Chapter 4– Statistical Process

Control (SPC)

Operations Management
by
Roberta Russell & Bernard W. Taylor, III
 Lecture Outline
 Basics of statistical process control
 Control charts
 Control charts for attributes
 Control charts for variables
 Control charts patterns
 SPC with Excel and Operations Management tools
 Process capability
 Basics of Statistical Process
Control
 Statistical process control
(SPC)
 A statistical procedure
using control charts to see
if any part of the
production process is not
functioning properly and
could cause poor quality
 Sample
 Subset of items produced
to use for inspection
 Basics of Statistical Process
Control (cont.)
 Control charts:
 Graphs that visually show if a sample is within
statistical control limits.
 Have two basic purposes: to establish the control
limits for a process and then to monitor the
process to indicate when it is out of control.
 Basics of Statistical Process
Control (cont.)
 All processes contain a certain amount of variability that
makes some variation between units inevitable.
 There are two reasons why a process might vary:
 The first is the inherent random variability of the process, which
depends on the equipment and machinery, engineering, the
operator, and the system used for measurement. This kind of
variability is a result of natural occurrences.
 The other reason for variability is unique or special causes that
are identifiable and can be corrected. These causes tend to be
nonrandom and, if left unattended, will cause poor quality. These
might include equipment that is out of adjustment, defective
materials, changes in parts or materials, broken machinery or
equipment, operator fatigue or poor work methods, or errors due to
lack of training.
 SPC: Process Variability
 All processes generate output that exhibits some degree of
variability. The issue is whether the output variations are
within an acceptable range. The issue is addressed by
answering two basic questions about the process
variations:
 Are the variations random? If nonrandom variations are present,
the process is considered to be unstable. Corrective action will need
to be taken to improve the process by eliminating the causes of
nonrandomness to achieve a stable process.
 Given a stable process, is the inherent variability of process output
within a range that conforms to performance criteria? This involves
assessment of a process’s capability to meet standards. If a process
is not capable, that situation will need to be addressed.
 SPC in Quality Management
 SPC
 Tool for identifying problems in order to make
improvements
 Contribute to the TQM goal of continuous improvements
and few or no defects by continually monitoring the
production process and making improvements.
 Quality Measures: Attributes and
Variables
 The quality of a product or service can be evaluated
using either an attribute of the product or service or
a variable measure.
 Quality Measures: Attributes and
Variables
 Attribute
 A product characteristic (color, surface texture, cleanliness)
that can be evaluated with a discrete response
 Good-bad; yes-no; acceptable or not.
 Referred to as a qualitative method
 Variable measure
 A product characteristic that is continuous and can be
measured.
 For example, weight, length, temperature, or time.
 Referred as a quantitative method (it is the result of some
form of measurement).
 Provides more information about a product.
 SPC Applied to Services
 Control charts have historically been used to monitor
the quality of manufacturing processes. However, SPC
is just as useful for monitoring quality in services.
 Nature of defect is different in services than in
manufacturing companies.
 Service defect is a failure to meet customer requirements.
For example, an empty soap dispenser in a restroom or a
faulty tray on a DVD player.
 SPC Applied to Services
 Control charts for service processes tend to use quality
characteristics and measurements such as time and
customer satisfaction (determined by surveys,
questionnaires, or inspections)
 SPC Applied to Services (cont.)
 Hospitals
 Timeliness and quickness of care, staff responses to requests,
accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork,
speed of admittance and checkouts.
 Grocery stores
 Waiting time to check out, frequency of out-of-stock items, quality of
food items, cleanliness, customer complaints, checkout register
errors.
 Airlines
 Flight delays, lost luggage and luggage handling, waiting time at
ticket counters and check-in, agent and flight attendant courtesy,
accurate flight information, passenger cabin cleanliness and
maintenance.
 SPC Applied to Services (cont.)
 Fast-food restaurants
 Waiting time for service, customer complaints, cleanliness, food
quality, order accuracy, employee courtesy.
 Catalogue-order companies
