UNIVERSITY OF SOUTH AFRICA
College of Economic and Management Sciences
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MNO2602: Quality Man-
agement and Techniques
Assignment 4 — 1st Semester, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MNO2602
Module Code:
Quality Management and Techniques
Module Name:
Assignment 4
Assignment:
1st Semester 2026
Semester:
40
Total Marks:
Submitted in partial fulfilment of the requirements for MNO2602 — UNISA 2026
,UNISA | MNO2602 Quality Management and Techniques
Question 1: Process Variation and Control Charts
1.1 Random Variation versus Nonrandom Variation
Every production process produces some degree of variation in output. Understanding where
that variation comes from is central to quality management, because the source determines
what action, if any, a manager should take (Montgomery, 2020).
Random variation (also called common cause or chance variation) is the background noise
inherent in any process. It arises from a large number of small, independent causes that are
always present, such as minor fluctuations in raw material properties, slight differences in am-
bient temperature, or natural variation in operator effort. No single cause dominates. Because
these causes are part of the system itself, eliminating them requires a fundamental redesign of
the process rather than operator intervention. A process that exhibits only random variation
is said to be in statistical control, and its output is predictable within defined limits (Steven-
son, 2021:430).
Nonrandom variation (also called assignable cause or special cause variation) is variation
that can be traced to a specific, identifiable source. Examples include a worn cutting tool, a
batch of substandard raw materials, an undertrained operator, or a machine that has shifted
out of alignment. Unlike random variation, nonrandom variation is not always present. It
appears at specific times and creates patterns that are statistically detectable on a control
chart. When nonrandom variation is detected, the process is said to be out of control, and the
root cause must be found and corrected (Besterfield, 2019:315).
Key Distinction
The practical difference is one of action. Random variation calls for system-level
change, which is usually a management responsibility. Nonrandom variation calls
for investigation and correction of a specific cause, which operators can often handle
directly.
1.2 Nonrandom Signals on a Process Control Chart
A control chart plots sample statistics (such as the sample mean) over time, bounded by up-
per and lower control limits. As long as all points fall randomly within the limits, the process
is in control. Certain patterns, however, signal that nonrandom variation is present (Steven-
Page 2 of 12
,UNISA | MNO2602 Quality Management and Techniques
Table 1: Comparison: Random vs Nonrandom Variation
Aspect Random Variation Nonrandom Variation
Also known as Common cause / chance cause Assignable cause / special cause
Origin Many small, unidentifiable One specific, identifiable cause
causes
Predictability Predictable; within control limits Unpredictable; produces unusual
patterns
Process status In statistical control Out of statistical control
Corrective action System redesign (management) Identify and remove the specific
cause
son, 2021:434–436):
a) A point beyond the control limits. When a single plotted point falls above the up-
per control limit or below the lower control limit, this is the clearest signal that something
has gone wrong. The probability of this happening by chance alone (for a process with only
random variation) is very small, so such a point strongly suggests an assignable cause.
b) A run. A run is a sequence of consecutive points that all fall on the same side of the cen-
treline. As a general rule, eight or more consecutive points above or below the centreline sug-
gest that the process mean has shifted. The longer the run, the less likely it is due to chance.
c) A trend. A trend occurs when a series of consecutive points move steadily upward or
downward without reversing direction. Six or more points continually increasing or decreasing
suggests a gradual drift in the process, perhaps caused by tool wear or gradual contamination.
d) Cycling. This is a repeating wave pattern in which points rise and fall in a regular, pre-
dictable cycle. It may indicate a shift pattern where different operators or machines alternate,
or an environmental factor that fluctuates periodically such as temperature.
e) Hugging the centreline. When nearly all points cluster very close to the centreline, this
may seem reassuring but can indicate that the subgroups have been improperly formed by
mixing data from two different process streams, artificially reducing apparent variation.
f ) Hugging the control limits. When points consistently fall near the upper or lower con-
trol limit rather than in the middle zone, this can indicate that two populations with different
means are being sampled together.
