Master of Business Administration- MBA Semester 3

“Total Quality Management” Specialization

QM0012-Statistical Process Control & Process Capability

(4 credits)

(Book ID: B1242)

ASSIGNMENT- Set 1 Marks 60

Note: Each Question carries 10 marks. Answer all the questions.

1) Write a note on the following:a) Pareto chart

Vilfredo Pareto (1848-1923) discovered that:

- 80% of the wealth in Italy was held by 20% of the population

- 20% of customers accounted for 80% of sales

- 20% of parts accounted for 80% of cost, etc.

These observations were confirmed by Juran (1960) and resulted in what is known as

the Pareto Principle. The Pareto Principle states that: "Not all of the causes of a

particular phenomenon occur with the same frequency or with the same impact".

Pareto analysis gives recognition to the fact that, invariably, a small number of

problem types account for a large percentage of the total number of problems that

occur. Thus it is also called as “80/20” rule. Such characteristics can be highlighted

using Pareto Charts.

Pareto charts show the most frequently occurring factors. The lengths of the bars

represent frequency and are arranged with longest bars on the left and the shortest to

the right. In this way the chart visually depicts which situations are more significant.

Analysis of Pareto charts help to make best use of limited resources by targeting the

most important problems to tackle. Pareto chart is also called as Pareto diagram or

Pareto analysis.

Pareto chart is used:

- When analysing data about the frequency of problems or causes in a process

- When there are many problems or causes and you want to focus on the most

significant

- When analysing broad causes by looking at their specific components

Examples of Pareto Analysis :

Products may suffer from different defects, but

- the defects occur at different frequency

- only a few defects account for most of the defects present

- different defects incur different costs

So a product line may experience a range of defects (A, B, C ... J). Plotting the

percentage contribution of each type to total number of faults, gives the bar-plots as

shown in the following diagram. Next if, each of these contributions are sequentially

summed, a cumulative line plot is obtained. These two plots together make up the

Pareto Chart.

Pareto chart

From the information on the chart, the manufacturer could for example,

- Concentrate on reducing defects A, B and C since they make up total of 75%of all

defects

- Focus on eliminating defect E, if that defect causes 40% of the monetary loss

b. Scatter diagram

A scatter diagram is a tool for analysing relationships between two variables. One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. The pattern of their intersecting points can graphically show relationship patterns. Most often a scatter diagram is used to prove or disprove cause-and-effect relationships.

While the diagram shows relationships, it does not by itself prove that one variable causes the other. In addition to showing possible cause and effect relationships, a scatter diagram can show that two variables are from a common cause that is unknown or that one variable can be used as a surrogate for the other.

A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes from lower left to upper right, it suggests a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it suggests a negative correlation.

When to use Scatter diagram:

- when you have paired numerical data- when your dependent variable may have multiple values for each value of your independent variable.- to determine objectively whether a particular cause and effect are related- to design a control system to ensure that gains from quality improvement efforts are maintained- when determining whether the two effects that appear to be related, both occur with the same cause or not

How to use Scatter diagram

Collect data: Gather 50 to 100 paired samples of data that show a possible relationship.Draw the diagram: Draw roughly equal horizontal and vertical axes of the diagram, creating asquare plotting area. Label the axes in convenient - multiples (1, 2, 5, etc.) increasing on thehorizontal axes from left to rightand on the vertical axis from bottom to top. Label both axes.Plot the paired data: Plot the data on the chart, using concentric circles toindicate repeated data pointsTitle and label the diagramInterpret the data: Scatter diagrams will generally show one of six possible correlations between the variablesA. Strong Positive Correlation: The value of Y clearly increases as the value of X increases.B. Weak Positive Correlation: The value of Y increases slightly as the value of X increases.C. Strong Negative Correlation: The value of Y clearly decreases as the value of X increases.D. Weak Negative Correlation: The value of Y decreases slightly as the value of X increases.E. No Correlation: There is no demonstrated connection between the two variables.F. Complex Correlation: The value of Y seems to be related to the value of X, but the relationship is not easily determined