 Order accuracy, operator knowledge and courtesy, packaging,
delivery time, phone order waiting time.
 Insurance companies
 Billing accuracy, timeliness of claims processing, agent availability and
response time.
 Where to Use Control Charts?
 Most companies do not use control charts for every
step in a process.
 Control charts are used at critical points where the
process has a tendency to go out of control or where
the process is particularly harmful and costly if it goes
out of control.
 Examples
 At the beginning of a process because it is a waste of time and money to
begin a production process with bad supplies.
 Before a costly or irreversible point, after which product is difficult to
rework or correct
 Before or after assembly or painting operations that might cover defects.
 Before the outgoing final product or service is delivered.
 Control Charts
 Control chart
 A graph that virtually shows if a sample is within statistical
control limits.
 Control limits
 Upper and lower bands of a control chart
 Types of charts
 Attributes
 p-chart
 c-chart
 Variables
 Mean ( x bar-chart)
 Range ( R-chart)
Process Control Chart
 Sampling And Sampling Distribution
 In statistical process control, periodic samples of process
output are taken and sample statistics, such as sample
means or the number of occurrences of a certain type of
outcome, are determined.
 The sample statistics can be used to judge randomness of
process variations.
 The sample statistics exhibit variation, just as processes do.
 The variability of sample statistics can be described by its
sampling distribution, a theoretical distribution that
describes the random variability of sample statistics.
 The most frequently used distribution is the normal
distribution.
Normal Distribution
Type I and Type II Errors
 Type I and Type II Errors:
Illustration
 Consumer’s risk (Type II Error) is the risk that problems
with a product that does not meet quality will go undetected
and thus enter the market. This can lead to financial losses
and other losses, including reputation loss, loss of market, or
even loss of lives.
 Producer’s risk (Type I Error), on the other hand, is the
risk that a good quality product will be rejected or marked as
a bad product by the consumer or the buyer.
 Type I and Type II Errors:
Illustration
Richie is an operational analyst at a large multinational firm that
manufactures engines for major jet manufacturers across the
globe. He is visiting one of the company's manufacturing units
for a scheduled quality check. Richie is accompanied by his
manager Kathy, who is preparing him to take over her
responsibilities in the near future. Kathy and Richie start their
tour of the firm with a conversation about consumer’s and
producer’s risk.
Kathy tells Richie that the engines manufactured by the firm are
critically important. The safety of the aircraft as well as the
passengers depends on the engines. It is, therefore, necessary
that the company produces products to the best specifications
and quality.
 Type I and Type II Errors:
Illustration
 If the engines have quality issues, and the consumer (i.e. the
jet manufacturer) accepts them, then the jet manufacturer
faces consumer’s risk. The airline that buys those jets will also
experience consumer’s risk.
 If the jet manufacturer rejects the engines even if they are up
to the specifications, there would be no risk to the consumer.
Instead, there would be producer’s risk. Producer’s risk occurs
when the engines are made to the specifications but the
consumer rejects them for some reason.
 A Process is in Control If …
1. …… no sample points outside limits
2. …… most points near process average
3. …… about equal number of points above and below
centerline
4. ……. Points appear randomly distributed
 Control Charts for Attributes
 p-chart
 Uses portion defective in a sample
 c-chart
 Uses number of defective items in a sample.
 Tips to Select a p- or c-Chart
 Use a p-chart:
1. When observations can be placed into one of two
categories that can be classified as good or bad, pass or
fail, operate or don’t operate.
2. When it is possible to distinguish between defective and
nondefective items and to state the number of defectives
as a percentage of the whole.
 Tips to Select a p- or c-Chart
 Use a c-chart:
 When the proportion of defective cannot be determined.
 When only the number of occurrences per unit of measure
can be counted. Examples of occurrences and units of
measure include:
1. Scratches, chips, dents, or errors per item
2. Cracks or faults per unit of distance (meters, miles, etc.)
3. Breaks or tears per unit of area (square yard, square meter, etc.)
4. Bacteria or pollutants per unit of volume (gallon, cubic foot, etc.)
5. Calls, complaints, failures, equipment breakdowns, or crimes per
unit of time (i.e. hour, day, month, year)
 p-chart

