Undergraduate Project written by EBERE on ANALYSIS OF VARIATION IN GSK
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Transcript of Undergraduate Project written by EBERE on ANALYSIS OF VARIATION IN GSK
CHAPTER ONE
INTRODUCTION
1.1 Background of Study
Analysis of variance (ANOVA) was first used by behavioral scientists in the 1930s,
use of Analysis of Variance grew quickly after World War II, and exactly paralleled
incorporation of statistical significance testing in general. Detailed consideration
of this history suggests several reasons for the pattern of slow growth, followed
by rapid institutionalization. In particular, ANOVA stood duty as a warrant of
scientific legitimacy among behavioral scientists, a fact that may also be relevant
to understanding recent critiques by psychologists of its overuse and misuse.
Sir Ronald Fisher introduced the term "variance" and proposed a formal analysis
of variance in a 1918 article The Correlation between Relatives on the Supposition
of Mendelian Inheritance. His first application of the analysis of variance was
published in 1921. Analysis of variance became widely known after being included
in Fisher's book (1925) ,Statistical Methods for Research Workers.
One of the attributes of analysis of variance which ensured its early popularity
was computational elegance. The structure of the additive model allows solution
for the additive coefficients by simple algebra rather than by matrix calculations.
In the era of mechanical calculators this simplicity was critical. The determination
of statistical significance also required access to tables of the F function which
were supplied by early statistics texts.
Analysis of variance is a collection of statistical models used in order to analyze
the differences among group means and their associated procedures. In the
1
ANOVA setting, the observed variance in a particular variable is partitioned into
components attributable to different sources of variation. In its simplest form,
ANOVA provides a statistical test of whether or not the means of several groups
are equal, and therefore generalizes the t-test to more than two groups. As
doing multiple two-sample t-tests would result in an increased chance of
committing a statistical type I error, analysis of variance are useful in comparing
(testing) three or more means (groups or variables) for statistical significance.
Analysis of variance is a particular form of statistical hypothesis testing heavily
used in the analysis of experimental data. A statistical hypothesis test is a method
of making decisions using data. A test result (calculated from the null
hypothesis and the sample) is called statistically significant if it is deemed unlikely
to have occurred by chance, assuming the truth of the null hypothesis. A
statistically significant result, when a probability (p-value) is less than a threshold
(significance level), justifies the rejection of the null hypothesis, but only if the a
priori probability of the null hypothesis is not high.
In the typical application of ANOVA, the null hypothesis is that all groups are
simply random samples of the same population. For example, when studying the
effect of different treatments on similar samples of patients, the null hypothesis
would be that all treatments have the same effect (perhaps none). Rejecting the
null hypothesis would imply that different treatments result in altered effects.
By construction, hypothesis testing limits the rate of Type I errors (false positives
leading to false scientific claims) to a significance level. Experimenters also wish to
limit Type II errors (false negatives resulting in missed scientific discoveries). The
Type II error rate is a function of several things including sample size (positively
2
correlated with experiment cost), significance level (when the standard of proof is
high, the chances of overlooking a discovery are also high) and effect size (when
the effect is obvious to the casual observer, Type II error rates are low).
The terminology of analysis of variance is largely from the statistical design of
experiments. The experiment adjusts factors and measures responses in an
attempt to determine an effect. Factors are assigned to experimental units by a
combination of randomization and blocking to ensure the validity of the
results. Blinding keeps the weighing impartial. Responses show a variability that is
partially the result of the effect and is partially random error.
Analysis of variance is the synthesis of several ideas and it is used for multiple
purposes. As a consequence, it is difficult to define concisely or precisely.
Analysis of variance is difficult to teach, particularly for complex experiments,
with split-plot designs being notorious. In some cases the proper application of
the method is best determined by problem pattern recognition followed by the
consultation of a classic authoritative test.
Analysis of variance technique is mostly applied among mathematicians working
in the area of quality control and assurance, project management, supply chains,
planning and operations.
3
1.2 Statement of problem
This project is bent on applying statistics of variance in analyzing and monitoring
differences between the actual disparities of product characteristics versus the
target, spot trends, issues, opportunities and threats to short-term or long-term
success.
