S6-1 Operations Management Statistical Process Control Supplement 6.
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Transcript of S6-1 Operations Management Statistical Process Control Supplement 6.
S6-1
Operations Operations ManagementManagement
Statistical Process ControlStatistical Process ControlSupplement 6Supplement 6
S6-2
OutlineOutline Statistical Process Control (SPC).
Mean charts or X-Charts.
Range chart or R-Charts.
Control charts for attributes.
Managerial issues and control charts.
Acceptance Sampling.
S6-3
Statistical technique to identify when non-random variation is present in a process.
All processes are subject to variability. Natural causes: Random variations.
Assignable causes: Correctable problems. Machine wear, unskilled workers, poor materials.
Uses process control charts.
Statistical Process Control (SPC)Statistical Process Control (SPC)
S6-4
Produce GoodProvide Service
Stop Process
No
Yes
Is process in control?
Take Samples
Find Out Why
CreateControl Chart
Start
Statistical Process Control StepsStatistical Process Control Steps
Take Sample
Inspect Sample
S6-5
Process Control ChartsProcess Control Charts
Plot of Sample Data Over Time
0
20
40
60
80
1 5 9 13 17 21
Time
Sam
ple
Val
ue
Upper control limit
Lower control limit
S6-6
Process is not in control if: Sample is not between upper and lower control
limits.
A non-random pattern is present, even when between upper and lower control limits.
Based on sample being normally distributed.
Control ChartsControl Charts
S6-7
Distribution of Sample MeansDistribution of Sample Means
x means sample of Mean
n
xx
Standard deviation of
the sample means
(mean)
x2 withinfall x all of 95.5%
x3 withinfall x all of 99.7%
x3 x2 x x x1 x2 x3
S6-8
X
As sample size gets large enough,
distribution of mean values becomes approximately normal for any population distribution.
Central Limit Theorem
XX
Central Limit TheoremCentral Limit Theorem
S6-9
ControlCharts
RChart
VariablesCharts
AttributesCharts
XChart
PChart
CChart
Continuous Numerical Data
Categorical or Discrete Numerical Data
Control Chart TypesControl Chart Types
S6-10
Characteristics for which you focus on defects.
Categorical or discrete values. ‘Good’ or ‘Bad’. # of defects.
AttributesAttributesVariablesVariables
Quality CharacteristicsQuality Characteristics
Characteristics that you measure, e.g., weight, length.
Continuous values.
S6-11
Shows sample means over time.
Monitors process average.
Example: Weigh samples of coffee.
Collect many samples, each of n bags. Sample size = n.
Compute mean and range for each sample.
Compute upper and lower control limits (UCL, LCL).
Plot sample means and control limits.
XX Chart Chart
S6-12
X Chart Control Limits - Std. Dev. of Process Is Known
sample mean at time i
xx zσxxLCLzσxxUCL
n
ix
x
n
i 1
nσ
xσ
= known process standard deviation
S6-13
Each sample is 4 measurements.
Process mean is 5 lbs.
Process standard deviation is 0.1 lbs.
Determine 3 control limits.
XX Chart - Example 1 Chart - Example 1
85.441.0
35
15.541.0
35
xLCL
xUCL
S6-14
X Chart Control Limits - Std. Dev. of Process is Not Known
sample range at time i
A2 is from Table S6.1
RAxxLCLRAxxUCL 22
n
iRn
iR 1
sample mean at time i
n
ix
x
n
i 1
S6-15
Factors for Computing Control Factors for Computing Control Chart LimitsChart Limits
SampleSize, n
MeanFactor, A2
UpperRange, D4
LowerRange, D3
2 1.880 3.268 0
3 1.023 2.574 0
4 0.729 2.282 0
5 0.577 2.115 0
6 0.483 2.004 0
7 0.419 1.924 0.076
8 0.373 1.864 0.136
9 0.337 1.816 0.184
10 0.308 1.777 0.223
S6-16
Each sample is 4 measurements.
Determine 3 control limits. sample mean range. 1 5.02 .12 4.96, 5.03, 5.01, 5.08 2 4.99 .08. 3 4.97 .13. 4 5.03 .18. 5 4.99 .14.
XX Chart - Example 2 Chart - Example 2
905.413.0729.05095.513.0729.05
xLCLxUCL
13.00.5 Rx
S6-17
XX Chart - Example 2 Chart - Example 2
4.9
5.0
5.1
Time
Sam
ple
Mea
n
Upper control limit
Lower control limit
S6-18
sample values mean range 6 5.05, 5.00, 4.80, 4.95 4.95 0.25 7 5.00, 5.10, 5.10, 5.00 5.05 0.10 8 4.80, 5.20, 5.10, 5.00 5.025 0.40
4.9
5.0
5.1
Time
Sam
ple
Mea
n
Upper control limit
Lower control limit
Example 2 – New SamplesExample 2 – New Samples
S6-19
Shows sample ranges over time. Sample range = largest - smallest value in sample.
