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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[1] Bhote, K.R. and Bhote, A.K., (1991).World-class quality: using design of

experiments to make it happen,2nd Edition, American Management Association,

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[2] De Feo, Joseph A.; Barnard, William, (2005). JURAN Institute's Six Sigma

Breakthrough and Beyond - Quality Performance Breakthrough Methods. Tata

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[3] Duncan, A. J., (1986).Quality Control and Industrial Statistics.5th edition.

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[4] Fisher, Ronald (2001). "Studies in Crop Variation. An examination of the yield

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[5]. Freedman, David A.(2005). Statistical Models: Theory and Practice,

Cambridge University Press.

[6]Gelman, Andrew (2005). "Analysis of variance, Why it is more important than

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[7] Jose, Arturo(2012). Defects reduction in a rubber gloves manufacturing

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41