UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Economic and Management Sciences
⋄
ASSIGNMENT 4
Semester 1, 2026
⋄
Module Code: MNO2602
Module Name: Quality Management and Techniques
Assignment No.: Assignment 4
Semester: 1st Semester 2026
Submitted in partial fulfilment of the requirements for MNO2602
at the University of South Africa.
,UNISA | MNO2602 Quality Management – Assignment 4
Question 1: Statistical Process Control – Variation and Attributes
1.1 Random Variation versus Nonrandom Variation
In statistical process control, understanding the nature of variation is fundamental to manag-
ing quality effectively (Montgomery, 2020). All processes exhibit some degree of variability,
but that variability can be classified into two distinct types: random variation and nonrandom
variation.
Random Variation (Common Cause Variation)
Random variation refers to the natural, inherent fluctuation that exists in every process. It
arises from a large number of small, independent causes that collectively produce a stable and
predictable pattern of variability around a process mean (Besterfield, 2019). These causes are
always present in the process and cannot be completely eliminated without fundamentally
redesigning the process itself.
Characteristics of random variation include:
• It is stable and statistically predictable over time.
• The process is considered to be in control when only random variation is present.
• Individual observations are scattered randomly around the process mean, with no dis-
cernible pattern.
• Examples include minor differences in raw material properties, small fluctuations in ma-
chine settings, or slight changes in the skill of different operators on a given day.
Reducing random variation requires a fundamental change to the process, such as investing
in better equipment, using higher-grade materials, or redesigning the process entirely (Mont-
gomery, 2020).
Nonrandom Variation (Special Cause Variation)
Nonrandom variation arises from specific, identifiable causes that are not part of the normal
process design. These causes are intermittent and produce patterns that are statistically un-
usual (Besterfield, 2019). When nonrandom variation is present, the process is said to be out
of control.
Characteristics of nonrandom variation include:
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,UNISA | MNO2602 Quality Management – Assignment 4
• It is unpredictable and assignable to a specific cause.
• It produces patterns that deviate significantly from what random chance would suggest.
• Examples include a broken machine component, a poorly trained operator, a faulty batch
of raw materials, or a sudden change in environmental conditions such as temperature or
humidity.
• Once the special cause is identified and removed, the process returns to a state of statisti-
cal control.
Key Distinction
Core Distinction: Random variation is the expected background “noise” of a pro-
cess and indicates a stable, in-control process. Nonrandom variation is a signal that
something unusual has occurred, pointing to a specific, assignable cause that must be
investigated and corrected (Montgomery, 2020:195).
1.2 Nonrandom Signals on a Process Control Chart
A process control chart plots sample statistics over time against upper and lower control limits
(UCL and LCL). When only random variation is present, points fall within the control limits
in a random pattern. The following nonrandom signals indicate that a special cause may be
present (Besterfield, 2019; Montgomery, 2020):
(a) Points Outside the Control Limits
The most obvious nonrandom signal is when one or more data points fall above the UCL
or below the LCL. This indicates that the process has shifted or that an extreme event has
occurred. Immediate investigation is warranted (Besterfield, 2019).
(b) A Run
A run occurs when seven or more consecutive points fall on the same side (above or below) of
the centreline, even if all points remain within the control limits. This pattern suggests that
the process mean has shifted (Montgomery, 2020). For example, if luggage delivery times at
a hotel are consistently above the average for seven consecutive days, a special cause such as
staff shortage is likely.
(c) A Trend
A trend is identified when a series of consecutive points (typically six or more) move steadily
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, UNISA | MNO2602 Quality Management – Assignment 4
in one direction, either all increasing or all decreasing. A trend may indicate gradual tool
wear, operator fatigue, or a slow deterioration of materials (Besterfield, 2019).
(d) Cycles
Cycles are periodic, repetitive patterns of variation in the data. They may be caused by shift
changes, scheduled maintenance intervals, seasonal factors, or periodic changes in raw material
batches (Montgomery, 2020).
(e) Hugging the Centreline
When an unusually large number of points cluster very close to the centreline, this may indi-
cate that data from two or more processes with different means have been mixed together. It
can also result from incorrect subgroup sampling (Besterfield, 2019).
Critical Consideration
Recognising these nonrandom signals allows quality practitioners to distinguish between
the need to manage a process (address special causes) and the need to improve the
process (reduce common cause variation). Acting on random variation as if it were a
special cause only makes process performance worse – a phenomenon Deming called
“tampering” (Montgomery, 2020:196).
1.3 Types of Attributes
Attribute data refers to quality characteristics that are measured by counting rather than by a
continuous numerical scale. Besterfield (2019) identifies the following main types of attributes:
(a) Defectives (Go/No-Go)
A unit is classified as either defective or non-defective based on whether it conforms to all
specifications. The unit as a whole is either accepted or rejected. This type of attribute is
used in the p chart (proportion defective) and the np chart (number of defectives). For ex-
ample, a ceramic tile is classified as defective if it has a surface deformity or fails to meet
dimensional specifications, regardless of how many flaws it may have.
