Control chart for variables ( quality assurance)

COURSE TITLE: QUALITY ASSURANCE (MSN4213)
Course Instructor: Umer Hayat
Department of Mechanical Engineering
University of Central Punjab
Control Charts for Variables
Text Book: Quality Improvement by D.H, Besterfield (9th Edition)
Chapter 6

Introduction
 Concept of variation: No 2 things are alike
 Variation exists - even if variation small and appears same, precision
instruments show differences
 Ability to measure variation is necessary before it can be controlled.
3 categories of variation:
 Within piece - e.g. surface roughness
 Piece to piece - eg. dimensions
 Time to time - different outcomes e.g. morning & afternoon,
tool wear, workers tired
2

Sources of Variation
 Source of variation - combination of equipments, materials,
environment, operator, etc.
 Equipment -tool wear, electrical fluctuations for welding
 Material -tensile strength, moisture content (e.g. raw material)
 Environment -temperature, light, humidity etc.
 Operator -method, SOP followed, motivation level, training
3

Causes of Variation: Chance and Assignable
4
Unavoidable
Out of Control

Causes of Variation: Chance and Assignable
 Chance Causes of variation are inevitable. Because they are numerous
and individually of relatively small importance, they are difficult to
detect or identify.
 Those causes of variation that are large in magnitude, and therefore
readily identified, are classified as assignable causes.
 When only chance causes are present in a process, the process is
considered to be in a state of statistical control. It is stable and
predictable.
 However, when an assignable cause of variation is also present, the
variation will be excessive, and the process is classified as out of
control.
5

Control Chart Method
 In order to indicate when observed variations in quality are greater than
could be left to chance, the control chart method of analysis and presentation
of data is used.
 The control chart method for variables is a means of visualizing the variations
that occur in the central tendency and dispersion of a set of observations.
 It is a graphical record of the quality of
a particular characteristic. It shows whether
or not the process is in a stable state.
6

 The two dashed outer lines are the upper and lower control limits.
These limits are established to assist in judging the significance of the
variation in the quality of the product or service.
 Control limits are frequently confused with specification limits, which
are the permissible limits of a quality characteristic of each individual
unit of a product.
 The control limits are usually established at ±3 standard deviations
from the central line.
 Number of items between ±3σ equals 99.73%, i-e, 9973 times out of
10,000, the subgroup values will fall between the upper and lower
limits, and when this occurs, the process is considered to be in control.
7

Example Explanation
 The frequency with which the operator inspects a product at a
particular work center is determined by the quality of the product.
 The inspection results for subgroup 2 show that the third observation,
X3 , has a value of 57, which exceeds the upper control limit. However,
57 value is an individual observation and does not relate to the control
limits. Therefore, the fact that an individual observation is greater than
or less than a control limit is meaningless.
 Subgroup 4 has an average value of 44, which is less than the lower
control limit of 45. Therefore, subgroup 4 is out of control, and the
operator will report this fact to the departmental supervisor. The
operator and supervisor will then look for an assignable cause and, if
possible, take corrective action.
10

11
❑ A control chart is a
statistical tool that
distinguishes
between natural and
unnatural variation.
❑ Unnatural variation
is the result of
assignable causes.
❑ Natural variation is
the result of chance
causes.

Types of Control Charts
12
ത
𝑋

Objectives of Variable Control Charts
13

Variable Control Chart –X(average)-R chart
Steps:
1. Select quality characteristic
2. Choose rational subgroup
3. Collect data
4. Determine trial limits and central line
5. Establish revised central line and control limits
6. Achieve the objective
15

Step 1: Select Quality Characteristic
 The variable that is chosen for an ത
𝑋 and R chart must be a quality
characteristic that is measurable and can be expressed in numbers.
 Quality characteristics that can be expressed in terms of the seven
basic units—length, mass, time, electrical current, temperature,
substance, or luminous intensity—are appropriate, as well as any of
the derived units, such as power, velocity, force, energy, density, and
pressure.
 Those quality characteristics affecting the performance of the product
or service will normally be given first attention. Pareto analysis can be
used to establish priorities.
16

Step 2: Choose Rational Subgroup
 The data that are plotted on the control chart consist of groups of items
that are called rational subgroups.
 A rational subgroup is one in which the variation within the group is due
only to chance causes.
 Two ways selecting subgroup samples
 Select subgroup samples at one instant of time or as close as possible
 Select period of time products are produced (most commonly used)
 Number of samples per subgroup:
 choose n = 4 or 5 → use R-chart
 when n  10 → use s-chart
17

Step 2: Choose Rational Subgroup
Subgroup Calculations:
 Say, 4000 parts/day
 75 samples
 If n = 4 19 subgroups
 Or n = 5 15 subgroups
18

Step 3: Collect Data
19
First measurement of 6.35 is recorded as 35.

Step 4: Determine Trial Centre Line and Control
Limits
21

 If an analysis of the preliminary data shows good control, then X(bar)
and R can be considered as representative of the process and these
become the standard values, X0 and R0 .
 Good control can be briefly described as that which has no out-of-
control points, no long runs on either side of the central line, and no
unusual patterns of variation.
 Most processes are not in control when first analyzed.
23
Step 4: Determine Trial Centre Line and Control
Limits

Example 6-1
25
An analysis of Figure 6-5 shows that there are out-of-control
points on the X(bar) chart at subgroups 4, 16, and 20 and an out-
of-control point on the R chart at subgroup 18.

Step 5: Establish Revised Central Line and
Control Limits
 Most processes are not in control when first analyzed.
 The R chart is analyzed first to determine if it is stable. Because the
out-of-control point at subgroup 18 on the R chart has an assignable
cause (damaged oil line), it can be discarded from the data. The
remaining plotted points indicate a stable process.
 The X(bar) chart can now be analyzed. Subgroups 4 and 20 had an
assignable cause, but the out-of-control condition for subgroup 16 did
not. It is assumed that subgroup 16’s out-of-control state is due to a
chance cause and is part of the natural variation.
26

 Subgroups 4 and 20 for the X chart and subgroup 18 for the R
chart are not part of the natural variation and are discarded from the
data, and new ധ
𝑋 and R values are computed with the remaining data.
 By discarding out-of-control points with assignable causes, the central
line and control limits are more representative of the process.
27
Control Limits

28
Control Limits

Example 6-3
 The preliminary data for the initial 25 subgroups are not plotted with
the revised control limits. These revised control limits are for reporting
the results for future subgroups
31

Step 6: Achieve the Objective
 Posting a quality control chart appears to be a psychological signal to
the operator to improve performance.
 Most workers want to produce a quality product or service; therefore,
when management shows an interest in the quality, the operator
responds.
32

Step 6: Achieve the Objective
 At the end of January, new central lines and control limits were
calculated using the data from subgroups obtained during the month.
 It is a good idea, especially when a chart is being initiated, to
calculate standard values periodically to see if any changes have
occurred.
 The generation of ideas by many different personnel is the most
essential ingredient for continuous quality improvement.
 Quality improvement occurs when the plotted points of the ത
𝑋 chart converge
on the central line, or when the plotted points of the R chart trend
downward, or when both actions occur.
 If a poor idea is tested, then the reverse occurs. +
 If the idea is neutral, it will have no affect on the plotted point pattern.
33

Control chart for variables ( quality assurance)

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