5. spc control charts

QUALITY TOOLS &
TECHNIQUES
By: -
Hakeem–Ur–Rehman
Certified Six Sigma Black Belt (SQII – Singapore)
IRCA (UK) Lead Auditor ISO 9001
MS–Total Quality Management (P.U.)
MSc (Information & Operations Management) (P.U.)
IQTM–PU
1
TQ T
STATISTICAL PROCESS CONTROL
CONTROL CHARTS

Focus of Six Sigma and Use of SPC
2
Y=F(x)
To get results, should we focus our behavior on the Y or X?
Y
Dependent
Output
Effect
Symptom
Monitor
X1 . . . XN
Independent
Input
Cause
Problem
Control
If we find the “vital few” X’s, first consider using SPC on the
X’s to achieve a desired Y?

VARIATIONS
3
 The Devil is in the Deviations. No two things can ever be made
exactly alike, just like no two things are alike in nature.
 Variation cannot be avoided in life! Every process has variation. Every
measurement. Every sample!
We can’t eliminate all variations but we can control them!

INTRODUCTION TO SPC
 In 1924, Shewhart applied the terms of "assignable-
cause" and "chance-cause" variation and introduced the
"control chart" as a tool for distinguishing between the
two.
 Shewhart stressed that bringing a production process
into a state of "statistical control", where there is only
chance-cause variation, and keeping it in control, is
necessary to predict future output and to manage a
process economically.
 Central to an SPC program are the following:
 Understand the causes of variability:
 Shewhart found two basic causes of variability:
 Chance causes of variability
 Assignable causes of variability
4

CommonCause Vs SpecialCause Variability
5
COMMON CAUSE ATTRIBUTES SPECIAL CAUSE ATTRIBUTES
Generally small variability in each
measurement due to “natural”
reasons. Common cause issues result in
minor fluctuations in the data
Generally larger variability in each
measurement due to “unnatural”
reasons. A cause can be assigned for the
fluctuations in the data.
Common cause = chance cause =
statistical control = stable & predictable =
natural pattern of variability = variability
inside the historical experience base
Special causes = assignable causes =
systemic causes = unstable & erratic =
unnatural pattern of variability =
variability outside the historical
experience base
Common cause variability is
institutionalized and accepted as “that’s
the way things are”
Special cause variability are sore thumbs
that standout and are fixable. They are
big surprises. They are “exceptions to
that’s the way things are”
When the reason for common cause
variability is identified, it becomes
special causes
Many small special causes are
identifiable but may be treated as
uneconomical to correct or control

CommonCause Vs SpecialCause Variability
6
COMMON CAUSE ATTRIBUTES SPECIAL CAUSE ATTRIBUTES
Wikipedia gives the following 16 item list
for common cause variability:
1. Inappropriate procedures
2. Incompetent employees
3. Insufficient training
4. Poor design
5. Poor maintenance of machines
6. Lack of clearly defined standing
operating procedures (SOPs)
7. Poor working conditions, e.g. lighting,
noise, dirt, temperature, ventilation
8. Machines not suited to the job
9. Substandard raw materials
10. Assurement Error
11. Quality control error
12. Vibration in industrial processes
13. Ambient temperature and humidity
14. Normal wear and tear
15. Variability in settings
16. Computer response time
Wikipedia gives the following 11 item list
for special cause variability:
1. Poor adjustment of equipment
2. Operator falls asleep
3. Faulty controllers
4. Machine malfunction
5. Computer crashes
6. Poor batch of raw material
7. Power surges
8. High healthcare demand from elderly
people
9. Abnormal traffic (click-fraud) on web
ads
10. Extremely long lab testing turnover
time due to switching to a new
computer system
11. Operator absent