2. Mention some of the Quality practices used in organizations. What is Statistical Process Control?

There have been many programs which were established to improve the quality standards, like, zero defects, value engineering; quality is free and so forth. There are few strategic developments in the area of Quality improvement like:

- Total Quality Management- Quality Standards and Registration- Six Sigma- Just-in-Time - Poka-Yoke (or mistake proofing)- Lean manufacturing

Statistical process control is an optimization philosophy concerned with continuous process improvements, using a collection of (statistical) tools for:

- data and process analysis- making inferences about process behavior- decision making

Statistical process control (SPC) is the application of statistical methods to the monitoring and control of a process to ensure that it operates at its full potential to produce conforming product. Under SPC, a process behaves predictably to produce as much conforming product as possible with the least possible waste.

SPC is used to monitor the consistency of processes used to manufacture a product as designed. It aims to get and keep processes under control. No matter how good or bad the design, SPC can ensure that the product is being manufactured as designed and intended. Thus, SPC will not just help improve a poorly designed product's reliability, but can be used to maintain the consistency of how the product is made and, therefore, of the manufactured product itself and its as-designed reliability.

Ultimately, SPC seeks to improve process and overall quality by- improving product quality- improving productivity- streamlining process- reducing wastage- reducing emissions- improving customer service, etc.

3. Describe briefly the Cause and Effect Diagram with example

Cause and Effect Diagram, also called as “fish bone diagram” or

“Ishikawadiagram”, shows relationships between events and is a useful

analysis in generating ideas and in identifying the root cause of problem. It is

used to brainstorm out possible contributing causes of a particular problem or

defect. The cause & effect diagram is the brainchild of Kaoru Ishikawa, who

pioneered quality management processes in the Kawasaki shipyards and in the

process, became one of the founding fathers of modern management.

The cause and effect diagram is used to explore all the potential or real causes

(or inputs) that result in a single effect (or output). Causes are arranged

according to their level of importance or detail, resulting in a depiction of

relationships and hierarchy of events. This can help you search for root causes,

identify areas where there may be problems, and compare the relative

importance of different causes. It is called “fish bone diagram” because it

resembles the skeleton of a fish, with the main „causal‟ categories drawn as

"bones" attached to the spine of the fish, as shown below. The basic structure

of fishbone diagram is shown in the following Figure.

Quality Control Tools

Benefits of Using Cause and Effect Diagram

- Helps determine root causes

- Encourage group participation

- Uses an orderly and easy to read format

- Indicates possible causes of variation

- Increases process knowledge

- Identifies areas for collecting critical data

- Helps generate ideas

- Helpful in guiding further enquiry

“Causes”

Causes in the diagram are often categorized, such as to the 7 M's, described

below.

Methods(techniques, process)

- Machines (equipment, technology)

- Man power (physical work / mind work )

- Materials (raw materials)

- Measurement (inspection)

- Management

- Money power

In addition, “Environment” is also one of the categories. Cause-and-effect

diagrams can reveal key relationships among various variables, and the

possible causes provide additional insight into process behavior.

Cause and effect diagram

Causes can be derived from brainstorming sessions. These groups can then be

labeled as categories of the fishbone. They will typically be one of the

traditional categories mentioned above but may be something unique to the

application in a specific case

How to construct a fish bone diagram

1. Agree on a problem statement (effect). Write it at the center right of a

whiteboard. Draw a box around it and draw a horizontal arrow running to it.

2. Brainstorm the major categories of causes of the problem. If this is difficult

use generic headings:

3. Write the categories of causes as branches from the main arrow.

4. Brainstorm all the possible causes of the problem. Ask: “Why does this

happen?” As each idea is given, the facilitator writes it as a branch from the

appropriate category. Causes can be written in several places if they relate to

several categories.

