page 18

Sample 1	Sample 2	Sample 3
1.6	0.1	2.7
1.3	2.5	2.7
1.9	2.1	4.9
1.9	3.3	1.5

#2 What problems can be seen in this control chart?

UCL

R

LCL

#3. Draw the Pareto diagram for the data below. The data indicates the number of reported errors made when taking fast food orders by telephone

Operator Tom Dick Harry

Day
Monday	12	8	3
Tuesday	9	7	7
Wednesday	7	9	9
Thursday	8	4	2
Friday	21	9	24
Saturday	28	12	9

3.2 CONTROL CHARTS FOR ATTRIBUTES

******** Clarify section

•ATTRIBUTE - a nonconformity that cannot, or will not be measured

•NONCONFORMITY- A flaw in a product that will not always make it unsellable.

• p-chart (for nonconforming units)

Select attributes, same as if constructing a Pareto chart or using matrix analysis

Select a subgroup size large enough to get a reasonable count

page 19

sub-group		size(n)		nonconform.	proportion
				(np)	(p)
1		10		1	.1
2		20		1	.05
3		30		3	.1
4		30		2	.067
5		30		5	.17
6		30		4	.13
		150		16

Collect Data

∑

np

16

Calculate and

construct chart

p =

=

= 0.11

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

--------

∑

n

150

·

p( 1 – p)

0.3

UCL =

p + 3

0.11 + 3

------------------- =

--------- = 0.19

n

12.4

( 1 –

)

p

p

LCL = p – 3

= 0.03

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

n

(not less than 0)

(*note based on Binomial distribution)

0.19

UCL

p

0.11

0.03

LCL

p-chart

• p-chart control limits can vary if the sample size varies.

page 20

		∑	np
p =
		------------	stays the same
			n							varies for each sample
					± 3		( 1	–		)
UCL, UCL =						p			p
				p
							ni

UCL

p

LCL

• np-chart (nonconforming units) - almost identical to p-chart, except not normalized to 0 to 1 scale, so it is more sensitive to sample size changes, but it is easier to maintain.

UCL

np0

LCL

np =	∑	np	UCL, LCL = np0 ± 3 np0( 1 – p0)
	------------
0	∑	n

p0 - the historical value for fraction nonconforming

•c-chart (for count of nonconformities) - Best used when there is a small number of errors in a huge sample space, and the nonconforming events are independent.

page 21

Select attributes

e.g a pop can,

Serial #

count of

or a sheet of money

nonconformities

as with p-chart

1207

12

13

1321

10

Select a unit to

1352

15

inspect (only 1

1401

13

unit or product is

1425

examined for flaws)

63

Collect Data

∑

c

63

=

12.6

Construct Chart

c = ---------

= -----

n

5

UCL =

+ 3

= 12.6 + 3

12.6 = 24

c

c

LCL =

– 3 12.6

=

**Note based on Poisson distribution

c

24

UCL

12.6

c

0.6

LCL

0

• u-chart - similar to c-chart, except it can handle different sample group sizes (e.g. a rivet department dealing with different sizes of riveted parts).

page 22

		c			∑	c
	=	--		=
					---------
		n			∑	n	UCL, LCL =	±	3 --
									n

UCL

 

LCL

• choosing an attribute chart

	CHART	nonconforming	nonconformities
		units
Sample	constant	np	c (n=1)
size
	constant	p	u
	or varies

READING: chapter 7, pg. 235-273

PROBLEMS: pg 273- #1, 4, 6, 9, 13, 18, 19, 21, 24