Objectives of SPC Charts
 All control charts have one primary purpose!
 To detect assignable causes of variation that cause
significant process shift, so that:
 investigation and corrective action may be undertaken
to rid the process of the assignable causes of variation
before too many nonconforming units are produced.
 In other words, to keep the process in statistical control.
 The following are secondary objectives or direct benefits
of the primary objective:
 To reduce variability in a process.
 To Help the process perform consistently & predictably.
 To help estimate the parameters of a process and
establish its process capability.
7

SPCCharts provides
 Developed by Dr Walter A. Shewhart of Bell Laboratories from 1924
 Graphical and visual plot of changes in the data over time ; This is necessary
for visual management of your process.
 Charts have a Central Line and Control Limits to detect Special Cause
variation.
 Usually, its sample statistic is plotted over time. Sometimes, the actual value
of the quality characteristic is plotted.
8
Each point is usually a
sample statistic (such as
subgroup average) of
the quality characteristic
Center Line represents
mean operating level
of process
LCL & UCL are
vital guidelines for
deciding when
action should be
taken in a process

Control Chart Anatomy
9
Common Cause
Variation
Process is “In
Control”
Special Cause
Variation
Process is “Out
of Control”
Special Cause
Variation
Process is “Out
of Control”
Run Chart of
data points
Process Sequence/Time Scale
Lower Control
Limit
Mean
+/-3sigma
Upper Control
Limit

Control and Out of Control
10
Outlier
Outlier
68%
95%
99.7%3
2
1-1
-2
-3

INTERPRETING CONTROL
CHART (Cont…)
12
RULE – 1: “A Process is assumed to be out of control if a
single point plots outside the control limits.”

CHART (Cont…)
13
RULE – 2: “A Process is assumed to be out of control if two
out of the three consecutive points fall outside the (2
SIGMA) warning limits on the same side of the center line.”

CHART (Cont…)
14
RULE – 3: “A Process is assumed to be out of control if four
out of five consecutive points fall beyond the one Sigma
limit on the same side of the center line.”

CHART (Cont…)
15
RULE – 4: “A Process is assumed to be out of control if
nine or more consecutive points fall to one side of the
center line.”

INTERPRETINGCONTROLCHART(Cont…)
16
RULE – 5: “A Process is assumed to be out of control if
there is a run of six or more consecutive points steadily
increasing or decreasing.”

TYPES OF CONTROL CHART
17
 There are two main categories of Control Charts, those
that display attribute data, and those that display
variables data.
 Attribute Data: This category of Control Chart displays
data that result from counting the number of occurrences
or items in a single category of similar items or
occurrences. These “count” data may be expressed as
pass/fail, yes/no, or presence/absence of a defect.
 Variables Data: This category of Control Chart displays
values resulting from the measurement of a continuous
variable. Examples of variables data are elapsed time,
temperature, and radiation dose.

TYPES& SELECTIONOFCONTROLCHART
18
What type of
data do I have?
Variable Attribute
Counting defects
or defectives?
X-bar & S
Chart
I & MR
Chart
X-bar & R
Chart
n > 10 1 < n < 10 n = 1
Defectives Defects
What subgroup
size is available?
Constant
Sample Size?
Constant
Opportunity?
yes yesno no
np Chart u Chartp Chart c Chart
Note: A defective unit can have
more than one defect.

CONTROL CHARTS FOR
ATTRIBUTE DATA
 There are 4 types of Attribute Control Charts:
19
 Subgroup size for Attribute Data is often 50 – 200.

Calculatethe parametersof the “P” Control
Charts with the following:
20
Where:
p: Average proportion defective (0.0 – 1.0)
ni: Number inspected in each subgroup
LCLp: Lower Control Limit on P Chart
UCLp: Upper Control Limit on P Chart
inspecteditemsofnumberTotal
itemsdefectiveofnumberTotal
p 
in
pp )1(
3pUCLp


Center Line Control Limits
in
pp )1(
3pLCLp


Since the Control Limits are a function of sample
size, they will vary for each sample.

