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• How to implement a process of continual improvement throughout the organisation?
• Which causes of waiting time in the hospital should we be working on?

How To Do It

1. Define the problem or issue to be explored. Use Problem Definition and ensure that you state the problem as clearly and unambiguously as possible.
2. Brainstorm for ideas, but instead of everyone shouting out ideas, everyone silently writes down their ideas on sticky notes or index cards.
3. When the brainstorm is complete mix up all of the notes or cards and stick them on the wall or spread them out on a table.
4. Let the group arrange the notes or cards into related groups as follows:

• Take two cards that are related in some way and put them together.
• Find other cards that belong to this group and put them with the first two.
• Build other groups of cards in the same way until all of the cards have been grouped (about 10 groups maximum).

More on the improvement network

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that’s necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.

Students (and scholars too) often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.

There is a famous book: G. Polya, “How to Solve It “, 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. It was first published in 1945. This is a serious attempt by a master at transferring problem solving techniques.

Summary taken from G. Polya, “How to Solve It”

1. UNDERSTANDING THE PROBLEM
   • First. You have to understand the problem.
   • What is the unknown? What are the data? What is the condition?
   • Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
   • Draw a figure. Introduce suitable notation.
   • Separate the various parts of the condition. Can you write them down?
2. DEVISING A PLAN
   • Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually aplan of the solution.
   • Have you seen it before? Or have you seen the same problem in a slightly different form?
   • Do you know a related problem? Do you know a theorem that could be useful?
   • Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
   • Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?
   • Could you restate the problem? Could you restate it still differently? Go back to definitions.
   • If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other?
   • Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?
3. CARRYING OUT THE PLAN
   • Third. Carry out your plan.
   • Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?
4. Looking Back
   • Fourth. Examine the solution obtained.
   • Can you check the result? Can you check the argument?
   • Can you derive the solution differently? Can you see it at a glance?
   • Can you use the result, or the method, for some other problem?

Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something. In fact, they often are a bad way! You learn by doing. For example, it’s questionable that we should have programming classes at all, most people learn programming much more quickly and enjoyably by picking a programming problem they are interested in and care about, and solving it. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That’s a much more exciting way to learn than taking classes!

Here are some suggestions regarding class work:

• Always strive for understanding as opposed to memorization.
• If this means you have to go back, do it! Don’t postpone clarifying a point you miss because everything new will build on it.
• It may be intimidating to be faced with a 1,000 page book and having to spend a day understanding a single page. But that does not mean that you’ll have to spend a thousand days understanding the whole book. In understanding that one page you’ll gain experience that makes the next page easier, and that process feeds on itself.
• Read the sections covered in class before you come to class. That’s one of the most useful ways in which you can spend your time, because it will dramatically increase the effectiveness of the lecture.
• Do exercises. The teacher may suggest some, put you can pick them on your own from the textbook or make up your own. Select them by the amount of interest they hold for you and the degree of curiosity they stimulate in you. Avoid getting into a mode where you do a large number of exercises that are distinguished only by the numerical values assigned to some parameters.
• Always check your answers for plausibility.
• Whenever you do a problem or follow a new mathematical thread explicitly formulate expectations. Your expectations may be met, which causes a nice warm feeling (and you should probably also look for a new and different problem). But otherwise there are two possibilities: you made a mistake from which you can recover, now that you are aware of it, or there is something genuinely new that you can figure out and which will teach you something. If you don’t formulate and check expectations you may miss these opportunities.
• Find a class mate who will work with you in a team. Have one of you explain the material to the other, on a regular basis, or switch periodically. Explaining math to others is one of the best ways of learning it.

Be open and alert to the use of new technology. (I know you are because you are reading this web page.) You can go from here directly to computing help. But don’t neglect thinking about the problem and understanding it, its solution, and its ramifications. The purposes of technology are not to relieve you of the need to think but:

• To check your answers.
• To take care of routine tasks efficiently.
• To do things that can’t possibly be done by hand (like the visualization of large data sets).
• Keep in mind R.W. Hamming’s famous maxim: The purpose of computing is insight, not numbers.
• Once you are done with a course Keep Your Textbook and refer back to it when you need to. You have spent so much time with that book that you know it intimately and know how to use it and where to find the information you need. The small amount of money you might get by selling it does not come close to offsetting the loss in time and energy you waste being thwarted by a lack of understanding a particular piece of mathematics that you easily refamiliarize yourself with by consulting your old friend, the textbook. Here’s a more passionate elaboration on this theme.

http://www.math.utah.edu/~alfeld/math.html

http://en.wikipedia.org/wiki/Problem_solving

• Who? Who was involved?
• What? What happened (what’s the story)?
• When? When did it take place?
• Where? Where did it take place?
• Why? Why did it happen?
• How? How did it happen?