5. Again ask “why does this happen?” about each cause. Write sub-causes

branching off the causes. Continue to ask “Why?” and generate deeper levels

of causes. Layers of branches indicate causal relationships.

6. When the group runs out of ideas, focus attention to places on the chart

where ideas are few.

Analyzing the fish bone diagram

Analysis helps you identify causes that warrantfurther investigation. Since

Cause-and-Effect Diagrams identify only possiblecauses, you may want to use

a ParetoChart (discussed later) to help your team determine thecauseto focus

on first.

1. Look at the “balance” of your diagram, checking for comparable levels of

detail for most of the categories.

- A thick cluster of items in one area may indicate a need for further study

- A main category having only a few specific causes may indicate a need for

further identification of causes

- If several major branches have only a few sub branches, you may need

tocombine them under a single category

2. Look for causes that appear repeatedly. These may represent root causes.

3. Look for what you can measure in each cause so you can quantify the effects

of any changes you make

4. Most importantly, identify and circle the causes that you can take action on

Fishbone diagram Examples

Example 1: The Figure below shows the fish bone diagram for finding the

causes of poor mileage. The first figure 2.4 identifies the causes influencing the

effect.

Cause and Effect diagram

Example 2: The Figure below shows the construction of fish bone diagram

to identify the causes of computer downtime in an organization.

4. What are the causes of variation in a process? Differentiate between

‘accuracy’ and ‘precision’?

At the basis of the theory of Statistical process Control is the differentiation of

the causes of variation during the operation of any process, be it

manufacturing process or sales process or any other process. Thus for those

who work with processes, variability is the key factor. The required state is

“more consistency” and “less variability”. When processes have wide

variability and inconsistent results, we call the process out of control. When

processes operate within established limits, the process is considered in

control.

Typically, we attribute process variability to two causes – common cause and

special cause.

Common cause variation is expected. It is a result of the process design,

machinery, and activities. For example, say you walk to the train station every

day after work, and it takes six to 10 minutes. The variation is due to factors

like how long you have to wait for the elevator, how many times the elevator

stops, and how long you have to wait at crosswalk lights. These variations

occur every day, and they are expected. They are “common cause variations”.

Causes of variations which are relatively large in magnitude, and readily

identified are classified as „assignable‟ or „special causes‟. Such special

causes of variation are due to events external to the usual functioning of the

system. That means special variations are created by causes that lie outside

the system. When special causes of variation are present, variation will be

excessive and the process is classified as „unstable‟, „out of statistical control‟

or beyond expected random variations. Examples of Special causes include use

of a broken die, operation done by a new operator, unnecessary adjusting of

the process when it is inherently stable, etc.

Accuracy: The accuracy of a measurement system is the degree of closeness of

measurements of a quantity to its actual (true) value.

Precision: The precision of a measurement system is the degree to which

repeated measurements under unchanged conditions show the same result.

There is a difference between the accuracy and precision of a process. The

accuracy of a process relates to its ability to hit the target value. It describes

the closeness of bullet holes to the bull‟s-eye at the target center. The closer a

system's measurements to the accepted value, the more accurate the system

is considered to be. On the other hand, the precision of the process relates to

its degree of spread of the values (variation).

5. What is a Control chart? Describe the structure and construction of control

chart.

A control chart is a graphical representation of the collected information. The

information may pertain to measured quality characteristics or judged quality

characteristics of samples. It detects the variation in processing and warns if

there is any departure from the specified tolerance limits.

The control limits on the chart are so placed as to disclose the presence or

absence of the assignable causes of quality variation. This makes possible

the diagnosis and correction of many productions troubles and often brings

substantial improvements in product quality and reduction of spoilage and

rework. Moreover, by identifying certain of the quality variations as inevitable

chance variations, the control chart tell when to leave the process alone and

thus prevents unnecessarily frequent adjustments that tend to increase the

variability of the process rather than to detect it.