CONTROLCHARTSFORATTRIBUTEDATA
21
P Chart With constant sample size: EXAMPLE
Frozen orange juice concentrate is packed in 6- oz cardboard cans. A
metal bottom panel is attached to the cardboard body. The cans are
inspected for possible leak. 20 samplings of 50 cans/sampling were
obtained. Verify if the process is in control.
Choose Stat > Control Charts >Attributes
Charts > P

22
P Chart with constant sample size: EXAMPLE
(Cont…)
Interpreting the results
Sample 15 is outside the upper control limit; Indicating special case.

23
P Chart With Variable sample size: EXAMPLE
Suppose you work in a plant that manufactures picture
tubes for televisions. For each lot, you pull some of the
tubes and do a visual inspection. If a tube has scratches on
the inside, you reject it. If a lot has too many rejects, you
do a 100% inspection on that lot. A P chart can define
when you need to inspect the whole lot.
1. Open the worksheet EXH_QC.MTW.
2. Choose Stat > Control Charts >Attributes Charts >
P.
3. In Variables, enter Rejects.
4. In Subgroup sizes, enter Sampled. Click OK.

24
P Chart with Variable sample size: EXAMPLE
(Cont…)
P Chart of Rejects
Test Results for P Chart of Rejects
TEST 1. One point more than 3.00 standard deviations from center line.
Test Failed at points: 6

Calculatethe parametersofthe “np”Control
Chartswiththe following:
25
Since the Control Limits AND Center Line are a function
of sample size, they will vary for each sample.
subgroupsofnumberTotal
itemsdefectiveofnumberTotal
pn  )1(3pnUCL inp ppni 
p)-p(1n3pnLCL iinp 
Where:
np: Average number defective items per subgroup
LCLnp: Lower Control Limit on nP chart
UCLnp: Upper Control Limit on nP chart

26
ATTRIBUTE CONTROL CHARTS
(Cont…)
NP Chart: EXAMPLE
You work in a toy manufacturing company and your job is to
inspect the number of defective bicycle tires. You inspect
200 samples in each lot and then decide to create an NP
chart to monitor the number of defectives. To make the NP
chart easier to present at the next staff meeting, you decide
to split the chart by every 10 inspection lots.
1. Open the worksheet TOYS.MTW.
2. Choose Stat > Control Charts > Attributes Charts > NP.
3. In Variables, enter Rejects.
4. In Subgroup sizes, enter Inspected.
5. Click NP Chart Options, then click the Display tab.
6. Under Split chart into a series of segments for display
purposes, choose Number of subgroups in each segment and
enter10.
7. Click OK in each dialog box.

27
(Cont…)
NP Chart: EXAMPLE (Cont…)
Inspection lots 9 and 20 fall above the upper control limit, indicating that
special causes may have affected the number of defectives for these lots. You
should investigate what special causes may have influenced the out-of-control
number of bicycle tire defectives for inspection lots 9 and 20.

Calculatethe parametersofthe “c”ControlCharts
with thefollowing:
28
subgroupsofnumberTotal
defectsofnumberTotal
c  c3cUCLc 
c3cLCLc 
Where:
c: Total number of defects divided by the total number of subgroups.
LCLc: Lower Control Limit on C Chart.
UCLc: Upper Control Limit on C Chart.

29
(Cont…)
C Chart: EXAMPLE
Suppose you work for a linen manufacturer. Each 100 square yards of
fabric can contain a certain number of blemishes before it is rejected. For
quality purposes, you want to track the number of blemishes per 100
square yards over a period of several days, to see if your process is
behaving predictably.
1. Open the worksheet EXH_QC.MTW.
2. Choose Stat > Control Charts > Attributes Charts > C.
3. In Variables, enter Blemish.
Because the points fall in a
random pattern, within the
bounds of the 3s control limits,
you conclude the process is
behaving predictably and is in
control.

