27 Statistical Quality Control – Various Tools

Kajal Kiran

27.1 OBJECTIVES

After reading this chapter, students will be able to

grasp the concept of statistical control
explain the seven tools of quality control
understand new tools of quality control
elaborate the situations under which these tools can be used
comprehend how these tools work

27.2 INTRODUCTION

In the contemporary business world, competition is increasing at a fast pace. To survive in this competitive world, a business firm has to manage the whole of organizational affairs in a more efficient and effective manner and to ensure quality goods and services. However, the term quality is a relative term and hence difficult to describe. From Customer’s point of view, quality is value i.e. ability of product or service to serve the intended purpose at a price which he is willing to pay. In other words, quality is perceived by customer as fitness for use. For a manufacturer, quality means conformance to specifications. A manufacturer has to exercise control over quality as it is the foundation for creating demand, fixing competitive price and securing market share. Quality Control is the process of seeing that everything goes as has been planned and if required ,taking corrective measures to ensure that goods produced are as per pre-determined standards. In the words of John D. Mchellan” Quality Control develops plans for inspection, analyses reports from inspection , establishes pattern for sampling control and acceptances and keep[s the production department informed about the defects.”Thus quality control involves determining requirements of quality of a manufacturing concern, keeping record of quality standards and inspection reports, fixing certain quality limits within which variations in quality are allowed and then deciding whether to accept or reject the goods on the basis of ability of goods to meet quality standards.

Under Statistical quality control, statistical techniques are applied to determine the extent to which the product meets the standards of quality and precision and the extent to which its quality deviates from the standard quality. Walter S. Schewhart and Harold F.Dodge of the Bell Laboratories U.S.A. introduced the concept of Statistical Quality Control (SQC) shortly after First World War I . Law of probability is the base of SQC. SQC can be described as a system for controlling the quality of production within specified limits. The use of SQC techniques increased during world war II.

Under inspection plan, quality is checked after the production has already taken place, thus resulting in loss from rejecting the final products not meeting the quality standards. In SQC, quality is checked at every level of production so that remedial actions may be taken at early stage. SQC aims not only to determine the magnitude of chance cause variation but also to detect assignable causes of variation which helps manufacturing organizations to install statistical control at various stages of production.

27.3 TOOLS OF STATISTICAL QUALITY CONTROL

Quality control is a formal approach to the analysis of performance and systematic efforts to improve it. In other words, it is the systematic approach to reduction or elimination of waste, rework and losses in production process. There are certain simple tools and techniques which can be effectively used for quality Management and quality control.

Bar Chart/ Histogram

A Histogram is a graphic presentation of discrete data. The length of the bars indicates the value or frequency. The items presented through bars are usually ranked from high to low. Bar charts put the light on variations in a set of data. It enables to see patterns that are difficult to see in a simple table of numbers. Using this information, further investigation could be carried to find out the reasons of variations. For example: number of defects detected in each lot is as under

Batch/Lot	1	2	3	4	5	6	7	8
No. of defects	2	5	9	13	17	12	4	2

The above information can be presented with the help of a histogram

Cause and Effect Diagram

This technique enables to identify the most probable causes affecting problem, a condition or a project. The technique employs effective ways of recording the probable causes of a particular effect with the help of cause and effect diagram. These are also called Ishikawa diagram, Fishbone diagram or Fishikawa. This tool helps to segregate primary (major) causes and secondary (minor) causes of variation in quality and in this way enable the manufacturer to frame suitable policies to handle the different type of causes in an effective manner in order to exercise control over quality. Generally the major causes of problem in a manufacturing unit are 5 Ms( Machines, Methods, Men/women ,Material and Measurement) and one E( Environment). These diagrams also focus on minor causes associated with major causes e.g. minor causes linked with men/women may be poor supervision, lack of concentration, inadequate training etc.