Page 3 of 12
,UNISA | MNO2602 Quality Management and Techniques
Implementation Insight
In South African manufacturing, run signals and trend signals are particularly common
when seasonal humidity changes affect material properties or when ageing machin-
ery drifts gradually out of specification. Recognising these signals early avoids costly
defective batches.
1.3 Types of Attributes
In quality control, data falls into two broad categories: variables (measured on a continuous
scale) and attributes. Attributes are quality characteristics that are assessed by determin-
ing whether an item conforms to a standard or by counting the number of nonconformities
(Besterfield, 2019:251). There are two main types:
a) Defectives (nonconforming units). A unit is classified as either defective or not de-
fective. The item as a whole either passes or fails inspection. No partial credit is given. For
example, a ceramic tile is either accepted or rejected based on whether any of its character-
istics fall outside specification. The proportion of defectives in a sample is tracked using a
p chart (fraction defective) or an np chart (number of defectives). This type of attribute is
useful when the item cannot be used at all if it fails, making a pass/fail decision the most
practical approach.
b) Defects (nonconformities). Here, the number of individual nonconformities within
a single unit is counted. A unit can have multiple defects and still be put into service. For
example, a roll of fabric may have several weaving flaws, each counted separately. A motor
vehicle might have paint blemishes, trim misalignments, and a loose fitting all recorded on the
same unit. The count of defects per unit is monitored using a c chart (when the sample size is
constant) or a u chart (when sample size varies). This approach is valuable when each defect
independently affects the product’s quality or customer perception.
Critical Consideration
The distinction between a defective and a defect matters for chart selection. Using a p
chart when a c chart is appropriate, or vice versa, produces control limits that do not
reflect the true process behaviour, leading to incorrect decisions.
Page 4 of 12
, UNISA | MNO2602 Quality Management and Techniques
Question 2: Control Chart Construction
2.1 Control Limits for the x̄ Chart (Range as Measure of Dispersion)
The following data records the luggage delivery times (in minutes) at a hotel over five days,
with three observations per day (n = 3):
Table 2: Luggage Delivery Times per Day (minutes)
Day Obs 1 Obs 2 Obs 3 x̄ R
1 6.7 11.7 9.7 9.37 5.00
2 7.6 11.4 9.0 9.33 3.80
3 9.5 8.9 9.9 9.43 1.00
4 9.8 13.2 6.9 9.97 6.30
5 11.0 9.9 11.3 10.73 1.40
Total 48.83 17.50
Step 1: Calculate the subgroup means and ranges
For each day, the sample mean x̄i and range Ri = xmax − xmin are computed as shown above.
6.7 + 11.7 + 9.7 28.1
Day 1: x̄1 = = = 9.37, R1 = 11.7 − 6.7 = 5.00
3 3
7.6 + 11.4 + 9.0 28.0
Day 2: x̄2 = = = 9.33, R2 = 11.4 − 7.6 = 3.80
3 3
9.5 + 8.9 + 9.9 28.3
Day 3: x̄3 = = = 9.43, R3 = 9.9 − 8.9 = 1.00
3 3
9.8 + 13.2 + 6.9 29.9
Day 4: x̄4 = = = 9.97, R4 = 13.2 − 6.9 = 6.30
3 3
11.0 + 9.9 + 11.3 32.2
Day 5: x̄5 = = = 10.73, R5 = 11.3 − 9.9 = 1.40
3 3
¯ and average range R̄
Step 2: Calculate the grand mean x̄
P
x̄i 9.37 + 9.33 + 9.43 + 9.97 + 10.73 48.83
¯=
x̄ = = = 9.77 minutes
k 5 5
P
Ri 5.00 + 3.80 + 1.00 + 6.30 + 1.40 17.50
R̄ = = = = 3.50 minutes
k 5 5
Step 3: Determine the control chart factor
Page 5 of 12
College of Economic and Management Sciences
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MNO2602: Quality Man-
agement and Techniques
Assignment 4 — 1st Semester, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
MNO2602
Module Code:
Quality Management and Techniques
Module Name:
Assignment 4
Assignment:
1st Semester 2026
Semester:
40
Total Marks:
Submitted in partial fulfilment of the requirements for MNO2602 — UNISA 2026
,UNISA | MNO2602 Quality Management and Techniques
Question 1: Process Variation and Control Charts
1.1 Random Variation versus Nonrandom Variation
Every production process produces some degree of variation in output. Understanding where
that variation comes from is central to quality management, because the source determines
what action, if any, a manager should take (Montgomery, 2020).