1.3 Justification for the study
Analysis of variance is relevant in detecting any difference between groups on
some variable. The study is highly relevant in testing equality among several
means by comparing variance among groups relative to variance within groups.
1.4 Scope of the study
This study only covers the problem of variation in production and filled weights of
products.
1.5 Aim and objective of the study1. A key manufacturing performance objective is the establishment of stable
and predictable processes that limits variation to what can be described as
random, minimum variation around target values. The study aims at finding
a solution in stabilizing production.
2. Excessive variation in manufacturing is outside the upper and lower
acceptable limits defined in manufacturing or product specifications, which
can lead to product discard. Hence, the study aims at eliminating variation
in the weight of products. Otherwise, there could be product rejects and
reworks, decreasing manufacturing process efficiency and increasing
manufacturing costs.
3. To use control charts in monitoring the variance.
4
1.6 Definition of key concept terms
Study variable
A study variable is the variable of interest.
Sample
A sample includes a subset, fraction or a part of individuals from within a
particular population.
Analysis of Variance
Analysis of Variance is a statistical test used to determine if more than two
population means are equal.It is a statistical technique used to analyze variation
in a response variable (continuous random variable) measured under conditions
defined by discrete factors (classification variables, often with nominal levels).
Sigma
Sigma is a statistical notation for the standard deviation parameter that can be
used to quantify how far a given process deviates from perfection.
Six Sigma
Six Sigma is measuring the number of "defects" in a process and figuring out how
to eliminate them in order to get the process more in line with its goal.
Defects
Defects can be used in a more general context; the term could refer to any issue
that causes concern to a company, such as defective products, out-of-specs
products, inconsistency in production volumes.
5
Quality Control
Quality control reviews the factors involved in manufacturing and production; it
can make use of statistical sampling of product items to aid decisions in process
control or in accepting deliveries
Quality assurance
Quality assurance is a way of preventing mistakes or defects in manufactured
products and avoiding problems when delivering solutions or services to
customers.
Histogram
A histogram is a graphical representation of the distribution of numerical data. It
is an estimate of the probability distribution of a continuous variable (quantitative
variable)
Pareto chart
A Pareto chart, is a type of chart that contains both bars and a line graph, where
individual values are represented in descending order by bars, and the cumulative
total is represented by the line.
Process
A process is a unique combination of tools, materials, methods, and people
engaged in producing a measurable output; for example a manufacturing line for
machine parts. All processes have inherent statistical variability which can be
evaluated by statistical methods.
6
Root cause analysis
Root cause analysis (RCA) is a method of problem solving used for identifying
the root causes of faults or problems. A factor is considered a root cause if
removal thereof from the problem-fault-sequence prevents the final undesirable
event from recurring; whereas a causal factor is one that affects an event's
outcome, but is not a root cause. Though removing a causal factor can benefit an
outcome, it does not prevent its recurrence within certainty.
Control charts
Control charts, also known as Shewhart charts or process-behavior
charts, statistical process control are tools used to determine if a manufacturing
or business process is in a state of statistical control.
Fishbone Diagram
Fishbone diagrams also called cause-and-effect diagrams are causal diagrams
that show the causes of a specific event. Common uses of the fishbone diagram
are product design and quality defect prevention, to identify potential factors
causing an overall effect.
7
CHAPTER TWO
LITERATURE REVIEW
Motorola in the mid-1980s proposed six sigma as an approach to improve
productivity and quality as well as reducing operational costs. The sigma’s name
originated from the greek alphabet and in quality control terms sigma (δ) has
been traditionally used to measure the variation in a process or its output. Six
Sigma level refers to a process which only produces 3.4 defects per every one
million product produced. Six Sigma methodology and Control charts aided the
company in reducing variation and defects and thereby increasing profit and
reducing customer’s returns [3].
Xiaojun [9] made use of ANOVA test to check for mean shift so as to monitor the
variation of material expiration and quality reject in a pharmaceutical company by
minimizing discard practices. He identified raw material expiration as one of the
primary discard causes. He focused on minimizing raw materials expiration by
developing appropriate raw material inventory control procedures.