Control Chart

A control chart is a statistical technique to control the quality of the product being manufactured. A control chart also known as process chart or quality control chart is the graphic presentation which depicts whether sample quality falls within the normal range of variation. There are two lines on each graph which indicate the tolerance limits (upper control limit and lower control limit) within which the variations of quality will be permitted. If the data plotted falls outside the tolerance limits, the process is considered to be out of control and the sample is rejected. It warrants the determination of assignable causes and immediate actions to improve the quality. Control charts can be classified into two categories (i) Control charts for variables (where quality characteristics can be measured e.g. height, weight, diameter etc.) and (ii) Control charts for attributes (where quality characteristics cannot be measured e.g. air bubbles in a glass, poor print of cloth etc.)

Flow Chart

Flow chart is a pictorial representation of various stages in the process to break down the complex procedure into the manageable parts for examination and better understanding so that sources of trouble and wastages can be put to light. A flow chart involves a series of symbols connected with each other in a logical manner, depicting activities, decisions and databases and thus finding out how the process actually proceeds. The important symbols used in flow chart are:-

Pareto Analysis

This technique is used for ordering causes or problems from the most to the least significant. It involves creating a preliminary list of problem classifications( Types of Defect- Crack, Scratch, Stain, Dent, Gap, Hole, Others), find out the occurrence in each problem classification, arranging each classification from highest to lowest and then constructing bar chart. This diagram portraits, in decreasing order, the relative contribution of each cause to the total. The relative contribution is based on number of occurrence, cost linked with each cause or the quality damage

The above diagram depicts that nearly 63% of defect is due to holes and poor mix. Thus improvement efforts should focus firstly on elimination of holes and poor mix. However , the rest of the defects like stains , not enough component, torn and others should not be ignored.

Scatter Diagrams

A scatter diagram shows the correlation between two variables in a process. It can highlight possible relationship and provides indication as to what can be expected in the future. In scatter diagrams generally “cause” variable is labeled on X axis and the “effect” variable is labeled on Y axis. The diagram is interpreted by considering the strength and direction of the diagram. For example scatter diagram can be used to identify the relationship between production speed of an operation and the number of defective parts made , the relationship between drill speed and smoothness of cut finish etc.

The above diagram shows that quality of finishing can be improved by increasing the drill speed.

Check Sheet

The check sheet is a form (document) used to collect data in real time at the location where the data is generated. The data it captures can be quantitative or qualitative. When the information is quantitative, the check sheet is sometimes called a tally sheet. Following is the example of a check sheet of a restaurant:

Problem

Sun

Mon

Tues

Wed

Thu

Fri

Sat

Total

Long wait

//// /

///

////

Parking

///

////

Table not clean

///

Bad Server

Cold Food

////

Others

Total

NEW TOOLS FOR QUALITY IMPROVEMENT

In 1976, the union of Japanese scientists and Engineers(JUSE) saw the need for tools to promote innovation, communicate information and successfully plan major projects. A team researched and developed the seven new quality control tools often called the seven tools listed in an order that moves from abstract analysis to detailed planning.

Affinity Diagram

The affinity diagram method (KJ method) facilitates to organize large number of ideas in a way that natural relationships among various ideas can be established. These diagrams are normally used after a brainstorming session or for analyzing verbal data when decision making involves consideration of a number of facts, issue is very complex to be understood and group consensus is required.

For example: after a brainstorming session, each participant wrote his/her idea relating to a cause on an index card resulting in a number of ideas like

Now with the help of affinity diagram, the possible ideas are then arranged into groups of similar causes which can be formulated on the functional areas.

Relations Diagram

It is a technique developed to show casual relationship and helps to link different aspects of a complex situation. These diagrams examine the inter-relationship among the causes existing within a specific grouping (as stated in affinity diagrams).On the left side, the problem is stated and the causes are placed as per their relationship to the problem. The farther the cause is placed, the weaker is the relationship.

The directed lines depict causal relationship. These diagrams can be used to formulate promotional plans for introduction of total quality control, design steps to handle customer complaints, develop quality assurance policies, improve quality in manufacturing process etc.

