Management quality management Lec 4

1. Quality Management
- A control chart monitors variation in a characteristic of a product or service
overtime.
- Information gained from analyzing a control chart forms the basis for process
improvement.
- A principal benefit of a control chart is the attempt to separate special causes
of variation from common causes of variation.
Causes of variation
Special Common
- Represent large fluctuations or
patterns in the data that are not
part of a process.
- They represent problems that can
be corrected without the change
of the system.
- Also, they are called assignable
causes of variations.
- Inherent variability that exits in a
process.
- They represent small causes of
variability that operate randomly,
and can be reduced by changing
the system.
- Also, they are called chance
causes of variations.
- Note: The systematic changes are the responsibility of the management (i.e.
not the workers involved in the process).
- Control charts help to prevent 2 types of errors
Type of error Details
First - Treating common cause
variation as a special cause.
- Results in over adjusting the
process (i.e. tampering).
- Tampering increases the
variation of the process.
Second - Treating special causes
variation as common cause
variation.
- Results in not taking immediate
corrective action as necessary
- To construct a control chart, you collect samples from the output of a process
overtime (i.e. subgroups).
- For each subgroup, you calculate the value of a statistic associated with a CTQ
variable (i.e. critical_ to_ quality variable).

2. - Common used statistics include sample proportion for categorical variables,
and the mean & range of a numerical variable.
- Plot the values over time and add control limits to the chart where
Upper control limit(UCL)=Process mean+3 * standard deviation
Lower control limit(LCL) =Process mean –3*standard deviation
- You evaluate the control chart by trying to find
i- Any pattern that might exist in the values over time.
ii- Whether any points fall outside the control limits.
PanelA
- Process
stable.
- Contains
common
causes only.
PanelB
- Special
causes exist
PanelC
- Consecutive
points above
the mean
line
- Consecutive
points below
the mean
line
- Two other simple rules allow you to detect a shift in the mean (i.e. trend
detection)
i- Eight or more consecutive points that lie above/below the
center line.
ii- Eight or more consecutive points that move upward/downward
in value.
- A process whose control chart indicates an out_of_control condition (i.e. a
point outside the limits and/or exhibit a trend) is said to be out of control.
- An out of control process includes common and special causes of variation.
- A process whose control chart does not indicate any out_of_control condition
is said to be in control.
- An in control process contains only common causes of variation.

3. - When the process is an in_ control process, you must determine whether the
amount of common cause variation in the process is small enough to satisfy
the customers of the product or service.
- If common variations are
i- Small: use chart continuously to monitor the process and to
make sure it remains in control.
ii- Large: alter the process. These alterations are the responsibility
of the management.
Control chart for the proportion (p chart)
- Used for categorical variables.
- Used to monitor and analyze the proportion of nonconforming items in
repeated samples selected from a process.
𝑃̅ ± 3√
𝑃̅(1 − 𝑃̅)
𝑛̅
Where
- 𝑛̅ =
∑ 𝑛 𝑖
𝑘
1
𝑘
- 𝑃̅ =
∑ 𝑥𝑖
𝑘
1
∑ 𝑛 𝑖
𝑘
1
- 𝑥𝑖 =⋕ of nonconforming items in subgroup i.
- 𝑛𝑖 = size for subgroup i.
- 𝑘 =⋕ of subgroups selected.
- 𝑛̅ = mean subgroup size.
- 𝑃̅ =average proportion of nonconforming items.
Note: any negative value of LCL means that the LCL does not exist.

4. Control charts for the range and the mean
- For numerical variables such as money, weight, etc.
- Charts are used in pairs (I.e. range chart for dispersion or variability and mean
chart for the process mean).
- Range chart is examined first. If it indicated out of control then the
interpretation of mean chart is misleading.
R chart
- used when sample size ≤10 (i.e we consider the range of the sample/subgroup
data as a measure of dispersion). This is the most common case.
- If sample size>10, we consider the standard deviation of the sample/subgroup
data as a measure of dispersion.
- Control limits for the range
UCL =𝐷4 𝑅̅
LCL=𝐷3 𝑅̅
Where
𝑅̅ =
∑ 𝑅𝑖
𝑘
1
𝑘
k=⋕ of subgroups , and 𝐷3 & 𝐷4 are obtained from the given
table.
𝑥̅ chart
- Control limits for the 𝑥̅ chart
UCL= 𝑥̿ + 𝐴2 𝑅̅
LCL= 𝑥̿ - 𝐴2 𝑅̅
Where we get 𝐴2 from the given table, k=⋕ of subgroups, and 𝑥̿ =
𝛴 𝑖=1
𝑘
𝑥̅
𝑘
.

5. The C Chart
- Nonconformities are defects, faults, errors, or imperfections in a product or a
service.
- An area of an opportunity is an individual unit of a product or service, a unit
of time, unit of space, or unit of area.
- To monitor and analyze number of nonconformities in an area of opportunity,
use C chart.
- Examples of number of nonconformities in an area of opportunity may be as
follows:
a- The number of typographical errors on a printed page.
b- The number of hotel customers filing complaints in a given week.
- C chart process assumes Poission distribution.
Control limits for the C chart
𝐶̅±3√𝐶̅
UCL=𝐶̅+3√𝐶̅
LCL=𝐶̅-3√𝐶̅
𝐶̅=
∑ 𝑐 𝑖
𝑘
𝑖=1
𝑘
k= number of units sampled
ci= number of nonconformities in unit i
-

6. Process capability
- A customer who believes that a product or service has met or exceeded his or
her expectations will be satisfied. Hence, quality is defined by customers.
- Specification limits are technical requirements set by management in response
to customers' needs and expectations.
- The upper/lower specification limit (USL/LSL) is the largest/smallest value a
CTQ can have and still conform to customers expectations.
- Hence, the process capability is the ability of a process to consistently meet
specified customer driven requirements. This can be done by estimating the
percentage of products or services that are within specifications.
P(an outcome will be within specification) = P( LSL<x<USL)
=P(
𝐿𝑆𝐿−𝑥̿
𝑅̅
𝑑2
< Z <
𝑈𝑆𝐿−𝑥̿
𝑅̅
𝑑2
)
Where
𝑑2 is obtained from the given table, and
We assumed normal distribution for the x values.
Capability index
- 𝐶 𝑝=
𝑈𝑆𝐿−𝐿𝑆𝐿
6(
𝑅̅
𝑑2
)
- Larger 𝐶 𝑝 means better capability of the process.
- 𝐶 𝑝is a measure of process potential, and not the actual performance.
- To measure the capability of the process in terms of actual process
performance use CPL, CPU, and 𝐶 𝑝𝑘
Where
CPL=
𝑥̿− 𝐿𝑆𝐿
3(
𝑅̅
𝑑2
)
CPU==
𝑈𝑆𝐿−𝑥̿
3(
𝑅̅
𝑑2
)
𝐶 𝑝𝑘=min(CPL,CPU)
The last measures the actual process performance