Random variation (also called common cause or chance variation) is the background noise
inherent in any process. It arises from a large number of small, independent causes that are
always present, such as minor fluctuations in raw material properties, slight differences in am-
bient temperature, or natural variation in operator effort. No single cause dominates. Because
these causes are part of the system itself, eliminating them requires a fundamental redesign of
the process rather than operator intervention. A process that exhibits only random variation
is said to be in statistical control, and its output is predictable within defined limits (Steven-
son, 2021:430).
Nonrandom variation (also called assignable cause or special cause variation) is variation
that can be traced to a specific, identifiable source. Examples include a worn cutting tool, a
batch of substandard raw materials, an undertrained operator, or a machine that has shifted
out of alignment. Unlike random variation, nonrandom variation is not always present. It
appears at specific times and creates patterns that are statistically detectable on a control
chart. When nonrandom variation is detected, the process is said to be out of control, and the
root cause must be found and corrected (Besterfield, 2019:315).
Key Distinction
The practical difference is one of action. Random variation calls for system-level
change, which is usually a management responsibility. Nonrandom variation calls
for investigation and correction of a specific cause, which operators can often handle
directly.
1.2 Nonrandom Signals on a Process Control Chart
A control chart plots sample statistics (such as the sample mean) over time, bounded by up-
per and lower control limits. As long as all points fall randomly within the limits, the process
is in control. Certain patterns, however, signal that nonrandom variation is present (Steven-
Page 2 of 12
,UNISA | MNO2602 Quality Management and Techniques
Table 1: Comparison: Random vs Nonrandom Variation
Aspect Random Variation Nonrandom Variation
Also known as Common cause / chance cause Assignable cause / special cause
Origin Many small, unidentifiable One specific, identifiable cause
causes
Predictability Predictable; within control limits Unpredictable; produces unusual
patterns
Process status In statistical control Out of statistical control
Corrective action System redesign (management) Identify and remove the specific
cause
son, 2021:434–436):
a) A point beyond the control limits. When a single plotted point falls above the up-
per control limit or below the lower control limit, this is the clearest signal that something
has gone wrong. The probability of this happening by chance alone (for a process with only
random variation) is very small, so such a point strongly suggests an assignable cause.
b) A run. A run is a sequence of consecutive points that all fall on the same side of the cen-
treline. As a general rule, eight or more consecutive points above or below the centreline sug-
gest that the process mean has shifted. The longer the run, the less likely it is due to chance.
c) A trend. A trend occurs when a series of consecutive points move steadily upward or
downward without reversing direction. Six or more points continually increasing or decreasing
suggests a gradual drift in the process, perhaps caused by tool wear or gradual contamination.
d) Cycling. This is a repeating wave pattern in which points rise and fall in a regular, pre-
dictable cycle. It may indicate a shift pattern where different operators or machines alternate,
or an environmental factor that fluctuates periodically such as temperature.
e) Hugging the centreline. When nearly all points cluster very close to the centreline, this
may seem reassuring but can indicate that the subgroups have been improperly formed by
mixing data from two different process streams, artificially reducing apparent variation.
f ) Hugging the control limits. When points consistently fall near the upper or lower con-
trol limit rather than in the middle zone, this can indicate that two populations with different
means are being sampled together.