Tree Diagram

It breaks down the main subject i.e. broad category into basic elements of finer and finer levels of details to identify and sequence the activities required to achieve an objective. These are either horizontal or vertical tree structures connecting the various elements. These can be used to establish a design quality plan for the development of a new product, formulate objectives ,policies and implementation steps, pursue specifications of increased efficiency in parts and control functions etc.

Matrix Diagram

It depicts the relationship among groups of information. Matrix diagram involves arrangement of elements in a problem situation in rows and columns on a chart that highlights the presence or absence of relationship among the collected pairs of elements. Matrix diagrams:

determine the relationship between pair of lists
demonstrate the relationship between ideas
facilitate prioritizing processes and resources
help to effectively organize the collected data.

Matrix diagram are very useful to better analyze many to many relationship like

The above relationship can be better understood with the help of matrix diagram where relationship between the two items can be shown in the square or cell where column and row of the two items intersect.

Matrix diagram of the above example can be formed as below:

Matrix Data Analysis

Out of the seven new quality tools, it is the only mathematical technique for analyzing matrices. The relationship between the elements sorted out by matrix diagram is quantified by obtaining numerical data for intersection call. The results of these analyses are presented in form of a chart. Matrix data analysis charts help to classify items by identifying two main features common to all items and then using a standard X-Y chart by plotting each item as a point.

For example:

Measured Item	Feature 1	Feature 2
Item A	9	7
Item B	4	-5
Item C	-6	-7
Item D	-9	2
Item E	-4	5

Matrix Data Analysis Chart

The shaded area shows the clustering and positioning of items relative to each other. In other words these charts are helpful to find group of items which behave in similar manner.

Arrow Diagram

Arrow diagram shows the required order of tasks in a project or process, the best schedule for the entire project; such diagrams are used by PERT and CPM. These diagrams chalk out the plan for putting together a multi task complex set of various interdependent activities. The following diagram shows the way in which various tasks are interdependent. The task 2 can not start until task 1 is complete. Task 3 and Task 4 cannot start until task 2 is completed. Similarly task 5 is dependent on the completion of task 3 and task 4.

Process Decision Program Chart

PDPC systematically identifies what might go wrong in a plan under development. PDPC method anticipates possible outcomes in response to various kinds of problems and prepares counter measures that will lead to best possible solution.

27.4 APPLICATION OF SQC TOOLS: Root Cause Analysis

Root Cause Analysis (RCA) is a method that is used to address a problem or non-conformance, in order to get to the “root cause” of the problem. It is used so we can correct or eliminate the cause, and prevent the problem from recurring. Root cause analysis (RCA) is a systematic process for identifying “root causes” of problems or events and an approach for responding to them. RCA is based on the basic idea that effective management requires more than merely “putting out fires” for problems that develop, but finding a way to prevent them. 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 with certainty. RCA is simply the application of a series of well known, common sense techniques which can produce a systematic, quantified and documented approach to the identification, understanding and resolution of underlying causes. Below are the steps involved in application of RCA.

Steps involved in application of RCA

Define the Problem: Try and use SMART principles, i.e. Specific; Measurable, Actions oriented; Realistic; Time constrained. Unless the problem is defined accurately, the RCA whole process maybe prone to failure. This phase will usually also define how the RCA will be run as a Project.

Understand the Problem: Check the information, obtaining real data regarding the problem, gaining a clear understanding of the issues. This is when the various tools and techniques, such as Cause and Effect, brainstorming, etc, can be used.

Immediate Action: Implement temporary counter-measures at the place of the problem. The further away from the problem source the solution is determined, the less likely that the solution will be effective.

Corrective Action: Determine and prioritize the most probable underlying causes of the problem, as the temporary counter-measure may not resolve the root cause. Taking corrective actions to at least mitigate or preferably eliminate the causes.