 z= number of standard deviations from process average

 = sample proportion defective; an estimate of process
average.
 = standard deviation of sample proportion
 where n is the sample size.
 p-chart
The Western Jeans Company produces Denim jeans. The
company wants to establish a p-chart to monitor the
production process and maintain high quality. Western
believes that approximately 99.74% of the variability in the
production process (corresponding to 3 sigma limits) is
random and thus should be within control limits, whereas
0.26% of the process variability is not random and suggests
that the process is out of control.
The company has taken 20 samples (one per day for 20
days), each containing 100 pairs of jeans (n = 100), and
inspected them for defects, the results of which are as
follows:
Sample Number of Defectives Proportion Defectives
1 6 0.06
2 0 0
3 4 0.04
4 10 0.1
5 6 0.06
6 4 0.04
7 12 0.12
8 10 0.1
9 8 0.08
10 10 0.1
11 12 0.12
12 10 0.1
13 14 0.14
14 8 0.08
15 6 0.06
16 16 0.16
17 12 0.12
18 14 0.14
19 20 0.2
20 18 0.18
200
Construction of p-chart (cont.)
Construction of p-chart (cont.)
c-Chart
 c-Chart: Example
The Ritz Hotel has 240 rooms. The hotel’s housekeeping department is
responsible for maintaining the quality of the rooms’ appearance and
cleanliness. Each individual housekeeper is responsible for an area
encompassing 20 rooms. Every room in use is thoroughly cleaned, and its
supplies, toiletries, and so on are restocked each day. Any defects that the
housekeeping staff notice that are not part of the normal housekeeping service
are supposed to be reported to hotel maintenance. Every room is briefly
inspected each day by a housekeeping supervisor. However, hotel
management also conducts inspection tours at random for a detailed, thorough
inspection for quality-control purposes.
An inspection sample includes 12 rooms, that’s, one room selected at random
from each of the twelve 20-room blocks serviced by a housekeeper. Following
are the results from 15 inspection samples conducted at random during a one-
month period.
 c-Chart: Example
Sample Number of Defects
1 12
2 8
3 16
4 14
5 10
6 11
7 9
8 14
9 13
10 15
11 12
12 10
13 14
14 17
15 15
190
 c-Chart: Example
The hotel believes that approximately 99% of the defects (corresponding to 3-
sigma limits) are caused by natural, random variations in the housekeeping and
room maintenance service, with 1% caused by nonrandom variability. It wants
to construct a c-chart to monitor the housekeeping service.
 c-Chart: Example

12.67
The control limits are computed using z = 3.00, as
follows:

L
c-Chart (cont.)
 Control Chart for Variables
 Range chart (R-Chart)
 Uses amount of dispersion in a sample

 Mean chart (x-bar Chart)

 Uses process average of a sample
 x-bar Chart: Standard Deviation
Known

LCL

Where

= standard deviation of sample means =

k = number of samples

n = sample size (i.e number of observations in each sample).

 X-bar Chart Example: Standard
Deviation Known
The Goliath Tool Company produces slip-ring
bearings, which look like flat doughnuts or washers.
They fit around shafts or rods, such as drive shafts in
machinery or motors. At an early stage in the
production process for a particular slip-ring bearing,
the outside diameter of the bearing is measured.
Employees have taken 10 samples (during a 10-day
period) of 5 slip-ring bearings and measured the
diameter of the bearings. The individual observations
from each sample (or subgroup) are shown as
follows:
x-bar Chart Example: Standard
Deviation Known (cont.)
 X-bar Chart Example: Standard
Deviation Known
From past historical data it is known that the process
standard deviation is 0.08. The company wants to
develop a control chart with 3-sigma limits to monitor
this process in the future.
 x-bar Chart: Standard Deviation
Known