(b) Defects (Count of Nonconformities)
A defect (or nonconformity) is a specific instance in which a quality characteristic fails to
meet a specification. A single unit may have more than one defect and may still be accepted
if the defects are minor. The number of defects in a unit or sample is counted rather than
Page 3 of 13
College of Economic and Management Sciences
⋄
ASSIGNMENT 4
Semester 1, 2026
⋄
Module Code: MNO2602
Module Name: Quality Management and Techniques
Assignment No.: Assignment 4
Semester: 1st Semester 2026
Submitted in partial fulfilment of the requirements for MNO2602
at the University of South Africa.
,UNISA | MNO2602 Quality Management – Assignment 4
Question 1: Statistical Process Control – Variation and Attributes
1.1 Random Variation versus Nonrandom Variation
In statistical process control, understanding the nature of variation is fundamental to manag-
ing quality effectively (Montgomery, 2020). All processes exhibit some degree of variability,
but that variability can be classified into two distinct types: random variation and nonrandom
variation.
Random Variation (Common Cause Variation)
Random variation refers to the natural, inherent fluctuation that exists in every process. It
arises from a large number of small, independent causes that collectively produce a stable and
predictable pattern of variability around a process mean (Besterfield, 2019). These causes are
always present in the process and cannot be completely eliminated without fundamentally
redesigning the process itself.
Characteristics of random variation include:
• It is stable and statistically predictable over time.
• The process is considered to be in control when only random variation is present.
• Individual observations are scattered randomly around the process mean, with no dis-
cernible pattern.
• Examples include minor differences in raw material properties, small fluctuations in ma-
chine settings, or slight changes in the skill of different operators on a given day.
Reducing random variation requires a fundamental change to the process, such as investing
in better equipment, using higher-grade materials, or redesigning the process entirely (Mont-
gomery, 2020).
Nonrandom Variation (Special Cause Variation)
Nonrandom variation arises from specific, identifiable causes that are not part of the normal
process design. These causes are intermittent and produce patterns that are statistically un-
usual (Besterfield, 2019). When nonrandom variation is present, the process is said to be out
of control.
Characteristics of nonrandom variation include:
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,UNISA | MNO2602 Quality Management – Assignment 4
• It is unpredictable and assignable to a specific cause.
• It produces patterns that deviate significantly from what random chance would suggest.
• Examples include a broken machine component, a poorly trained operator, a faulty batch
of raw materials, or a sudden change in environmental conditions such as temperature or
humidity.
• Once the special cause is identified and removed, the process returns to a state of statisti-
cal control.
Key Distinction
Core Distinction: Random variation is the expected background “noise” of a pro-
cess and indicates a stable, in-control process. Nonrandom variation is a signal that
something unusual has occurred, pointing to a specific, assignable cause that must be
investigated and corrected (Montgomery, 2020:195).
1.2 Nonrandom Signals on a Process Control Chart
A process control chart plots sample statistics over time against upper and lower control limits
(UCL and LCL). When only random variation is present, points fall within the control limits
in a random pattern. The following nonrandom signals indicate that a special cause may be
present (Besterfield, 2019; Montgomery, 2020):
(a) Points Outside the Control Limits
The most obvious nonrandom signal is when one or more data points fall above the UCL
or below the LCL. This indicates that the process has shifted or that an extreme event has
occurred. Immediate investigation is warranted (Besterfield, 2019).
(b) A Run
A run occurs when seven or more consecutive points fall on the same side (above or below) of
the centreline, even if all points remain within the control limits. This pattern suggests that
the process mean has shifted (Montgomery, 2020). For example, if luggage delivery times at
a hotel are consistently above the average for seven consecutive days, a special cause such as
staff shortage is likely.
(c) A Trend
A trend is identified when a series of consecutive points (typically six or more) move steadily
Page 2 of 13
, UNISA | MNO2602 Quality Management – Assignment 4
in one direction, either all increasing or all decreasing. A trend may indicate gradual tool
wear, operator fatigue, or a slow deterioration of materials (Besterfield, 2019).
(d) Cycles
Cycles are periodic, repetitive patterns of variation in the data. They may be caused by shift
changes, scheduled maintenance intervals, seasonal factors, or periodic changes in raw material
batches (Montgomery, 2020).
(e) Hugging the Centreline
When an unusually large number of points cluster very close to the centreline, this may indi-
cate that data from two or more processes with different means have been mixed together. It
can also result from incorrect subgroup sampling (Besterfield, 2019).
Critical Consideration
Recognising these nonrandom signals allows quality practitioners to distinguish between
the need to manage a process (address special causes) and the need to improve the
process (reduce common cause variation). Acting on random variation as if it were a
special cause only makes process performance worse – a phenomenon Deming called
“tampering” (Montgomery, 2020:196).
1.3 Types of Attributes
Attribute data refers to quality characteristics that are measured by counting rather than by a
continuous numerical scale. Besterfield (2019) identifies the following main types of attributes:
(a) Defectives (Go/No-Go)
A unit is classified as either defective or non-defective based on whether it conforms to all
specifications. The unit as a whole is either accepted or rejected. This type of attribute is
used in the p chart (proportion defective) and the np chart (number of defectives). For ex-
ample, a ceramic tile is classified as defective if it has a surface deformity or fails to meet
dimensional specifications, regardless of how many flaws it may have.
(b) Defects (Count of Nonconformities)
A defect (or nonconformity) is a specific instance in which a quality characteristic fails to
meet a specification. A single unit may have more than one defect and may still be accepted
if the defects are minor. The number of defects in a unit or sample is counted rather than
Page 3 of 13
