7. CHECK SHEETS
Used to keep a record
of the number and type
of discontinuities over a
specified period of time
or within a certain
batch of product.
PARETO CHART
A graphical representation ranking
discontinuities from the most to
least significant. Used to help
brainstorm what discontinuities, if
worked upon first, would be the
most likely to produce the greatest
improvement in quality.
Class Example
Our manufacturing procedure is composed of several steps. Several of these
procedures have lead to discontinuities noticed upon inspection. The steps causing
defectives are as follows:
∀• Caulking 198 defectives
∀• Fitting 25 defectives
∀• Connections 103 defectives
∀• Torque 18 defectives
∀• Gapping 72 defective
A Pareto Diagram will be developed.
8.
9.
10. WHY-WHY DIAGRAMS
A systematic representation of causes of why some
occurrence happens. Used to guide brainstorming sessions.
11.
12. FLOW CHARTS
Flow charts are graphical representations of the steps involved
in a process. Constructing a flow chart helps give a better
understanding of the systems involved.
Process
DecisionData
Process
Process
Terminator
Yes
No
Control
transfer
13. CAUSE AND EFFECT DIAGRAMS (Fishbone Diagram)
Used in brainstorming session to help identify the causes of quality
losses. This diagram is particularly useful after the flow chart and
the Pareto diagrams have been developed.
QUALITY
(Effect)Cause
Step 1:Decide on the quality characteristic {e.g. Reduction of
wobble during machine rotation}
Step 2:Set up the fish bone backbone
Step 3:Identify main factors causing effect {e.g. Workers,
Materials, Inspection, Tools}
Step 4: Add Cause to each branch
14.
15. Benefits of Cause and Effect Diagram
• Making diagram is educational in itself
• Outline relationship
• Note what samples need to be taken
• Guide for discussion
• Causes are actively sought and results written on diagram
• Appropriate data collected - no time wasted
• Shows level of technology
17. CONTROL CHARTS
• Used to test if the process is in control
• Used to see if significant changes have occurred in the
process over time
“Indiscreet” or
“Continuous Data
Chart” or “X-R Chart”
Measurement at time intervals
Measurements compared -
control over time.
Examples:
Length (mm) Volume (cc)
Weight (gm) Power (kwh)
Time (sec) Pressure (psi)
Voltage (v)
“Discrete Data Charts” or
“pn-p charts”
Inspection on lot or batch
Note # good/defective
# of parts inspected in the lot = n
Fraction of defective in lot = p
Number of defectives = pn
18. - R CHART CONSTRUCTIONX
In the manufacturing process for this example parts are being
machined with a nominal diameter of 13 mm. Samples are
taken at the following times of day: 6:00, 10:00, 14:00, 18:00
and 22:00, for 25 consecutive days. The diameter
measurements from these samples are presented on the table in
the next slide.
Class Example
19.
20. Step 1: Collect Data
Step 2: Sort data into subgroups (i.e. lots, order #, days, etc.)
n = size of the subgroup {in this example 5 times per day)
k = number of subgroups {in this example 25 days}
Step 3: Find the mean for each subgroup ( X )
X =
X X X X
n
n1 2 3+ + +.....
Step 4: Find Range for each subgroup ( R )
R = X largest value - X smallest value
21. Step 5: Find Overall Mean ( X )
X =
X X X X
k
k1 2 3+ + +...
Step 6: Find average value of range ( R ) R =
R R R R
k
k1 2 3+ + +...
Step 7: Complete control limits using attached table
For X Control Chart
Central Line - CL = X
Upper Control Limit - UCL = X +A2 R
Lower Control Limit - LCR = X - A2 R
For R Control Chart
Central Line - CL = R
Upper Control Limit - UCL = D4 R
Lower Control Limit - LCR = D3 R
25. P CONTROL CHART CONSTRUCTION
An inspector at the end of the manufacturing line for the
production of car wheel rims, at the end of each shift,
inspects the lot of wheel rims made during that shift. On
good days when the welder is running properly, over 400
wheels are made per batch. On poor days, as low as 50 to 60
wheels are made per batch. The inspector marks on his/her
“check sheet” for each batch the total number of wheels
inspected and the number of defects returned for rework in
each lot.
Class Example
26.
27. Step 1: Collect Data
Step 2: Divide data into subgroups (usually days or lot). Subgroup size should be
greater than 50 units.
n = number in each subgroup
pn = number of defects in each subgroup
Step 3: Compute fraction of defectives (for %, multiply by 100)
p = pn/n
Step 4: Find the Average Fraction of Defectives ( p )
p =
( )
( )
total defectives
total inspected
=
pn
n
∑
∑
Step 5: Compute the Control Limits for each Lot
Central Line CL = p
Upper Control Limit UCL = p + 3
p p
n
( )1−
Lower Control Limit LCR = p - 3
p p
n
( )1−
29. PN CONTROL CHART CONSTRUCTION
Class Example
On an assembly line of windshield wiper motors, the inspector selects
randomly 100 motors per hour to examine. The inspector notes on the
“check sheet” the number of defective motors in each 100 selected.
30. Step 1: Collect Data (lot size set constant)
Step 2: Calculate Values p =
∑
∑
n
pn
CL = p n
UCL = p n + 3 pn p( )1−
LCL = p n - 3 pn p( )1−
Step 3: Plot Chart