Jose,et al [7] considered defects reduction in a rubber gloves manufacturing
process by applying six sigma principles and DMAIC ( Define, Measure, Analyze,
Improve, Control ) problem solving methodology to improve quality. They
demonstrated the empirical application of six sigma and DMAIC to reduce product
defects within a rubber gloves manufacturing organization, they went further to
investigate defects, root causes and provide a solution to reduce or even
eliminate defects. The analysis indicated that the oven’s temperature and
conveyor’s speed influenced the amount of defective gloves produced. In
particular, the design of experiments (DOE) and two-way analysis of variance
8
(ANOVA) techniques were combined to statistically determine the correlation of
the oven’s temperature and conveyor’s speed with defects as well as to define
their optimum values needed to reduction eliminate the defects. As a result, a
reduction of about 50% in the “leaking” gloves defect was achieved, which helped
the organization studied to reduce its defects per million opportunities (DPMO)
from 195,095 to 83,750 and thus improve its sigma level from 2.4 to 2.9 .After the
analyses carried out, the improvement project found that the oven’s temperature
and conveyor’s speed had a statistically significant impact on the production of
leaking gloves. By considering this, a reduction in the amount of defects was
obtained by determining the optimum oven’s temperature and conveyor’s speed.
Hanna and Lott [8] worked on the application of statistical quality control
procedures to production of highway pavement concrete. The following are step-
by-step guide procedures they developed.
“Step 1 . Select material or items of construction for which numerical acceptance
limits are to be developed.
Step 2 .List significant quality characteristics of each material or item. Analyze
historical data or otherwise obtain preliminary estimate of normal variation on
which sampling plan will be based.
Step 3 . Design plan that will insure randomness of sampling. Specify in detail the
methods of sampling and testing on which acceptance will be based.
Step 4 . Apply sampling plan to material or item of construction produced under
acceptable routine. Conditions and usual job control. Take a minimum of 50
samples in duplicate of each of 3 representative locations.
9
Step 5 . Divide each duplicate sample into two portions as identical as possible.
(600 portions from the 10 duplicate samples)
Step 6 . Obtain measurement of selected characteristics on each portion of rot
tine methods which will be used in acceptance testing.
Step 7. For each characteristic compute average level, overall variance, variance
due to sampling procedure and variance due to testing error.
Step 8. Classify the characteristics with respect to criticality and multiply the
sigma of each characteristic by acceptance tolerance(T ) appropriate to its
classification.
Step 9 . Compare limit(s) obtained in Step 8 with existing limits and/or
engineering requirements. Adopt if a reasonable comparison is obtained. If limits
appear too wide, examine sources of variance to determine if construction or
process controls must be tightened, or if variance due to sampling and tests can
be reduced.
Step 10 . Apply statistically obtained limits on trial basis concurrently with
governing current specifications.”
The above steps yielded an improved production.
Mazda Motors famously used an Ishikawa (Fishbone) diagram in the development
of the Miata sports car, where the required result was “Horse and Rider as One”.
Ishikawa diagrams were popularized in the 1960s by Kaoru Ishikawa, who
pioneered quality management processes in the Kawasaki shipyards, and in the
process became one of the founding fathers of modern management [6]. The
basic concept was first used in the 1920s, and is considered one of the seven basic
tools of quality control. It is known as a fishbone diagram because of its shape,
similar to the side view of a fish skeleton. Ishikawa diagram, in fishbone shape,
10
showing factors of Equipment, Process, People, Materials, Environment and
Management, all affecting the overall problem. Smaller arrows connect the sub-
causes to major causes. The main results of the analysis in Mazda Motors was
later discovered to be such aspects as "touch" and "braking" with the lesser
causes including highly granular factors such as "50/50 weight distribution" and
"able to rest elbow on top of driver's door". Every factor identified in the diagram
was included in the final design [1].
Other early adopters of Six Sigma include Honeywell (previously known
as AlliedSignal) and General Electric, where Jack Welch introduced the method. At
2013, about two-thirds of the Fortune 500 organizations had begun Six Sigma
initiatives with the aim of reducing costs and improving quality [2].