Confirm the Solution: After the measures have been determined and implemented the success of the adopted approach needs to be established. Having confirmed the success of the suggested solution then rules or control methods need to be established that will avoid the problem ever happening again. This is probably the most important phase in the RCA, but the one most often missed.

Tools of RCA:-

To support the RCA techniques different tools (Fig.6) are there which are well known and called as 7 Quality Control Tools which are as follows, These tools helps to identify the problem, to understand & analyze the problem & to find out the root cause of the problem:

Tools of RCA

27.5 SQC TOOLS: AN EXAMPLE

Soaps, breads, biscuits, shampoos and other products require packaging. A company lets’ call it Packaging India ltd. is into the business of manufacturing machines required to pack such products at very fast rate. These machines are fully automated. The process includes filling the conveyor belt with products that need to be packed for instance soaps. Also one of the major components in the machine is the paper required to pack such products. The supplier used to provide a complete roll of paper used for packing. The roll is mounted on the machine and when machine starts running soaps start getting into the machine and paper roll starts rolling. One end of the paper is stretched into the chuck where incoming soap is placed. The important aspect is that there has to be a perfect sensor in the system which would sense when to cut the paper from the roll. Only a piece of paper from entire roll is wrapped around one soap. Then next soap will enter the chuck and paper will be wrapped around it and then after packing that soap the paper needs to be cut by the cutter.

The manufacturer used to produce two variants of soap packaging machine. One machine used to pack detergent soaps and other variant packed bathing soap. The difference between two soaps with regard to packaging is critical. Detergent soaps are mostly packed in only one paper and that too of low quality. Whereas bathing soaps generally have two wrappers. The inside wrapper is simple paper whereas outside wrapper is glossy paper of very high quality. Thus packing bathing soaps is much more complex process than detergent soaps as it would require two paper rolls. It needs to be emphasized here that incase of packing of bathing soaps timing of wrapping inside paper and outside paper has to be synchronized perfectly. Imagine an incoming soap which should be packed firstly by inside paper which then gets cut by the cutter. Then outside paper is packed which is again cut after packing one soap.

This process is repeated at a fast rate as number of soaps is being packed. Under such scenario shop floor manger while operating the packaging machine faced a crucial problem. The cutter that is used to cut glossy paper was nut cutting where it was intended. It was cutting at a further distance of 2 inches than where it needs to cut. For instance, if a roller is of 2000 ft. and each soap require one feet of paper to get wrapped then each roller should wrap 2000 soaps. But if machine is cutting not at 12 inches (one feet) for one soap but at 14 inches then it would not be able to pack entire lot of 2000 soaps. Also the cutting plays havoc with writings and pictures on the outside paper.

The shop floor manager wanted to find the reason for this discrepancy. To find out the reasons for variation in quality measures the manager used various quality control tools such as process flow diagram which would indicate the entire process step wise and in detail. Scatter diagram was used to find causal relation between for instance, chuck speed and roller speed. Control charts were used to find which step of the entire process is going out of order and needs to be rectified. Thus SQC tools proved to be quite helpful in identification of causes of problem.

27.6 SUMMARY

Statistical quality control tools are powerful tools in the hand of management to exercise quality control and hence ensure quality management and quality improvement. Various statistical quality control tools also known as 7 quality tools include Histograms, Cause and effect diagrams, pareto charts, control charts, flow charts, scatter diagrams and check sheets. However with passage of time, to promote innovation, communicate information and successfully plan major projects., new tools for quality control have gained popularity . These new tools include Affinity diagrams, Relation diagrams, Tree diagrams, Matrix charts, Matrix Data Analysis charts, Arrow diagrams and Process decision Program Charts.

27.7 REFERENCES/ SUGGESTED READINGS

Nancy R. Tague, The Quality Tool Box, second edition, ASQ quality press 2004
Jain P.L, Quality Control and Total Quality Management , Tata McGraw- Hill,2001
Nair N G, Production and Operation Management, Tata McGraw- Hill, 2007