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 Number:
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
Process variation and control charts form the foundation of statistical process control (SPC), a
discipline introduced by Shewhart in the 1920s and further developed by Deming. Understand-
ing the nature of variation and the signals that control charts reveal is essential for maintain-
ing and improving process quality (Montgomery, 2020).
1.1 Random Variation versus Nonrandom Variation
Every process exhibits some degree of variation. The critical task of quality management is
to distinguish between variation that is inherent to the process and variation that signals a
problem requiring investigation (Evans and Lindsay, 2020).
Random Variation (Common Cause Variation)
Random variation, also referred to as common cause variation or chance variation, is the nat-
ural, unavoidable variability that exists in every process. It results from the cumulative effect
of many small, unidentifiable factors such as slight differences in raw materials, minor fluctu-
ations in temperature or humidity, and natural wear in machinery. These causes are inherent
in the design of the process and cannot be eliminated without fundamentally redesigning the
system. When only random variation is present, a process is said to be in statistical control.
On a control chart, random variation appears as data points that fluctuate randomly within
the upper and lower control limits, with no discernible pattern (Montgomery, 2020).
For example, the small differences in the delivery time of hotel luggage from one guest to the
next, caused by elevator wait times and room location, would constitute random variation.
Nonrandom Variation (Special Cause Variation)
Nonrandom variation, also called special cause variation or assignable cause variation, arises
from identifiable, specific sources that are not part of the normal process. These causes are
sporadic and can be traced and corrected. Examples include a machine that has drifted out
of calibration, an untrained employee, a defective batch of raw material, or a change in the
working environment. When nonrandom variation is present, the process is out of statistical
control and requires investigation and corrective action (Evans and Lindsay, 2020).
On a control chart, nonrandom variation manifests as points outside the control limits or as
recognisable patterns within the limits that suggest a systematic shift.
Page 2 of 13
,UNISA | MNO2602 Quality Management and Techniques
Key Distinction
Core distinction: Random variation is inherent to the system and can only be re-
duced by management through process redesign. Nonrandom variation is caused by
assignable, identifiable factors and can be corrected by operators or supervisors with-
out changing the fundamental process design. This distinction, first articulated by
Shewhart, underpins the entire philosophy of SPC (Montgomery, 2020).
1.2 Nonrandom Signals on a Process Control Chart
When a process control chart is used to monitor a process, certain patterns indicate the pres-
ence of nonrandom (assignable cause) variation. Quality practitioners use established rules
to identify these signals. The five main nonrandom patterns are discussed below (Evans and
Lindsay, 2020; Montgomery, 2020).
(a) Points Beyond the Control Limits
The most obvious signal is a single data point that falls above the upper control limit (UCL)
or below the lower control limit (LCL). Such a point provides strong statistical evidence that
a special cause has affected the process at that moment. Immediate investigation is warranted
to identify and eliminate the cause.
(b) Runs
A run occurs when a consecutive sequence of points all falls on the same side of the centreline.
A common rule is that eight or more consecutive points on one side of the centreline indicate
a shift in the process mean. A run suggests that the process average has moved in a sustained
manner, possibly due to tool wear, a change in material, or an operator adjustment.
(c) Trends
A trend is a steady, continuous movement of successive data points in one direction (upward
or downward) over time. A sequence of six or more points that consistently increase or consis-
tently decrease signals a systematic drift in the process. This often occurs due to progressive
tool wear, gradual temperature build-up, or operator fatigue.
(d) Cycles
Cycles are repeating, wave-like patterns in the data that occur at regular intervals. They
suggest a periodic cause such as a shift change, a recurring maintenance schedule, seasonal
Page 3 of 13
, UNISA | MNO2602 Quality Management and Techniques
temperature variation, or alternating suppliers. The periodicity of the pattern provides a clue
to the underlying assignable cause.
(e) Hugging the Centreline or Control Limits
Hugging occurs when data points cluster unusually close to the centreline or, conversely, un-
usually close to the control limits. Hugging the centreline may indicate that data from two
different processes or populations are being mixed (stratification). Hugging the control limits
may indicate that data from different distributions are being plotted together, inflating the
apparent spread.
Critical Consideration
These nonrandom signals are only meaningful when control limits are correctly calcu-
lated from the process data. Using specification limits in place of control limits is a
common and serious error that invalidates the chart entirely.
1.3 Types of Attributes
In quality management, attributes are qualitative characteristics of a product or service that
can be observed and counted but not measured on a continuous scale. Attributes are used
when measurement is impractical, costly, or when the quality characteristic is inherently dis-
crete (Evans and Lindsay, 2020).
(a) Defective (Nonconforming) Units
A defective unit is an entire item that fails to meet one or more specifications and is therefore
unacceptable for its intended use. The unit as a whole is classified as either conforming or
nonconforming. Attribute charts used to monitor defective units include the p chart (propor-
tion defective) and the np chart (number of defectives). For example, a ceramic tile that has a
surface crack and cannot be sold is a defective unit.
(b) Defects (Nonconformities)
A defect, or nonconformity, is a specific flaw or failure on a product. A single item can contain
multiple defects and still be classified differently depending on whether the defects are critical.
Attribute charts used to monitor defects include the c chart (number of defects per unit when
sample size is constant) and the u chart (defects per unit when sample size varies). For exam-
ple, a ceramic tile may have three surface blemishes (three defects) but could still be usable as
a second-grade product.