In recent years, some practitioners have combined Six Sigma ideas with lean
manufacturing to create a methodology named Lean Six Sigma [5]. The Lean Six
Sigma methodology views lean manufacturing, which addresses process flow and
waste issues, and Six Sigma, with its focus on variation and design, as
complementary disciplines aimed at promoting "business and operational
excellence".Companies such as GE, Verizon, GENPACT, and IBM use Lean Six
Sigma to focus transformation efforts not just on efficiency but also on growth. It
serves as a foundation for innovation throughout the organization, from
manufacturing and software development to sales and service delivery
functions[4].
11
CHAPTER THREE
RESEARCH METHODOLOGY
This chapter presents the problem solving approach used in eliminating variation
in a manufacturing company.
3.1 RELEVANT TOOLS AND CHARTS
Usually, there are some commonly recognized tools or diagrams for statistical
process variation control:
1. Run chart 2. Histogram 3. Pareto chart 4. Cause and effect or fishbone diagram 5. Control chart Some basic examples are shown in following which i have cited from (FredSpring,
1995) only for illustration the general characteristics.
1.Run Chart:The run chart tracks trends over a period of time. Points are tracked in the order
in which they occur. Each point represents an observation. We can often see
interesting trends in the data by simply plotting data on a run chart. A danger in
using run charts is that we might overreact to normal variations, but it is often
useful to put our data on a run chart to get a feel for process behavior.
12
Figure 3.1: Example of a run chart (Source : Thomas, 1997)
2.Histogram: The histogram (see Figure 2.2)is a bar chart that presents data that
have been collected over a period of time, and graphically presents these data by
frequency. Each bar represents the number of observations that fit within the
indicated range. Histograms are useful because they can be used to see the
amount of variation in a process. Using the histogram, we get a different
perspective on the data. We can see how often similar values occur and get a
quick idea of how the data are distributed.
Figure 3.2: Example of a Histogram (Source : Thomas, 1997)
13
3.Pareto Chart: The Pareto chart (see Figure 3.3) is a bar chart that presents data
prioritized in some fashion, usually either by descending or ascending order of
importance. Pareto diagrams are used to show attribute data. Attributes are
qualitative data that can be counted for recording and analysis; for example,
counting the number of each type of defect. Pareto charts are often used to
analyze the most often occurring type of defect.
Figure 3.3: An example of a Pareto chart (Thomas, 1997)
4.Cause-and-Effect/Fishbone Diagram: The cause-and-effect/fishbone diagram
(see Figure 2.4) is a graphical display of problems and causes. This is a good to
capture team input from a brainstorming meeting, from a set of defect data, or
from a check sheet.
14
Figure 3.4: A cause and effect/fishbone diagram example (Source : Thomas, 1987)
5.Control Chart: The control chart (see Figure 3.5) is basically a run charts with
upper and lower limits that allows an organization to track process performance
variation. Control charts are also called process behavior charts.
Figure 3.5: Example of a control chart (Source : Thomas, 1997)
15
Hence, I conclude by summarizing the uses of some statistical tools that would be
needed in this project;
1. Process flowchart – describes what is done in the industry.
2. Histograms and run chart–shows what the variation looks like
3. Graphs –can the variation be represented in a time series?
4. Pareto analysis –which are the big problems?
5. Cause and effect analysis and brainstorming –what causes the problems?
6. Control charts –what are the variations to be controlled and how would it
be done?
3.2 IMPORTANT FORMULAS
3.2.1 Process Capability Potential (Cp) Cp = USL−LSL6σ
Where
Cp = process capability potential.
USL = upper spec limit.
LSL = lower spec limit.
σ = estimated process common cause variability standard deviation.
16
3.2.2 Process Performance (Ppk)
Ppk = min (USL−X3 s , X́−LSL3 s )
Where
Ppk = process performance
X́ = process average (mean )
USL= upper spec limit.
LSL = lower spec limit.
s = estimated overall process standard deviation
3.2.3 Process Performance Potential (Pp)
Pp = USL−LSL6 s
Where
Pp = process performance potential
USL = upper spec limit.
LSL = lower spec limit.
s = estimated actual process standard deviation.
3.2.4 Product Reliability With A Constant Failure R = e−θt
Where
R = reliability
17
e = natural log
t = time.