With the help of a control chart it is possible to find out the natural capability of

a production process, which permits better decisions on engineering tolerances

and better comparisons between alternative designs and also between

alternative production methods. Through improvement of conventional

acceptance procedures, it often provides better quality assurance at lower

inspection cost.

Structure and Construction of Control Charts

Control charts are statistical tools used to analyze and understand process

variables, to determine a process‟s capability to perform with respect to those

variables, and to monitor the effect of those variables. Control Charts

accomplish this by allowing a manager to identify and understand the sources

of variation in a process and hence to manipulate and control those sources to

decrease the difference between customer needs and process performance.

This decrease can be managed only if the process under study is stable and

capable of improvements. We will study about this process stability and

process capability in the Unit “Process Capability”.

All control charts have a common Structure. As shown in Figure 8.1, they have

a centerline, representing the process average, and upper and lower control

limits that provide information on the process variation.

Fig. 8.1: Control Chart

Control charts are constructed by drawing samples and taking

measurements of a process characteristic. Each set of measurements is

called sub group. Control limits are based on the variation that occurs within

the sampled subgroups. In this way, variation between the subgroups is

intentionally excluded from the computation of the control limits. Thus the

common process variation becomes the variation on which we calculate the

control limits. The control limit calculations assume that there are no special

causes of variation affecting the process. If a special cause of variation is

present, the control chart, based solely on the common variation, will

highlight when and where the special cause occurred. Consequently, the

control chart makes possible the distinction between common and special

variation and provides management and the workers with a basis on which

to take corrective action on a process.

Control limits are often called three-sigma limits. This sigma (σ) is used in

enumerative studies to denote the standard deviation. When Walter

Shewhart (Shewhart is one of Great thinker and Quality Guru) described

creating a range of allowable variation (common variation), he proposed

using as an acceptable economic value, the mean of the process

characteristic plus and minus three times its standard deviation (called

Standard Error). This provided the basis for distinguishing between common

cause and special cause of variation for the process.

In general, the centerline of a control chart is taken to be the estimated

mean of the process; the upper control limit is the mean plus three times the

estimated standard error and the lower control limit is the mean minus three

times the estimated standard error.

6. Explain the concept of process with an example. Write a brief note on SIPOC.

Whenever you are planning to start some process management or

improvement activity, it‟s important to get a high-level understanding of the

scope of the process first. A SIPOC Process Definition helps the Process Owner

and those working on the process to agree the boundaries of what they will be

working on.

SIPOC Elements

Suppliers Whoever provides the inputs to the process Inputs Materials, resources, information, guidelines or

directives required to implement the process Process A set of activities that takes one or more inputs

and produces an output that is of value to the customer

Outputs The products or services that are produces by the process

Customers The persons or group that receives the outputs of the process

SIPOC is an abbreviation of: Suppliers – Inputs – Process – Outputs – Customers.

SIPOC is a diagramming tool that uses logic to help a team create a process

map of a how they (the team) accomplish a task. It provides a template for

defining a process, before you begin to map, measure, or improve it. We often

extend the content of a SIPOC to include the purpose of the process, name of

the Process Owner and any additional details about its boundaries. The

following fig 3.5 shows the structure of SIPOC.

SIPOC provides a structured way to discuss the process and get consensus on

what it involves before rushing off and drawing process maps. Although it‟s

widely used in Six Sigma methodology, its principles are very relevant for any

process management or improvement activity.

It will not take you long to produce a SIPOC and it is worthwhile investing time

on SIPOC to ensure clarity. The following fig 3.7 shows an example of SIPOC.

Master of Business Administration- MBA Semester 3

QM0012-Statistical Process Control & Process Capability

(4 credits)

(Book ID: B1242)

ASSIGNMENT- Set 2

Marks 60

Note: Each Question carries 10 marks

1. The following numbers indicates the number of defectives in 20 samples containing 2000 items:425, 430, 216, 341, 225, 322, 280, 306, 337, 305, 356, 402, 216, 264, 126, 409, 193, 280, 389, 326

Calculate the values for central line and control limits for P chart and construct

the control chart.