Page 3 of 12
,UNISA | MNO2602 Quality Management and Techniques
Implementation Insight
In South African manufacturing, run signals and trend signals are particularly common
when seasonal humidity changes affect material properties or when ageing machin-
ery drifts gradually out of specification. Recognising these signals early avoids costly
defective batches.
1.3 Types of Attributes
In quality control, data falls into two broad categories: variables (measured on a continuous
scale) and attributes. Attributes are quality characteristics that are assessed by determin-
ing whether an item conforms to a standard or by counting the number of nonconformities
(Besterfield, 2019:251). There are two main types:
a) Defectives (nonconforming units). A unit is classified as either defective or not de-
fective. The item as a whole either passes or fails inspection. No partial credit is given. For
example, a ceramic tile is either accepted or rejected based on whether any of its character-
istics fall outside specification. The proportion of defectives in a sample is tracked using a
p chart (fraction defective) or an np chart (number of defectives). This type of attribute is
useful when the item cannot be used at all if it fails, making a pass/fail decision the most
practical approach.
b) Defects (nonconformities). Here, the number of individual nonconformities within
a single unit is counted. A unit can have multiple defects and still be put into service. For
example, a roll of fabric may have several weaving flaws, each counted separately. A motor
vehicle might have paint blemishes, trim misalignments, and a loose fitting all recorded on the
same unit. The count of defects per unit is monitored using a c chart (when the sample size is
constant) or a u chart (when sample size varies). This approach is valuable when each defect
independently affects the product’s quality or customer perception.
Critical Consideration
The distinction between a defective and a defect matters for chart selection. Using a p
chart when a c chart is appropriate, or vice versa, produces control limits that do not
reflect the true process behaviour, leading to incorrect decisions.
Page 4 of 12
, UNISA | MNO2602 Quality Management and Techniques
Question 2: Control Chart Construction
2.1 Control Limits for the x̄ Chart (Range as Measure of Dispersion)
The following data records the luggage delivery times (in minutes) at a hotel over five days,
with three observations per day (n = 3):
Table 2: Luggage Delivery Times per Day (minutes)
Day Obs 1 Obs 2 Obs 3 x̄ R
1 6.7 11.7 9.7 9.37 5.00
2 7.6 11.4 9.0 9.33 3.80
3 9.5 8.9 9.9 9.43 1.00
4 9.8 13.2 6.9 9.97 6.30
5 11.0 9.9 11.3 10.73 1.40
Total 48.83 17.50
Step 1: Calculate the subgroup means and ranges
For each day, the sample mean x̄i and range Ri = xmax − xmin are computed as shown above.
6.7 + 11.7 + 9.7 28.1
Day 1: x̄1 = = = 9.37, R1 = 11.7 − 6.7 = 5.00
3 3
7.6 + 11.4 + 9.0 28.0
Day 2: x̄2 = = = 9.33, R2 = 11.4 − 7.6 = 3.80
3 3
9.5 + 8.9 + 9.9 28.3
Day 3: x̄3 = = = 9.43, R3 = 9.9 − 8.9 = 1.00
3 3
9.8 + 13.2 + 6.9 29.9
Day 4: x̄4 = = = 9.97, R4 = 13.2 − 6.9 = 6.30
3 3
11.0 + 9.9 + 11.3 32.2
Day 5: x̄5 = = = 10.73, R5 = 11.3 − 9.9 = 1.40
3 3
¯ and average range R̄
Step 2: Calculate the grand mean x̄
P
x̄i 9.37 + 9.33 + 9.43 + 9.97 + 10.73 48.83
¯=
x̄ = = = 9.77 minutes
k 5 5
P
Ri 5.00 + 3.80 + 1.00 + 6.30 + 1.40 17.50
R̄ = = = = 3.50 minutes
k 5 5
Step 3: Determine the control chart factor
Page 5 of 12