Page 4 of 13
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 Number:
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
Process variation and control charts form the foundation of statistical process control (SPC), a
discipline introduced by Shewhart in the 1920s and further developed by Deming. Understand-
ing the nature of variation and the signals that control charts reveal is essential for maintain-
ing and improving process quality (Montgomery, 2020).
1.1 Random Variation versus Nonrandom Variation
Every process exhibits some degree of variation. The critical task of quality management is
to distinguish between variation that is inherent to the process and variation that signals a
problem requiring investigation (Evans and Lindsay, 2020).
Random Variation (Common Cause Variation)
Random variation, also referred to as common cause variation or chance variation, is the nat-
ural, unavoidable variability that exists in every process. It results from the cumulative effect
of many small, unidentifiable factors such as slight differences in raw materials, minor fluctu-
ations in temperature or humidity, and natural wear in machinery. These causes are inherent
in the design of the process and cannot be eliminated without fundamentally redesigning the
system. When only random variation is present, a process is said to be in statistical control.
On a control chart, random variation appears as data points that fluctuate randomly within
the upper and lower control limits, with no discernible pattern (Montgomery, 2020).
For example, the small differences in the delivery time of hotel luggage from one guest to the
next, caused by elevator wait times and room location, would constitute random variation.
Nonrandom Variation (Special Cause Variation)
Nonrandom variation, also called special cause variation or assignable cause variation, arises
from identifiable, specific sources that are not part of the normal process. These causes are
sporadic and can be traced and corrected. Examples include a machine that has drifted out
of calibration, an untrained employee, a defective batch of raw material, or a change in the
working environment. When nonrandom variation is present, the process is out of statistical
control and requires investigation and corrective action (Evans and Lindsay, 2020).
On a control chart, nonrandom variation manifests as points outside the control limits or as
recognisable patterns within the limits that suggest a systematic shift.
Page 2 of 13
,UNISA | MNO2602 Quality Management and Techniques
Key Distinction
Core distinction: Random variation is inherent to the system and can only be re-
duced by management through process redesign. Nonrandom variation is caused by
assignable, identifiable factors and can be corrected by operators or supervisors with-
out changing the fundamental process design. This distinction, first articulated by
Shewhart, underpins the entire philosophy of SPC (Montgomery, 2020).
1.2 Nonrandom Signals on a Process Control Chart
When a process control chart is used to monitor a process, certain patterns indicate the pres-
ence of nonrandom (assignable cause) variation. Quality practitioners use established rules
to identify these signals. The five main nonrandom patterns are discussed below (Evans and
Lindsay, 2020; Montgomery, 2020).
(a) Points Beyond the Control Limits
The most obvious signal is a single data point that falls above the upper control limit (UCL)
or below the lower control limit (LCL). Such a point provides strong statistical evidence that
a special cause has affected the process at that moment. Immediate investigation is warranted
to identify and eliminate the cause.
(b) Runs
A run occurs when a consecutive sequence of points all falls on the same side of the centreline.
A common rule is that eight or more consecutive points on one side of the centreline indicate
a shift in the process mean. A run suggests that the process average has moved in a sustained
manner, possibly due to tool wear, a change in material, or an operator adjustment.
(c) Trends
A trend is a steady, continuous movement of successive data points in one direction (upward
or downward) over time. A sequence of six or more points that consistently increase or consis-
tently decrease signals a systematic drift in the process. This often occurs due to progressive
tool wear, gradual temperature build-up, or operator fatigue.
(d) Cycles
Cycles are repeating, wave-like patterns in the data that occur at regular intervals. They
suggest a periodic cause such as a shift change, a recurring maintenance schedule, seasonal
Page 3 of 13
, UNISA | MNO2602 Quality Management and Techniques
temperature variation, or alternating suppliers. The periodicity of the pattern provides a clue
to the underlying assignable cause.
(e) Hugging the Centreline or Control Limits
Hugging occurs when data points cluster unusually close to the centreline or, conversely, un-
usually close to the control limits. Hugging the centreline may indicate that data from two
different processes or populations are being mixed (stratification). Hugging the control limits
may indicate that data from different distributions are being plotted together, inflating the
apparent spread.
Critical Consideration
These nonrandom signals are only meaningful when control limits are correctly calcu-
lated from the process data. Using specification limits in place of control limits is a
common and serious error that invalidates the chart entirely.
1.3 Types of Attributes
In quality management, attributes are qualitative characteristics of a product or service that
can be observed and counted but not measured on a continuous scale. Attributes are used
when measurement is impractical, costly, or when the quality characteristic is inherently dis-
crete (Evans and Lindsay, 2020).
(a) Defective (Nonconforming) Units
A defective unit is an entire item that fails to meet one or more specifications and is therefore
unacceptable for its intended use. The unit as a whole is classified as either conforming or
nonconforming. Attribute charts used to monitor defective units include the p chart (propor-
tion defective) and the np chart (number of defectives). For example, a ceramic tile that has a
surface crack and cannot be sold is a defective unit.
(b) Defects (Nonconformities)
A defect, or nonconformity, is a specific flaw or failure on a product. A single item can contain
multiple defects and still be classified differently depending on whether the defects are critical.
Attribute charts used to monitor defects include the c chart (number of defects per unit when
sample size is constant) and the u chart (defects per unit when sample size varies). For exam-
ple, a ceramic tile may have three surface blemishes (three defects) but could still be usable as
a second-grade product.
Page 4 of 13