Waste can be applied to a variety of business scenarios from manufacturing through to service and can affect both the quality and cost of the end product. Waste is commonly divided into seven categories.

The seven wastes are:

Overproduction

• Producing more goods than the customer needs

Transportation

• Anywhere where goods are moved within a process

Waiting

• Where waiting time occurs, traditionally where one process waits for another to finish before it can start.

Inventory

• Typified by stock or materials that are not being used in the process or current activity.

Motion

• Poor planning and organizational layout often cause motion waste – for example if you commonly use a printer on the other side of the office that you have to walk to to retrieve your print jobs that is waste.

Over processing

• Where steps occur in the production process that do not add value to the end customer this is termed overproduction – for example authority processes often require multiple signatories.

Defects

• The process results in an error or requires rework – for example in manufacturing this could represent an item where components have been omitted from the construction.

Assessing the benefits of Value Stream Mapping Software
How to construct a deployment flowchart
Value based performance metrics
Using Affinity Diagrams
How to produce an Affinity Diagram
What is process mapping
How to produce a SIPOC diagram
What is value stream mapping
Value stream mapping icons and symbols
Establishing a data collection plan 2
Establishing a data collection plan 1

Methods and Models for Process Improvement

What are Visual controls
What is 5s
Poka yoke
What are the seven wastes

Analysis to facilitate continuous improvement

Supply Chain Responsiveness matrix
What is Productivity
What is lead time
What is Chi Square test
What is ANOVA
What is the 5 whys
What is a value add chart

• remove waste from processes
• focus on value to the customer

Concept taken from six sigma and kaizen

What is DMAIC

• Define
• Measure
• Analyze
• Improve
• Control

There are a variety of benefits in following DMAIC

• Firstly it’s a structured approach and provides a road map for solutions solving from start to finish and is tied into producing bottom line results for businesses.

• Secondly it supports an analytical approach through use of data, this helps ensure that accurate baselines can be established and improvements quantified – finally utilizing DMAIC is suited to challenging problems and the model helps find answers where both problems and solutions are likely to be complex

Define

Allow the project team to produce:

• A project charter or initiation document
• High level process maps
• Stakeholder analysis
• Project plans

First Steps

Projects are usually initiated by a project sponsor – the role of the sponsor is to select the project and produce the first draft of the project charter which is typically one of the first tasks within an improvement project. Whilst the contents of a project charter may vary it will typically cover the nature of the business problem, the goals, deliverables and structure of the project team.

Key steps in the Define stage

1. Produce and review Project charter/Initiation document
2. Define and Validate problems – ensure that the problem exists, and is important.
3. Define the Project Goal
4. Validate business rationalie for going ahead with project – eg. Financial
5. Develop Project Plans
6. Develop the project structure

Mesure

• Ensure that the current process is fully understood and that data is captured to both provide a benchmark of current activity/performance

• Compare against the customers needs and to enable the project team to drill down to the root cause of the issue(s).

Key steps

In the measure phase the key element is to ensure that the current state of the process is thoroughly understood therefore much of this phase is concerned with describing and measuring current activities – to do this efficiently a process map is usually required – value stream maps are used as they incorporate data such as inventory levels together with material and information flows rather than just being interested in the process flow.

A data collection plan is devised in order that accurate data is collected and analysis can be carried out and baselines be set.

There is often a gate review within the measure phase – this usually includes a review of the process map, data/measures, a capability review and an updated project charter/initiation document.
Deliverables

1. Current state map (often a value stream map)
2. Accurate data on important inputs/outputs – used for analyzing process flows, defects etc.
3. Baseline measures of process capability against expectations.

Analyze

Key Steps

This step in the process determines the root causes of issues and presents improvement opportunities.

