Operations Management MD021

1
Operations Management(MD021)

• Quality Control

2
Agenda

• Approaches to Quality Assurance
• Process Capability
• Control Charts for Statistical Process Control
  (SPC)
• How to Use Control Charts

3
Several Approaches to Quality Assurance
4
Quality assurance at several stages inside the
factory or service facility
Inspection and corrective action during production
Inspection before/after production
Quality built into the process
The least progressive
More progressive
5
Today, Information Technology allows us even to
build quality management into products in the
field
Inspection and corrective action during production
Quality mgmt built into the product
Inspection before/after production
Quality built into the process
Most progressive
More progressive
The least progressive
Examples On-Star (cars) Self-updating software
6
Inspection compares goods or services against a
standard

• If inspecting product, managers must decide
• How Much/How Often
• Where/When
• Centralized vs. On-site
• What to inspect? Attributes? Variables?

7
Inspection costs us money we must minimize
total costs
Total Cost
Cost of inspection
Cost of passing defectives
Less Inspection
More Inspection
8
Where to inspect in the process? many, many
potential points

• Possible inspection points
• Raw materials and purchased parts
• Finished products
• Before a costly operation
• Before an irreversible process
• Before a covering process
• Want to choose points in the process that will do
  the most good

9
Examples of Inspection Points
10
Process Capability
11
Process Capability

• Tolerances or specifications
• Range of acceptable values established by
  engineering design or customer requirements
• Process variability
• Natural variability in a process
• Process capability
• Process variability relative to specification

12
Process Capability

• The ratio of process variability to design
  specifications

Natural data spread
The natural spread of the data is 6s
-1s
-2s
-3s
2s
1s
3s
µ
Upper Spec
Lower Spec
13
3 Sigma vs. 6 Sigma Quality Six Sigma provides
fewer defectives
14
Process Capability
C. Process variability exceeds
specifications
15
Process Capability Ratio (Cp)
For a process to be capable, it must have a
capability ratio of at least 1.33
16
Process Capability Ratio (Cpk)
When process is not centered, Cpk is used.
For a process to be capable, Cpk must be at least
1.33
17
When the process is not capable of producing to
expected specifications, manager needs to improve
capability

• Simplify
• Eliminate steps, reduce parts, use modularity
• Standardize
• Use standard parts, standard procedures
• Mistake-proof
• Design parts and system so that mistakes cannot
  be made
• Upgrade equipment
• Replace and improve equipments
• Automate
• Replace manual processing with automated process

18
Limitations of Capability Indexes

• Process may not be stable it may change over
  time
• Process output may not be normally distributed
• When process is not centered, and operator uses
  Cp instead of Cpk

19
Control Charts for Statistical Process Control
(SPC)
20
SPC helps to make sure that we are producing
quality products

• Quality of Design
• Specifies the features/attributes of the
  good/service
• Quality of Conformance
• An issue of whether a certain unit adheres to the
  design specifications
• Statistical Process Control (SPC)
• Statistical evaluation of the output of a process
  during production
• Objective is to assure that we are conforming to
  design specifications, and identify when we are
  not

21
Statistical Process Control (SPC)

• Invented by Walter Shewhart at Western Electric
  in early 1900s
• Distinguishes between
• common cause variability (random)
• special cause variability (assignable)
• Based on repeated samples from a process

22
Statistical Process Control

• The essence of statistical process control is to
  assure that the output of a process is random so
  that future output will be random.
• Variations and Control
• Random variation Natural variations in the
  output of a process, created by countless minor
  factors
• Assignable variation A variation whose source
  can be identified

23
Statistical Process Control

• The Control Process
• Define what is to be controlled?
• Measure how will measurements be taken?
• Compare what is the standard for comparing?
• Evaluate must define out of control and
  evaluate based on this definition
• Correct take corrective action, if needed
• Monitor results ensure corrective action is
  successful

24
SPC uses control charts to monitor process output

• Control Chart
• Purpose to monitor process output to see if it
  is random
• A time ordered plot of representative sample
  statistics obtained from an on-going process
  (e.g. sample means)
• Upper and lower control limits define the range
  of acceptable variation