Monitors process variability.
Example: Weigh samples of coffee. Collect many samples, each of n bags.
Sample size = n.
Compute range for each sample & average range.
Compute upper and lower control limits (UCL, LCL).
Plot sample ranges and control limits.
RR Chart Chart
S6-20
sample range at time i
From Table S6.1
RR Chart Control Limits Chart Control Limits
n
R R
R D LCL
R D UCL
i
n
1i
3R
4R
S6-21
Each sample is 4 measurements.
Determine 3 control limits. sample mean range 1 5.02 .12 2 4.99 .08 3 4.97 .13 4 5.03 .18 5 4.99 .14
RR Chart - Example 2 Chart - Example 2
013.00297.013.0282.2
R
R
LCLUCL
13.00.5 Rx
4.96, 5.03, 5.01, 5.08
S6-22
RR Chart - Example 2 Chart - Example 2
0
0.2
0.3
Time
Sam
ple
Ran
ge
Upper control limit
Lower control limit
0.1
S6-23
sample values mean range 6 5.05, 5.00, 4.80, 4.95 4.95 0.25 7 5.00, 5.10, 5.10, 5.00 5.05 0.10 8 4.80, 5.20, 5.10, 5.00 5.025 0.40
Example 2 – New SamplesExample 2 – New Samples
0
0.2
0.3
Time
Sam
ple
Ran
ge
Upper control limit
Lower control limit
0.1
S6-24
Control Chart StepsControl Chart Steps Collect 20 to 25 samples of n=4 or n=5 from a
stable process & compute the mean and range.
Compute the overall mean and average range.
Calculate upper and lower control limits.
Collect new samples, and plot the means and ranges on their respective control charts.
S6-25
Control Chart Steps - ContinuedControl Chart Steps - Continued
Investigate points or patterns that indicate the process is out of control. Assign causes for the variations.
Collect additional samples and revalidate the control limits.
S6-26
Use of Control ChartsUse of Control Charts
S6-27
sample values mean range 1 4.9, 5.0, 5.1 5.0 0.2 2 5.2, 5.3, 5.4 5.3 0.2 3 5.5, 5.6, 5.7 5.6 0.2
4 5.8, 5.9, 6.0 5.9 0.2
Example 3Example 3
2454.52.0023.145.5
6546.52.0023.145.5
xLCLxUCL
2.045.5 Rx
02.00
5148.02.0574.2
RLCL
RUCL
S6-28
Example 3 – Control ChartsExample 3 – Control Charts
5.0
5.5
6.0
Time
Sam
ple
Mea
n
Upper control limit = 5.6546
Lower control limit = 5.2454
0.0
0.5
1.0
Time
Sam
ple
Ran
ge
Upper control limit = 0.5148
Lower control limit = 0
S6-29
sample values mean range 1 5.0, 5.0, 5.0 5.0 0.0 2 4.5, 5.0, 5.5 5.0 1.0 3 4.0, 5.0, 6.0 5.0 2.0
4 3.0, 5.0, 7.0 5.0 4.0
Example 4Example 4
20975.375.1023.10.5
79025.675.1023.10.5
xLCLxUCL
75.10.5 Rx
075.10
5045.475.1574.2
RLCL
RUCL
S6-30
Example 4 – Control ChartsExample 4 – Control Charts
3.0
5.0
7.0
Time
Sam
ple
Mea
n
Upper control limit = 6.79025
Lower control limit = 3.20975
0.0
3.0
6.0
Time
Sam
ple
Ran
ge
Upper control limit = 4.5045
Lower control limit = 0
S6-31
Attributes control chart.
Shows % of nonconforming items.
Example: Count # defective chairs & divide by total chairs inspected. Chair is either defective or not defective.
pp Chart Chart
S6-32
Attributes control chart.
Shows number of defects in a unit. Unit may be chair, steel sheet, car, etc. Size of unit must be constant.
Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs.
cc Chart Chart
S6-33
Quality testing for incoming materials or finished goods.
Procedure: Take one or more samples at random from a lot
(shipment) of items. Inspect each of the items in the sample. Decide whether to reject the whole lot based on
the inspection results.
Acceptance SamplingAcceptance Sampling
S6-34
Inspecting all items is too expensive. The larger the sample inspected:
The greater the cost for inspection. The less likely you are to accept a “bad” lot or to
reject a “good” lot.
Key questions: How many should be inspected in each lot? How confident are you in the accept/reject
decision?
Acceptance SamplingAcceptance Sampling