Calculatethe parametersofthe“u”ControlCharts
with thefollowing:
30
InspectedUnitsofnumberTotal
IdentifieddefectsofnumberTotal
u 
in
u
3uUCLu 
in
u
3uLCLu 
Where:
u: Total number of defects divided by the total number of units inspected.
LCLu: Lower Control Limit on U Chart.
UCLu: Upper Control Limit on U Chart.
Since the Control Limits are a function of
sample size, they will vary for each sample.

31
(Cont…)
U Chart: EXAMPLE
As production manager of a toy manufacturing company, you
want to monitor the number of defects per unit of motorized
toy cars. You inspect 20 units of toys and create a U chart to
examine the number of defects in each unit of toys. You
want the U chart to feature straight control limits, so you fix
a subgroup size of 102 (the average number of toys per
unit).
1. Open the worksheet TOYS.MTW.
2. Choose Stat > Control Charts > Attributes Charts > U.
3. In Variables, enter Defects.
4. In Subgroup sizes, enter Sample.
5. Click U Chart Options, then click the S Limits tab.
6. Under When subgroup sizes are unequal, calculate control limits,
choose Assuming all subgroups have size then enter 102.
7. Click OK in each dialog box.

32
(Cont…)
U Chart: EXAMPLE (Cont…)
Units 5 and 6 are above the upper control limit line, indicating that special
causes may have affected the number of defects in these units. You should
investigate what special causes may have influenced the out-of-control
number of motorized toy car defects for these units.

Calculatetheparametersofthe X–BarandR
ControlChartswith the following:
33
k
x
X
k
1i
i

k
R
R
k
i
i

RAXUCL 2x 
RAXLCL 2x 
RDUCL 4R 
RDLCL 3R 
Where:
Xi: Average of the subgroup averages, it becomes the Center Line of the Control Chart
Xi: Average of each subgroup
k: Number of subgroups
Ri : Range of each subgroup (Maximum observation – Minimum observation)
Rbar: The average range of the subgroups, the Center Line on the Range Chart
UCLX: Upper Control Limit on Average Chart
LCLX: Lower Control Limit on Average Chart
UCLR: Upper Control Limit on Range Chart
LCLR : Lower Control Limit Range Chart
A2, D3, D4: Constants that vary according to the subgroup sample size
Rbar (computed above)
d2 (table of constants for subgroup size n) (st. dev. Estimate) =

34
VARIABLE CONTROL CHARTS
X–Bar & R Charts: EXAMPLE
You work at an automobile engine assembly plant. One of the parts, a camshaft, must be
600 mm +2 mm long to meet engineering specifications. There has been a chronic
problem with camshaft length being out of specification, which causes poor-fitting
assemblies, resulting in high scrap and rework rates. Your supervisor wants to run X and R
charts to monitor this characteristic, so for a month, you collect a total of 100 observations
(20 samples of 5 camshafts each) from all the camshafts used at the plant, and 100
observations from each of your suppliers. First you will look at camshafts produced by
Supplier 2.
1. Open the worksheet
CAMSHAFT.MTW
2. Choose Stat > Control Charts >
Variables Charts for
Subgroups > Xbar-R.
3. Choose All observations for a
chart are in one column, then
enter Supp2.
4. In Subgroup sizes, enter 5.
5. Click OK.

35
(Cont…)X–Bar & R Charts: EXAMPLE (Cont…)
Test Results for Xbar Chart of
Supp2
TEST 1. One point more than 3.00
standard deviations from center
line.
Test Failed at points: 2, 14
TEST 6. 4 out of 5 points more
than 1 standard deviation from
center line (on one side of CL).
Test Failed at points: 9