Part of the process is to analyze value add and non value add activity within the process. Using the process maps/Value stream maps produced during the Measure DMAIC phase – the team looks for bottlenecks/constraints and where errors occur. There are a variety of tools available for this such as Failure Modes and Effects Analysis (FMEA).

After identifying the problems provide supporting evidence by generating theories as to why they occur (note this may require supporting further data).

Deliverables

• Evidence of root causes
• Supporting analysis and evidence (e.g. value add analysis)
• Updated Project Charter/Initiation document.

Improve

Steps and deliverables

The main deliverable from the Improve step is a solution(s) that affects the proven issues/problems (found earlier in the DMAIC process) affecting the business. Once deployed the solution should be stable and meet customer requirements

The first step is to develop possible solutions – there are a variety of ways of doing this and it’s likely that at first several solutions may present themselves while methods exist for improving, commonly project teams will brainstorm ideas based upon the “as is” process/value stream map and statistical data that has been collected – change agent teams are therefore required to evaluate possible ideas and develop the most suitable solution, often this is initiated via a “to be” process or value stream map – developing criteria that the solution must meet (e.g. critical quality requirements, customer needs etc) whilst removing the original problem areas. (this is important to remember that the chosen improvement must tackle the project goal!).

It’s common that once developed solutions may undergo pilot studies or experiments to ensure the optimal “fix” is selected. Once a solution has been selected a robust implementation plan will be required and a re-assessment of the Project charter will need to take place to ensure that the way forward

Control

Steps and deliverables

The Control phase usually sees the full scale deployment of the solution developed earlier in the DMAIC method. As such the main role of the project team is to transition the business to the new process. This can be a resource heavy part of the process with tasks such as training users, writing and deploying business critical documentation to ensure a smooth delivery.

Project teams should consider auditing the process following deployment and confirm that the solution has met the goal of the project sponsor and/or business case – due consideration should be given to the length of time following roll out that the audit takes place in most businesses it will be at least 6 months until this takes place.

When developing the transition plan pay particular attention to ensuring that a proper hand-over occurs – don’t make the mistake of thinking that a “five minute” handover will do – take the time to ensure that appropriate stakeholders have what they need to operate the revised process..

The key deliverables of this phase are:

• Documented transition back handing back the solution to the business owner
• Key Performance Indicators/Measures deployed
• Training, documents (including the business management system e.g. processes maps)

From http://leanyourcompany.com

IDEF0 Diagram Example

IDEF0 is a function modeling methodology for describing manufacturing functions, which offers a functional modeling language for the analysis, development, reengineering, and integration of information systems; business processes; or software engineering analysis.

It is build on the functional modeling language SADT

IDEF0 may be used to model a wide variety of automated and non-automated systems:

• For new systems, it may be used first to define the requirements and specify the functions, and then to design an implementation that meets the requirements and performs the functions.

• For existing systems, IDEF0 can be used to analyze the functions the system performs and to record the mechanisms (means) by which these are done. The result of applying IDEF0 to a system is a model that consists of a hierarchical series of diagrams, text, and glossary cross-referenced to each other. The two primary modeling components are functions (represented on a diagram by boxes) and the data and objects that inter-relate those functions (represented by arrows)

More on Wikipedia

SADT

SADT

Decomposition Structure

What is it good for ?

• to define user needs for IT developments (which is very used in the industrial Information Systems)
• to explain and to present an activity’s manufacturing processes, procedure

Diagrams

SADT uses two types of diagrams: activity models and data models. It uses arrows to build these diagrams. The SADT’s representation is the following:

• A main box where the name of the process or the action is specified
• On the left-hand side of this box, incoming arrows: inputs of the action.
• On the upper part, the incoming arrows: data necessary for the action.
• On the bottom of the box, incoming arrows: means used for the action.
• On the right-hand side of the box, outgoing arrows: outputs of the action.

The semantics of arrows for activities:

• Inputs enter from the left and represent data or consumables that are needed by the activity.
• Outputs exit from the right and represent data or products that are produced by the activity.
• Controls enter from the top and represent commands which influence the execution of an activity but are not consumed.
• Mechanisms identify the means, components or tools used to accomplish the activity. Represents allocation of activities.

The semantics of arrows for data:

• Inputs are activities that produce the data.
• Outputs consume the data.
• Controls influence the internal state of the data