θ = failure rate
3.2.5 Standard Deviation
Sample standard deviation = s = √∑ ¿¿¿¿
Where
s = population standard deviation
∑ = summation sign
Xi = observation value
X́ = sample mean
n = sample number of observations
3.3 ANOVAIn this project, one way (factor) ANOVA would be used. One way ANOVA
techniques can be used to study the effect of k (> 2) levels of a single factor. To
determine if different levels of the factor affect measured observations
differently, the following hypotheses are tested.
H0 : μi = μ all i = 1, 2, ……..,k
H1 : μi ≠ μ some i = 1, 2,……,k
where
μi = population mean for level i.
3.3.1 Notations used in ANOVA
18
Number of samples ( or levels ) = k
Number of Observation in ith sample = ni = 1,2,……………..,k.
Total number of observations = n = ∑ini
Observation j in ith sample = Xij , j = 1, 2,…….. ni
Sum of ni observations in ith sample = Ti =∑jX ij
Sum of all n observations = T = ∑iT i= ∑
i∑jX ij
3.3.2 Computational Formula
Total sum of squares, SST = ∑i∑jX ij
2 - T
2
n
Between Samples sum of squares, SSB = ∑i
T i2
ni - T
2
n
Within samples sum of squares, SSW = SST − SSB
Total mean square, MST = S STn−1
Between sample mean squares, MSB = S SBk−1
Within sample mean squares, MSW = S Swn−k
Degrees of freedom, = ( k – 1 )( n – k ) = ( n – 1 )
19
3.3.3 ANOVA Table
For a one factor analysis, the summary of the results of its analysis of variance in a
tabular form is:
Source of Variation Sum of
squares
Degrees of
freedom
Mean
square
F- ratio
Between samples
Within samples
SSB
SSW
k-1
n-k
MSB
MSW
M sBM SW
Total SST n-1
Table 3.1 : summary of the results in an ANOVA table
Decision rule
1. If P value < α (significance level) we reject H0 and accept H1.
2. If P value > α (significance level) we accept H0 and reject H1.
20
Yes
Rejected products
InspectionPacking
Shrink wrapperTray packer
No
Returning back to suppliers
Kills germs at high temperate
Laminate and strip applicator
ConveyorsStraw applicator
Quality Control
Raw materialsYesRaw materials testing Qualified
No
Mixing Pasteurizers
CHAPTER FOUR
ANALYSIS OF DATA
This chapter consists of sample of weights of Ribena and its production volume in
a particular time frame. Using the outlined methods, in chapter three, we analyze
the variation problem the company is facing and try to eliminate it.
4.1 RIBENA MANUFACTURING PROCESS FLOW CHART
Figure 4.1: Ribena Manufacturing Process Flow Chart
21
4.2 SAMPLE ON PRODUCTION VOLUME IN LINE C
line C
Date Target in trays Actual in trays
20-Jan-15 4,500 -
21-Jan-15 4,500 1,726
23-Jan-15 4,500 5,514
24-Jan-15 4,500 4,139
29-Jan-15 4,500 -
30-Jan-15 4,500 -
31-Jan-15 4,500 -
3-Feb-15 4,500 1,100
6-Feb-15 4,500 317
10-Feb-15 4,500 612
12-Feb-15 4,500 -
14-Feb-15 4,500 -
17-Feb-15 4,500 -
26-Feb-15 4,500 769
5-Mar-15 4,500 630
22
6-Mar-15 4,500 1,473
10-Mar-15 4,500 871
11-Mar-15 4,500 3,150
12-Mar-15 4,500 4,500
13-Mar-15 4,500 5,090
21-Mar-15 4,500 4,559
24-Mar-15 4,500 1,050
25-Mar-15 4,500 -
26-Mar-15 4,500 7
27-Mar-15 4,500 -
30-Mar-15 4,500 4,600
31-Mar-15 4,500 5,002
1-Apr-15 4,500 201
2-Apr-15 4,500 115
3-Apr-15 4,500 4,505
Table 4.1 : Production volume data for Ribena in line C
23
4.2.1 Control Chart For Ribena productivity
20-Jan-15
23-Jan-15
26-Jan-15
29-Jan-15
1-Feb-15
4-Feb-15
7-Feb-15
10-Feb-15
13-Feb-15
16-Feb-15
19-Feb-15
22-Feb-15
25-Feb-15
28-Feb-15
3-Mar-
15
6-Mar-
15
9-Mar-
15
12-Mar-
15
15-Mar-
15
18-Mar-
15
21-Mar-
15
24-Mar-
15
27-Mar-
15
30-Mar-
15
2-Apr-1
50
1000
2000
3000
4000
5000
6000
Ribena Production Volume -target(4500 trays)
Actual in trays
Figure 4.2: the corresponding control chart for production in line C
24
Date
outp
ut
MANMACHINES
Inaccurate
Variation
Out of dateLack ofMaintenance
Lack of motivation
MEASUREMENT
Lack of experience and training
MATERIALSMETHODS
Untidy workplace
High temperature
Inconsistency in checking the strip applicator
Under standard
Improper storage (warehouse)Restarting the machine severally due to power failure
ENVIRONMENT
From the above we see that from the sample of 30 production volumes, just 7
met the targeted production volume while the remaining 23 failed, hence this is a
big problem for the company because this would affect the profit of the company.