36
CAPABILITY SIXPACK (NORMAL
PROBABILITY MODEL)
A manufacturer of cable wire wants to assess if the
diameter of the cable meets specifications. A cable wire
must be 0.55 + 0.05 cm in diameter to meet engineering
specifications. Analysts evaluate the capability of the
process to ensure it is meeting the customer's requirement
of a Ppk of 1.33. Every hour, analysts take a subgroup of 5
consecutive cable wires from the production line and record
the diameter.
1. Open the worksheet CABLE.MTW
2. Choose Stat > Quality Tools > Capability Sixpack > Normal.
3. In Single column, enter Diameter. In Subgroup size, enter 5.
4. In Upper spec, enter 0.60. In Lower spec, enter 0.50.
5. Click Options. In Target (adds Cpm to table), enter 0.55. Click
OK in each dialog box.
EXAMPLE

37
CAPABILITY SIXPACK (NORMAL
PROBABILITY MODEL)EXAMPLE (Cont…)
INTERPRETING THE RESULTS:
On both the X-Bar chart and the R chart, the points are randomly distributed between the control limits, implying a stable
process .
If you want to interpret the process capability statistics, your data should approximately follow a normal distribution. On
the capability histogram, the data approximately follow the normal curve. On the normal probability plot, the points
approximately follow a straight line and fall within the 95% confidence interval. These patterns indicate that the data are
normally distributed.
But, from the capability plot , you can see that the interval for the overall process variation (Overall) is wider than the
interval for the specification limits (Specs). This means you will sometimes see cables with diameters outside the
tolerance limit [0.50, 0.60]. Also, the value of Ppk (0.80) is below the required goal of 1.33, indicating that the
manufacturer needs to improve the process.

38
CAPABILITY SIXPACK (BOX-COX
TRANSFORMATION)
Suppose you work for a company that manufactures floor
tiles, and are concerned about warping in the tiles. To
ensure production quality, you measure warping in ten tiles
each working day for ten days.
From previous analyses, you found that the tile data do not
come from a normal distribution, and that a Box-Cox
transformation using a lambda value of 0.5 makes the data
"more normal."
EXAMPLE
1. Open the worksheet TILES.MTW.
2. Choose Stat > Quality Tools > Capability Sixpack > Normal.
3. In Single column, enter Warping. In Subgroup size, enter 10.
4. In Upper spec, enter 8.
5. Click Box-Cox.
6. Check Box-Cox power transformation (W = Y**Lambda). Choose
Lambda = 0.5 (square root). Click OK in each dialog box.

39
CAPABILITY SIXPACK (BOX-COX
TRANSFORMATION)
EXAMPLE (Cont…)
The capability plot , however, shows that the process is not meeting
specifications. And the values of Cpk (0.76) and Ppk (0.75) fall below the
guideline of 1.33, so your process does not appear to be capable.

CONTROL LIMITS VS
SPECIFICATION LIMITS
 SPECIFICATION LIMITS (USL , LSL)
 determined by design considerations
 represent the tolerable limits of individual values of a
product
 usually external to variability of the process
 CONTROL LIMITS (UCL , LCL)
 derived based on variability of the process
 usually apply to sample statistics such as subgroup
average or range, rather than individual values 40

SAMPLING RISK
 Type I Error (Rejecting good parts)
 Concluding that the process is out of control when it is really in
control
 α = probability of making Type I error
= commonly known as the producer’s risk
= total of 0.27% for control limits of +/- 3s
Is process really out
of control? Or is the
point outside due to
random variation?
41

SAMPLING RISK (Cont…)
 Type II Error (Accepting bad parts)
 Concluding that the process is in control when it is really out of
control
 β = probability of making Type II error
= commonly known as the consumer’s risk
Is process really in
control? Or is the point
inside due to random
variation of the shifted
process?
42

CONTROL LIMITS
VS
SAMPLING RISKS
 By moving the control limits further from the center line, the risk of
a type-I error is reduced. (Producer’s Risk)
However, widening the control limits will increase the risk
of a type-II error. (Consumer’s Risk)
43