= 5.01

= 5.01 + 3() = 5.12

LCL = 5.01 – 3() = 4.90

x-bar Chart: Standard Deviation
Known
x-bar Chart Example: Standard
Deviation Unknown
Control Limits
x-bar Chart Example: Standard
Deviation Unknown
x-bar Chart Example: Standard
Deviation Unknown (cont.)
x-bar Chart Example: Standard
Deviation Unknown (cont.)
R-Chart
R-Chart Example
R-Chart Example (cont.)
R-Chart Example (cont.)
 Using x-Chart and R-Chart
Together
 Process average and process variability must be
in control
 It is possible for samples to have very narrow
ranges, but their averages might be beyond
control limits.
 It is possible for sample averages to be in
control, but ranges might be very large
 It is possible for an R-chart to exhibit a distinct
downward trend, suggesting some nonrandom
cause is reducing variation.
 Control Chart Patterns
 A Run is a sequence of sample values that display the same
characteristics (for e.g. 3 values above centerline followed by 2
values below centerline represent 2 runs of a pattern).
 Pattern test determines if observations within limits of a
control chart display a nonrandom pattern.
 To identify a pattern:
 8 consecutive points on one side of the centerline
 8 consecutive points up or down
 14 points alternating up or down
 2 out of 3 consecutive points in zone A (on one side of centerline)
 4 out of 5 consecutive points in zone A or B (on one side of centerline)
Control Chart Patterns (cont.)
Control Chart Patterns (cont.)
Zones for Pattern Tests
 Performing a Pattern Test
Sample x-bar Above/Below Up/Down Zone
1 4.98 B − B
2 5 B U C
3 4.97 B D B
4 4.96 B D A
5 4.99 B U C
6 5.01 − U C
7 5.02 A U C
8 5.05 A U B
9 5.08 A U A
10 5.03 A D B
 Sample Size Determination
 Attribute charts require larger sample sizes
 50 to 100 parts in a sample
 Variable charts require smaller samples
 2 to 10 parts in a sample
 Size may not be the only consideration in sampling
 Sample must come from a homogeneous source (for
example, from a single machine or same shift of workers)
SPC With Excel
SPC With Excel and OM Tools
 Process Capability
 Once the stability of a process has been established
(i.e., no nonrandom variations are present), it is
necessary to determine if the process is capable of
producing output that is within an acceptable range.
The variability of a process becomes the focal point of
the analysis.
 Three commonly used terms refer to the variability of
process output:
 Specifications or tolerances
 Process variability
 Process capability
 Process Capability
 Tolerances
 Design specifications reflecting customer requirements for a product or
engineering design.
 Specify a range of values above and below a designed target value
(a.k.a the nominal value) within which product units must fall to be
acceptable.
 Are not determined from the production process; they’re externally
imposed by the designers of the product or service.
 Process Capability
 Process variability
 reflects the natural or inherent (i.e., random) variability
in a process. It is measured in terms of the process
standard deviation.
 Control limits and process variability are directly related:
Control limits are based on sampling variability, and
sampling variability is a function of process variability.
 Process Capability
 Process capability
 Refers to the natural variation of a process relative to the variation
allowed by the design specifications.
 Process control charts are used for process capability to determine
if an existing process is capable of meeting design specifications
 Three main elements associated with process
capability:
 Process variability (the natural range of variation of the process)
 Process center (mean)
 Design specifications
Process Capability Analysis
Process Capability Analysis
Process Capability Analysis
 Process Capability
 Determining process capability is important as it helps
a company understand process variation.
 If it can be determined how well a process is meeting
design specifications, and thus what the actual level of
quality is, then steps can be taken to improve quality.
 Two ratios used to quantify the capability of a process
are the capability ratio () and the capability index ()
 Process Capability Ratio
Process capability ratio is one measure of the capability
of a process to meet design specifications.
 Process Capability Ratio
 If Cp is less than 1.0, then process range is greater
than tolerance range. The process is not capable of
producing within the design specifications all the time.
 If Cp = 1.0, tolerance range and process range are
virtually the same and process is capable of meeting
design specifications
 If Cp is greater than 1.0, tolerance range is greater
than process range and process is capable of meeting
design specifications.
 Process Capability Ratio

The Munchies Snack Food Company packages potato chips in

bags. The net weight of the chips in each bag is designed to be
9.0 oz, with a tolerance of 0.5 oz. The packaging process results
in bags with an average net weight of 8.80 oz and a standard
deviation of 0.12 oz. The company wants to determine if the
process is capable of meeting design specifications.
Computing Cp
 Process Capability Index
 Process capability index is a second measure of
process capability.
 The differs from the in that it indicates if the process
mean has shifted away from the design target, and
in which direction it has shifted.
 Process Capability Index
 Cpk indicates if the process mean has shifted away from
the design target and in which direction it has shifted
( that’s if the process is off center)
 If Cpk is greater than 1.0, then the process is capable of
meeting design specifications
 If Cpk is less than 1.0, the process mean has moved
closer to one of the upper or lower design specifications,
and it will generate defects.
 If Cpk = Cp, the process mean is centered on the design
(nominal) target.
Computing Cpk
Process Capability With Excel
Process Capability With Excel and
OM Tools
 Improving Process Capability
 Improving process capability requires changing the
process target value and/or reducing the process
variability that is inherent in a process. This might involve
simplifying, standardizing, making the process mistake-
proof, upgrading equipment, or automating.
 Improved process capability means less need for
inspection, lower warranty costs, fewer complaints about
service, and higher productivity. For process control
purposes, it means narrower control limits.