4.2.2 Product Reliability with a constant failure
Since, R = e-θt
θ = 23
t = 43 days
R=0, hence we can conclude that the reliability rate of the product is very low.
We go ahead to use the cause and effect (fishbone) diagram to deduce the causes and effects of these variations
4.2.3 Cause and Effect Diagram
Figure 4.3: cause and effect diagram for variation in Ribena Production
From the above cause and effect diagram we see the reasons for the variation in
production in the company, so we focus more on the waste which the company
accumulated while using the laminate and strip applicator. There are usually
irregularities in the weights of the products sometimes it becomes out of control
(outlier) and sometimes in control. We priotise the defects using pareto chart so
25
as to know which contributes more in the variation problem the company is
facing so that one could address the most common defect first.
4.2.4 Pareto Chart
Defects no of defects by type
Faulty Machine 12
Design 24
Customers reject 5
Leaks 10
Varying filled weight 30
Others 2
Table 4.2: Data collated on number of times defects occurred.
26
No 30 24 12 10 5 2Percent 36.1 28.9 14.5 12.0 6.0 2.4Cum % 36.1 65.1 79.5 91.6 97.6 100.0
Defects OtherCustomers rejectsleaksFaulty MachineDesignvarying filledweight
90
80
70
60
50
40
30
20
10
0
100
80
60
40
20
0
No
Per
cent
Pareto Chart of Defects
Figure 4.3: Pareto chart showing defects per percent
27
4.3 SAMPLE ON FILLED WEIGHTS OF RIBENA
RIBENA Spec. 162 - 164g
Date TimeProduct Jaw-1 Jaw-2 Jaw-3 Jaw-4 Mean
20-Jan-15 9:03amRTD Rib. 165 162 163 164 163.5
21-Jan-15 10:38amRTD Rib. 164 162 162 164 163
23-Jan-15 9:19amRTD Rib. 165 163 164 163 163.75
24-Jan-15 8:56amRTD Rib. 160 163 163 162 162
29-Jan-15 8:37amRTD Rib. 160 163 163 161 161.75
30-Jan-15 8:45amRTD Rib. 162 163 163 162 162.5
31-Jan-15 12:07pmRTD Rib. 166 163 163 163 163.75
3-Feb-15 1:03pmRTD Rib. 164 163 161 161 162.25
6-Feb-15 10:37amRTD Rib. 164 163 163 160 162.5
10-Feb-15 9:38amRTD Rib. 164 164 162 162 163
12-Feb-15 8:24amRTD Rib. 164 162 164 163 163.25
14-Feb-15 10:48amRTD Rib. 162 161 163 161 161.75
17-Feb-15 10:37amRTD Rib. 164 165 162 161 163
26-Feb-15 8:42amRTD Rib. 164 164 165 164 164.25
5-Mar-15 8:42amRTD Rib. 161 161 160 163 161.25
6-Mar-15 8:50amRTD Rib. 161 164 163 161 162.25
28
10-Mar-15 12:50pmRTD Rib. 161 161 162 162 161.5
11-Mar-15 8:57amRTD Rib. 163 162 164 164 163.25
12-Mar-15 9:57amRTD Rib. 162 163 163 161 162.25
13-Mar-15 8:57amRTD Rib. 163 160 163 162 162
21-Mar-15 8:45amRTD Rib. 164 164 163 166 164.25
24-Mar-15 1:38pmRTD Rib. 167 164 163 163 164.25
25-Mar-15 1:38pmRTD Rib. 165 163 164 163 163.75
26-Mar-15 1:38pmRTD Rib. 160 163 163 162 162
27-Mar-15 1:38pmRTD Rib. 160 163 163 161 161.75
30-Mar-15 9:03amRTD Rib. 162 163 163 162 162.5
31-Mar-15 10:38amRTD Rib. 166 163 163 163 163.75
1-Apr-15 9:19amRTD Rib. 164 163 161 161 162.25
2-Apr-15 8:56amRTD Rib. 164 163 163 160 162.5
3-Apr-15 8:37amRTD Rib. 164 164 162 162 163
Table 4.3: Data on filled weights of Ribena
The corresponding charts to the data above are:
4.3.1 Histogram
29
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30156
158
160
162
164
166
168
Ribena Filled Volume Histogram(spec 162-164)
no of observations
RIBE
NA
WEI
GHT
Figure 4.4: Histogram showing different Ribena filled weights.