Average Run Length (ARL)
 What does the ARL tell us?
 The average run length gives us the length of time (or number of
samples) that should plot in control before a point plots outside the
control limits.
 For our problem, even if the process remains in control, an out-of-
control signal will be generated every 370 samples, on average.
44
 “99.7% OF THE DATA”
 If approximately 99.7% of the data lies within 3σ of the mean (i.e., 99.7%
of the data should lie within the control limits), then 1 - 0.997 = 0.003 or
0.3% of the data can fall outside 3σ (or 0.3% of the data lies outside the
control limits). (Actually, we should use the more exact value 0.0027)
 0.0027 is the probability of a Type I error or a false alarm in this situation.
 SAMPLING FREQUENCY:
 For the X–Bar chart with 3s limits, a = 0.0027
 Therefore, in-control ARL = 1/0.0027 = 370.
 This means that if the process remains unchanged, one out-of-control
signal will be generated every 370 samples.

Calculatetheparametersofthe X–BarandS
ControlChartswith the following:
45
k
x
X
k
1i
i

k
s
S
k
1i
i

SAXUCL 3x 
SAXLCL 3x 
SBUCL 4S 
SBLCL 3S 
Where:
Xi: Average of the subgroup averages, it becomes the Center Line of the Control Chart
Xi: Average of each subgroup
k: Number of subgroups
si : Standard Deviation of each subgroup
Sbar: The average S. D. of the subgroups, the Center Line on the S chart
UCLX: Upper Control Limit on Average Chart
LCLX: Lower Control Limit on Average Chart
UCLS: Upper Control Limit on S Chart
LCLS : Lower Control Limit S Chart
A3, B3, B4: Constants that vary according to the subgroup sample size
Sbar (computed above)
c4 (table of constants for subgroup size n) (st. dev. Estimate) =

46
(Cont…)X–Bar & S Charts: EXAMPLE
You are conducting a study on the blood glucose levels of 9 patients
who are on strict diets and exercise routines. To monitor the mean and
standard deviation of the blood glucose levels of your patients, create
an X-Bar and S chart. You take a blood glucose reading every day for
each patient for 20 days.
1. Open the worksheet
BLOODSUGAR.MTW.
2. Choose Stat > Control Charts
> Variables Charts for
Subgroups > Xbar-S.
3. Choose All observations for a
chart are in one column,
then enter Glucoselevel.
4. In Subgroup sizes, enter 9.
Click OK.

47
(Cont…)X–Bar & S Charts: EXAMPLE (Cont…)

Calculatethe parametersofthe IndividualandMR
ControlChartswiththefollowing:
48
k
x
X
k
1i
i

k
R
RM
k
i
i

RMEXUCL 2x 
RMEXLCL 2x 
RMDUCL 4MR 
RMDLCL 3MR 
Where:
Xbar: Average of the individuals, becomes the Center Line on the Individuals Chart
Xi: Individual data points
k: Number of individual data points
Ri : Moving range between individuals, generally calculated using the difference
between each successive pair of readings
MRbar: The average moving range, the Center Line on the Range Chart
UCLX: Upper Control Limit on Individuals Chart
LCLX: Lower Control Limit on Individuals Chart
UCLMR: Upper Control Limit on moving range
LCLMR : Lower Control Limit on moving range
E2, D3, D4: Constants that vary according to the sample size used in obtaining the moving
range
MRbar (computed above)
d2 (table of constants for subgroup size n) (st. dev. Estimate) =

49
(Cont…)I & MR Charts: EXAMPLE
As the distribution manager at a limestone quarry, you
want to monitor the weight (in pounds) and variation in the
45 batches of limestone that are shipped weekly to an
important client. Each batch should weight approximately
930 pounds. you want to examine the same data using an
individuals and moving range chart.
1. Open the worksheet EXH_QC.MTW
2. Choose Stat > Control Charts > Variables Charts for
Individuals > I-MR.
3. In Variables, enter Weight.
4. Click I-MR Options, then click the Tests tab.
5. Choose Perform all tests for special causes, then click OK in
each dialog box.

