May 9, 2020 No Comments ›› OpenBook



In this work; cumulative sum (CUSUM) control Charts Schemes are designed to detect the increase or decrease in the accident rate in Ondo State, Nigeria. The designed schemes were applied on the monthly records of accidents in Ondo State from 2005-2014 to demonstrate the application of the techniques.  Span test was also used to test, if there are any differences between the groups into which the data are divided. Retrospective analyses are also carried out and the local means are computed.




1.1  Background to the Study

            There are many reasons why a product may have unsatisfactory quality. Statistical methods play a central role in quality improvement efforts and it is recognized as an efficient and powerful tool in dealing with the process control.

            Variation in any process is largely due to special causes. The assignable causes are due to a new operator, change of materials, excessive use of tool and possibly a new supplier. On the other hand, the nature variation that exist in people, machinery, and materials gives rise to common causes of variation (Shewhart, 1931)

            There are many methods to monitor the quality of manufacturing processes. Chief among them is the control chart. These charts give a graphical appearance of the process, giving ability to any manager with or without the knowledge of statistics to immediately understand if the process is under control or not. The wide use of and popularity of control charts is asa result of many reasons. Majorly among others is their proven ability to improve productivity, because the reduction of scrap and rework results in increase productivity, as increase in production capacity is measured in number of goods produced per hour and its decrease in cost. Their effective precaution of defect items is also valuable. The use of control chart helps of keep the process under control. The diagnostic property of control charts is significant as it allows the changes in the process by experienced operator or engineer, Edokpaet al (2013).

            The Control Chart is a tool used primarily for analyzing data, either discrete or continuous, which are generated over a periodof time. The concept was evolved by Walter-A-Shewhart, of Bell Telephone Laboratories, in 1924. At that time, he suggested that control chart could fulfill three basic functions, they are:

  1. To define a goal for an operation
  2. To aid in the attainment of the goal
  3. To judge whether the goal had been reached

As such it may be considered among the most versatile tools in statistical methods, Kayode (2013).

            This research work is aimed at extending the use of Cumulative Sum (CUSUM) chart in the monitoring of a univariate process. CUSUM procedures are often used to monitor the quality of manufacturing processes. The major objective is to identify persistent causes of variation in the process average. This ability is attributed to the fact that they have memory as they are based on successive sums of the observation minus a constant. Edokpaet al (2013). 

1.2        Functions and History of the Federal Road Safety Commission

The Federal Road Safety Commission was founded in December 13, 1988 by decree 45 of the then military government, with its jurisdiction limiting its operations to only Federal Highways. It was later extended by decree 35 of 28th August, 1992.

The Federal Road Safety Commission has seven zones and thirty-six sector commands. Ondo State sector command is under zone four, with its headquarters in Lagos. The objectives of the Federal Road Safety Commission (FRSC) are as follows:

  1. To determine and enforce speed limits for all categories of road and vehicles.
  2. To educate motorists and members of the public on the importance of discipline on the highways.

iii.        To arrest and prosecute persons for traffic offences committed on all highways.

  1. To make the highways safe for motorists and other road users.
  2. To cooperate with other bodies, group or agencies engaged in road safety activities.
  3. To give prompt attention and care to accident victims.

vii.       To make regulations in pursuance of any of the functions assigned to the commission.

viii.      To perform any other function relevant to and consistent with the overall objectives of the commission.

According to the Federal Road Safety Commission, accidents can be categorized as fatal or minor. Those that does not involve lost of lives are said to be minor, while those that claim lives are said to be fatal.

The data used for this work was collected from the Federal Road Safety Commission, Akure, the Ondo State capital.

1.3       Justification of the Study

            In any production process, there is usually a target value. We want our process to achieve the target for every productMaleshet al (2010). A process that operates in the presence of special causes of variability is said to be out-of-control. This type of variability can be detected with control charts giving us the ability to remove it effect and therefore reduce the overall variability Lowery et al (1992).

The most common control charts are the Shewhart type control charts. They are used to detect short time special causes of processes Sweet (1986)

            A major disadvantage of any Shewhart control chart is the chart is relatively insensitive to small shift in the process, on the order of about 1.5δ or less. One reason for this relatively poor performance in detecting small process shifts is that the Shewhart chart makes use of only the information in the last plotted points and it ignores the information in the sequence of points Montgomery (2001). This problem can be tacked by adding criteria such as the western Electric rules to a Shewhart chart, but the use of these rules reduces the simplicity and easy of interpretation of the chart Bissell (1969). These rules would also cause the in-control average run length of a Shewhart chart to drop below 370. This increase in false alarm rate can have serious practical consequences.

1.4       Statement of the Problem

            Over the years, the rate of road accident fatality has been on the increase in Nigeria and governments at all the levels are worried about this ugly trend that has no end in sight.

            In view of the above statement, this research work will examine the rate of accident in Ondo State, South-West Nigeria between 2005 to 2015 and build a retrospective analysis of the data obtained to know the actual month or year that have the highest prevalent rate and possible projection of its likely occurrence again in order to avert it.

1.5       Aims and Objectives of the Study

The aim of this research work is to examine methods to improve the quality of a product using statistical process control.The specific objectives of this research work are:-

  1. To determine whether there is an increase or decrease in accident fatalities in Ondo State between 2005 to 2015 using Cusum techniques.
  2. To use the span test whether all the data give a statistical significant value at respective sample.

iii.        To determine the month and year that have the highest accident rate using the retrospective analysis.

  1. To make recommendations to governments and FRSC based on the findings of the research work.

1.6       Significance of the Study

            The importance of this research work cannot be overemphasized. It will be very useful to FRSC to take quick and necessary decisions in their day to day activities.

            It will also help government at all levels to see how they could partner with the Federal Road Safety Commission to reduce Road accidents on our roads.

1.7       Scope of the Study

            This work intends to cover recorded monthly accident rate in Ondo State South-West Nigeria between January 2005 through to December 2014.We intend to use Cusum charts, span test, chi-square test and retrospective analysis to see whether there is increase or decrease in the rate of accident within the above specified period. The study will also present analytical and graphical approach to identifying sources of out- control signal from the CUSUM charts.

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