30
4.3.2 Run Chart
20-Jan-15
23-Jan-15
26-Jan-15
29-Jan-15
1-Feb-15
4-Feb-15
7-Feb-15
10-Feb-15
13-Feb-15
16-Feb-15
19-Feb-15
22-Feb-15
25-Feb-15
28-Feb-15
3-Mar-
15
6-Mar-
15
9-Mar-
15
12-Mar-
15
15-Mar-
15
18-Mar-
15
21-Mar-
15
24-Mar-
15
27-Mar-
15
30-Mar-
15
2-Apr-1
5156
158
160
162
164
166
168
165
164
165
160 160
162
166
164164 164164
162
164 164
161161 161
163
162
163
164
167
165
160160
162
166
164164164
162162
163163 163163163163163
164
162
161
165
164
161
164
161
162
163
160
164164
163163163163163163163
164
163
162
164
163 163163163
161
163
162
164
163
162
165
160
163
162
164
163163 163163
164
163163163163
161
163
162
164164
163
162
161
162
163
161
160
162
163
161161
164
163
161
162
164
161
162
166
163163
162
161
162
163
161
160
162
Ribena filled volume trend Spec(162-164)
Jaw-1Jaw-2Jaw-3Jaw-4
Figure 4.5: Run chart showing the trend of Ribena filled weights
The above run chart depicts so much noise and hence, we say that the process is
going out of control.
31
4.3.3 Capability Test
Lower Specification Limit 162
Upper Specification Limit 164
Sample Mean 162.758
Standard Deviation (Overall) 1.41419
Standard Deviation (Within) 1.29782
Process Capability Potential (Cp)
Cp = USL−LSL6σ
= 164−1626×1.29782 = 0.26
Process Performance Potential (Pp)
Pp = USL−LSL6 s
= 164−1626×1.41419=0.24
Since Cp and Pp are below 1.5, we conclude from the above test that the products
are not meeting the customer’s needs.
32
4.4 ANALYSIS OF VARIANCE ON THE FILLED WEIGHTS
Adopting a software called Minitab we use ANOVA to test the difference in
means.
One-way ANOVA:
Null hypothesis: All means are equal
Alternative hypothesis: At least one mean is different
Significance level α = 0.1
Equal variances were assumed for this analysis.
Analysis of Variance Table
Source of Variation Sum of squares
Degrees of freedom
Mean square
F- ratio P-value
Between samples
Within samples
13.49
224.50
3
116
4.497
1.935
2.32 0.079
Total 237.99 119
Table 4.4: ANOVA table
33
Means
Factor N Mean Standard deviation
90%Confidence Interval
Jaw 1 30 163.167 1.931 (162.746,163.588)
Jaw 2 30 162.833 1.085 (162.412,163.254)
Jaw3 30 162.800 0.997 (162.379,163.221)
Jaw 4 30 162.233 1.357 (161.812,162.654)
Table 4.5:Table showing the difference in means
Test statistics:
α = 0.1
Pvalue= 0.079
We know that if Pvalue < α, we reject the null hypothesis.