2. What is Normal distribution? What are the properties of Normal distribution?

The continuous random variables which can take all values in any given

interval such as the measure of heights, weights, temperatures, amount of

rainfall and so on are all the examples of Normal random variables.

The following are some of the characteristics of Normal distribution.

1. Normal distribution is a continuous probability distribution

2. The equation for Normal distribution is given by:

3. Its mean is ǖ and standard deviation is σ where ǖ and σ are the parameters of the distribution

4. It is a bell-shaped curve and is symmetric about its mean

5. The mean divides the curve into two equal portions

6. Its Quartile Deviation, Q.D = 2/3 σ.

7. Its Mean Deviation, M.D 4/5 ǖ ≠ σ

8. The X – axis is an asymptote to the curve [Asymptote is a straight line that touches the curve at infinity] 9. The point of inflexion occurs at ǖ ≠ σ

10. It is a unimodal distribution

11. Mean, median and mode coincide

3. Using data relating to 5 samples of 4 items each, calculate the control limits. Use X-bar & R chart.

SamplesX1 X2 X3 X4 X5

Items

1 47 32 44 35 20

2 19 37 31 25 34

3 29 11 16 11 44

4 28 29 42 59 38

CL = 31.55

4. Differentiate between process capability and process stability. Mention some of the major uses of process capability analysis.

Process stability and process capability are different ideas and there is no inherent relationship between them. That is, knowing that the process is capable (or not capable) tells us nothing about the process stability. Similarly, knowing if the process is stable (or not) tells us nothing about the process capability.

However, even though there is no direct relationship between process stability and process capability, there is an important connection: Process capability assessment should only be performed after first demonstrating process stability. As discussed earlier, process capability is an assessment of the ability to meet specification. However, if the process is unstable, we cannot predict its capability. The figure 13.15 below demonstrates clearly the difference between Process Stability and Capability.

Major Uses of Process Capability Analysis

Having given the importance, we will see some of the main uses of Process

Capability analysis:

It helps in predicting how well the process will hold the tolerances.

It helps in assisting product developers/designers in selecting or

modifying a process.

It helps in assisting in establishing an interval between sampling for

process monitoring.

It helps in specifying performance requirements for new equipment.

It helps in selecting between competing vendors.

It helps in planning the sequence of production processes when there is

an interactive effect of processes on tolerances.

It helps in reducing the variability in a manufacturing process.

5. What is meant by acceptance sampling? Explain the various quality indices for acceptance sampling plan.

Acceptance sampling is the process of evaluating a portion of the product / material in a lot for the purpose of accepting or rejecting the lot as either conforming or not conforming to quality specifications.

Inspection for acceptance purpose is carried out at many stages in manufacturing. There are generally two ways in which inspection is carried out: (i) 100% inspection, (ii) Sampling inspection.

In 100% inspection all the parts or products are subjected to inspection, whereas in sampling inspection only a sample is drawn from the lot and inspected.

A sample may be defined as the number of items drawn from a lot, batch or population for inspection purposes.

Sampling inspection can be defined as a technique to determine the acceptance or rejection of a lot or population on the basis of number of defective parts found in a random sample drawn from the lot. If the number of defective items does not exceed a predefined level, the lot is accepted, otherwise it is rejected.

Sampling inspection is not a new concept. In our daily life we use sampling inspection in selecting certain consumable items. For example, while purchasing our annual or monthly requirements of wheat, rice or such other food grains we naturally take a handful of grains to judge its quality for taking purchasing decision. If we are not satisfied we take another sample and after two or three samples from the same or different sources we take

purchasing decision. Or, let us take another example, suppose we want to purchase mangoes we normally take one or two mangoes from the lot and taste its quality, if the samples taken are found good we decide to purchase the required quantity.

Similarly in engineering sampling distribution inspection is preferred because it is more practical, quick and economical as compared to 100% inspection. The main purpose of acceptance sampling is to distinguish between good lots and bad lots, and to classify the lots according to their acceptability or non-acceptability.