50
(Cont…)I & MR Charts: EXAMPLE (Cont…)

51
(Cont…)I & MR Charts: EXERCISE
A shift engineer in the control room of a power plant is responsible for
continuous monitoring of sensors installed on the electric generator.
Given below is the record of temperature readings of one sensor which
were taken every hour and recorded on the shift register. Construct a
control chart and analyze the process for any special causes.
SHIFT A A A A A A A A
TIME 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
TEMP 16 20 21 8 28 24 19 16
SHIFT B B B B B B B B
TIME 17:00 18:00 19:00 20:00 21:00 22:00 23:00 24:00
TEMP 17 24 19 22 26 19 15 21
SHIFT C C C C
TIME 01:00 02:00 03:00 04:00
TEMP 17 22 16 14

52
RUN CHARTEXAMPLE
Suppose you work for a company that produces
several devices that measure radiation. As the
quality engineer, you are concerned with a
membrane type device's ability to consistently
measure the amount of radiation. You want to
analyze the data from tests of 20 devices (in
groups of 2) collected in an experimental chamber.
After every test, you record the amount of
radiation that each device measured.
1. Open the worksheet RADON.MTW.
2. Choose Stat > Quality Tools > Run Chart.
3. In Single column, enter Membrane.
4. In Subgroup size, enter 2. Click OK.

53
RUN CHART
EXAMPLE (Cont…)
The test for clustering is significant at the 0.05 level. Because the probability for
the cluster test (p = 0.022) is less than the a value of 0.05, you can conclude
that special causes are affecting your process, and you should investigate
possible sources. Clusters may indicate sampling or measurement problems.

54
CONTROL CHARTS
SELECTION EXERCISES

TYPES& SELECTIONOFCONTROLCHART
55
What type of
data do I have?
Variable Attribute
Counting defects
or defectives?
X-bar & S
Chart
I & MR
Chart
X-bar & R
Chart
n > 10 1 < n < 10 n = 1
Defectives Defects
What subgroup
size is available?
Constant
Sample Size?
Constant
Opportunity?
yes yesno no
np Chart u Chartp Chart c Chart
Note: A defective unit can have
more than one defect.

EXERCISE # 1
A ceramic tile manufacturing company has just secured a
contract with NASA to supply the tiles for the new space shuttle.
The manufacturing process is long and detailed, and only 20 to
25 tiles can be manufactured per day. NASA requires that the
tiles be subjected to specific measured tests to prove that they
are capable of withstanding repeated exposure to extreme high
temperatures. The tests required are destructive tests. Because
the tests are destructive tests and the production output per day
is low, the manufacturing company has decided to use a sample
size of one.
Which chart should be used?
data are measured  sample size = 1  use X and MR
charts
56

EXERCISE # 2
Mr. Fence runs a small alterations shop. Recently, there
has been an increase in the number of complaints
about the work done in his shop. He has decided that
at the end of each day, he will inspect all the work
completed that day for defects. Which chart should Mr.
Fence use?
 data are counted
 counting defects
 sample size varies (a different number of alterations
are completed each day)
 use a u chart
57

EXERCISE # 3
A boot manufacturer wants to check a certain style of
boot for possible defects in the sole stitching. The
defects include missed stitches, loose threads, and any
other observed defects. This particular style of boot is
produced at a rate of 100 pairs per hour. The manager
suggests checking 10 pairs per hour. Which chart
should be used?
 data are counted
 Counting defects
 sample size is constant (10 parts/hour)
 use a c chat 58

EXERCISE # 4
A process that packages a ready-to-make cake mix
automatically weighs each bag of mix before placing it
into its respective box. The specification for each bag
of mix is 8 + 0.01 ounces. If a bag weighs outside of
specs, it is automatically separated from the rest.
Which chart should be used?
data are measured  sample size = 1  use X and MR
charts
59

5. spc control charts

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