracked cases, and memory error.

The number of defects per calculator are: 6, 3, 2, 5, 6, 7, 4, 3, 7, 8, 9, 5

Step 1 – find the average number of defects per item, c.

c = 65 12 = 5.42

5

Step 2 – Find UCLc and LCLc

=

=

UCLc = c + 3 c

LCLc = c – 3 c

11.7

– 1.71 = 0

Since proportions cannot be negative, zero is used.

12

= 12

= 5

= 0

c

UCLc

LCLc1 2 3 4 5 6 7 8 9 10 11 12

121086420

Since all points fall within the limits, The number of defects per calculator is

acceptable.

Step 3 – Draw the c chart

p charts

c charts

In control

Out of control

In control

Out of control

% of defective products is acceptable

% of defective products NOT acceptable

# of defects per item is acceptable# of defects per item is NOT acceptable