Hence,
Since, 0.079 < 0.1 we reject and conclude that one or more means of the filled
weight for the different filling jaws are not equal at 0.1 level of significance.
Therefore, I infer that the filling jaws should be worked upon first by the
technicians to eliminate variation, waste and loss before further production.
34
4.5 SAMPLE ON PRODUCTION VOLUME AFTER SOME WEEKS OF ANALYSIS IMPLEMENTATION
line C
Date Target in trays Actual in trays
1-May-15 4,500 4000
2-May-15 4,500 3,550
3-May-15 4,500 5,002
4-May-15 4,500 4,009
5-May-15 4,500 3500
6-May-15 4,500 3900
7-May-15 4,500 5024
8-May-15 4,500 4,007
9-May-15 4,500 4,500
10-May-15 4,500 4,500
11-May-15 4,500 4700
12-May-15 4,500 4850
13-May-15 4,500 4700
14-May-15 4,500 4,850
15-May-15 4,500 4,500
16-May-15 4,500 4,500
17-May-15 4,500 4,500
35
18-May-15 4,500 3,950
19-May-15 4,500 4,000
20-May-15 4,500 5,090
21-May-15 4,500 4,559
22-May-15 4,500 4,670
23-May-15 4,500 5000
24-May-15 4,500 4000
25-May-15 4,500 4505
26-May-15 4,500 4,600
27-May-15 4,500 5,002
28-May-15 4,500 4,000
29-May-15 4,500 -
30-May-15 4,500 -
Table 4.6: Ribena Production volume data after some weeks of implementation
36
1-May
-15
3-May
-15
5-May
-15
7-May
-15
9-May
-15
11-May-
15
13-May-
15
15-May-
15
17-May-
15
19-May-
15
21-May-
15
23-May-
15
25-May-
15
27-May-
15
29-May-
150
1000
2000
3000
4000
5000
6000
Actual in traysTarget in trays
Figure 4.6: Control Chart for the production of Ribena after implementation of analysis
From the above we see that the variance in production has lessened and trends
have shifted upwards thereby reducing the noise.
Comparing the former production volume data to the present, we see that from
the present production volume data, the target was met during 18days while they
were close to meeting the target during 10 days, which is a better result and
hence we can conclude that the process is improving.
37
CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1 SUMMARY
This project has been able to show us the Importance of some quality tools in the
operations of a manufacturing company that wants a continuous improvement.
The basic aim of this study was to reduce variations in production and increase
the production volume (that is meeting the daily targeted volume in Production)
in the Nigerian Manufacturing Company with special reference to
GlaxoSmithKline Nigeria PLC.
While carrying out this study, the company assisted with data while the rest was
gotten from direct interview with the operators in the company, data derived was
analyzed as shown in the figures and tables in chapter four.
From the tables, we see at first the company wasn’t meeting the target in
production, using cause and effect diagram and pareto chart, the defects causing
the company’s variance was determined and hence the greatest defect was found
to be the varying filled weights. ANOVA was used to analyze the variance after the
capability test (which shows when the products meet the customers specification)
was done.
From the ANOVA test, we see that one or more means of the filled weights are
not equal at 90% confidence interval hence I suggested that the technicians first
work on the filling jaws because one or more is faulty and thus the result of the
analysis was a reduced variation in the company’s production.
38
5.2 CONCLUSION
The focal issue in operations is the ability to meet the customers need (quality)
and to meet the company’s target in production (profit),so quality control tools
should always be used by managers to implement this to avoid pending problems.
For a company to achieve a continuous improvement, all the leaders and workers
must contribute their quotas and also they ought to be ready to apply any
mathematical or statistical measure respectively.
5.3 RECOMMENDATIONS
I recommend that the company should introduce a monitoring and control
scheme for the managers to use in tracking issues encountered daily.
Finally, we can say that this project is a part of Operation research, since
Operation Research deals with application of advanced analytical methods,
mathematical modeling, statistical analysis and mathematical optimization to help
make better decisions, determine the maximum and minimum of some industrial
objective and solve problems.
Based on this Operation research, there is need for further researches on the
topic to explore more about this system and to investigate further into the
following areas:
1. Optimization of production in a manufacturing company.
2. Mathematical modeling in increasing production in a manufacturing
company.
39
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