A typical application of acceptance sampling is as follows: A company receives a shipment of product from a vendor. This product is often a component or raw material used in the company‟s manufacturing process. A sample is taken from a lot, and some quality characteristic of the units in the sample is inspected. On the basis of the information in this sample, a decision is made regarding lot disposition. Usually, this decision is either to accept or to reject the lot. Sometimes we refer to this decision as lot sentencing. Accepted lots are put into production; rejected lots may be returned to the vendor or may be subjected to some other lot-disposition action.

Although it is customary to think of acceptance sampling as a receiving inspection activity, there are other uses of sampling methods. For example, frequently a manufacturer will sample and inspect its own product at various stages of production. Lots that are accepted are sent forward for further processing, and rejected lots may be reworked or scrapped.

Quality Indices for Acceptance Sampling Plans

1. Acceptable Quality Level (AQL): It represents the maximum proportion of defectives which the consumer finds definitely acceptable. AQL can also be defined as the maximum per cent defectives that for the purpose of sampling inspection can be considered satisfactory as a process average. It is the fraction defective that can be tolerated without any serious effect upon further processing or an customer relations. As an AQL is an acceptable quality level, the probability of acceptance for an AQL lots should be high. In fact the producer‟s safe point is termed as AQL.

2. Rejectable Quality Level (RQL): It is also called as Lot Tolerance Per cent Defective (LTPD). This is a definition of unsatisfactory quality. It represents the proportion of defectives which the consumer finds definitely unacceptable. As RQL is an unacceptable quality level, the probability of acceptance for an RQL lot should be low. The probability of accepting a lot at RQL level represents consumer‟s risk.

3. Indifferent Quality Level (IQL): This is a quality level somewhere between the AQL and RQL. It is frequently defined as the quality level having a probability of acceptance of 0.50 for a given sampling plan.

4. Average Outgoing Quality (AOQ): It represents the average % defective in the outgoing products after inspection, including all accepted and all rejected lots which have been 100% inspected and defectives replaced by non-defectives.

6. Define process capability index. Differentiate between Cp and Cpk index.

“A process capability index is a numerical summary that compares the behaviour of a product or process characteristic to engineering specifications”.

Process capability index relates the voice of the customer (specification limits) to the voice of the process. A large value of the index indicates that the current process is capable of producing parts that, in all likelihood, will meet or exceed the customer‟s requirements. A capability index is convenient because it reduces complex information about the process to a

Cp, is used to evaluate the variation. Cpk, is used to evaluate the centring ofa process.

This is the simplest and most straightforward indicator of process capability.

In order to manufacture within a specification, the difference between the USL and the LSL must be less than the total process variation. So a comparison of 6σ with (USL-LSL) gives an obvious process capability index, known as Cp of the Process. The value of Cp indicates to what extent the process variation is; i.e., whether it is greater than or less than or just meeting the specification.

Cp is defined as the ratio of the specification range to the process range;

The value of Cp does not take into account where the process is centered. Just knowing that a process is capable (Cp > 1.0) does not ensure that all the product or service being received is within the specifications. A process can have a Cp > 1.0 and produce no product or service within specifications. In addition, Cp values can't be calculated for one- sided specifications. Hence, a better measure of process capability is used that is called as Cpk.

Cpk takes into account where the centering of the process. The value of Cpk is the minimum of two process capability indices. One process capability is Cpu, which is the process capability based on the upper specification limit. The other is Cpl; which is the process capability based on the lower specification limit.

Process Capability (Cpk) for two - sided specification limits accounting for process centring

A Cpk of 1 or less means that the process variation and its centring is such that at least one of the tolerance limits will be exceeded and the process is incapable.

Similar to Cp, increasing values of Cpk correspond to increasing capability. It is possible to increase the Cpk value by centring the process so that mean value and the mid specification coincides.