25
Control charts use time and money, and require
economic decisions

• Managers must make a number of decisions about
  using control charts
• At what point in the process to use control
  charts?
• What size samples to take?
• What type of control chart to use?
• Variables
• Attributes

26
Control Charts

• Are named according to the statistics being
  plotted, i.e., X bar, R, p, and c
• Have a center line that is the overall average
• Have limits above and below the center line at
  3 standard deviations (usually)

27
The empirical basis for control charting is a
statistical distribution
For example, the Normal distribution has certain
regions within which known percentages of
observations will be observed
28
Sampling distribution is determined by sampling
from a process
When we sample from a distribution for our
manufacturing/service process, we will calculate
average values that approximately follow the
Normal distribution
29
We can determine control limits within our
sampling distribution
30
Control charts essentially perform hypothesis
testing assuming small Type I error
31
SPC Errors

• Type I error
• Concluding a process is not in control when it
  actually is.
• Type II error
• Concluding a process is in control when it is not.

32
Control charts order observations from the sample
distribution
Ordered According to Time
33
If sample data stays within control limits, all
is OK if not the process is OUT OF CONTROL
34
Objective is to track improvements in mean and
variance of process
35
Control Charts for VariablesX-bar Chart and R
Chart
Variables generate data that are measured.

• Mean control charts
• Used to monitor the central tendency of a
  process.
• X bar charts
• Range control charts
• Used to monitor the process dispersion
• R charts

36
Control Charts for VariablesX-bar Chart and R
Chart

• Process Centering
• X bar chart
• X bar is a sample mean
• Process Dispersion (consistency)
• R chart
• R is a sample range

37
X bar charts

• Center line is the grand mean (X double bar)
• Points are X bars

-OR-
38
R Charts

• Center line is the grand mean (R bar)
• Points are R
• D3 and D4 values are tabled according to n
  (sample size)

39
X bar R charts are used together

• X-bar and R Charts are always used in tandem
• Data are collected (20-25 samples)
• Sample statistics are computed
• All data are plotted on the 2 charts
• Charts are examined for randomness
• If random, then limits are used forever

40
X-bar and R charts can detect a shifting process
mean
(process mean is shifting upward)
Sampling Distribution
UCL
Detects shift
LCL
UCL
Does notdetect shift
R-chart
LCL
41
X-bar and R charts can detect changing process
variance
Sampling Distribution
(process variability is increasing)
UCL
Does notreveal increase
LCL
UCL
R-chart
Reveals increase
LCL
42
Control Chart for Attributesp Chart and c Chart
Attributes generate data that are counted.

• p-Chart - Control chart used to monitor the
  proportion of defectives in a process
• c-Chart - Control chart used to monitor the
  number of defects per unit

43
Use of p-Charts

• When observations can be placed into two
  categories.
• Good or bad
• Pass or fail
• Operate or dont operate
• When the data consists of multiple samples of
  several observations each

44
Attribute Charts

• p charts used to track a proportion (fraction)
  defective

45
Use of c-Charts

• Use only when the number of occurrences per unit
  of measure can be counted non-occurrences cannot
  be counted.
• Scratches, chips, dents, or errors per item
• Cracks or faults per unit of distance
• Breaks or Tears per unit of area
• Bacteria or pollutants per unit of volume
• Calls, complaints, failures per unit of time

46
Attribute Charts

• c charts used to count defects in a constant
  sample size

47
Using Run Tests with Control Charts
48
Run Tests

• Run Test a test for randomness in the
  observations
• Even when points are within the control limits -
  the process still may not be random
• Many types of patterns in the data can suggest a
  non-random process

49
Nonrandom Patterns in Control charts

• Trend upward or downward
• Cycles wave patterns
• Bias systematically above or below the center
  line
• Mean shift a shift of the mean at some point in
  time
• Too much dispersion values are too spread out

50
Counting Runs
51
Run test equations