STATISTICAL ANALYSIS: STATISTICAL ANALYSIS:

PROBLEM SOLVING TOOLPROBLEM SOLVING TOOL

Dr. A. AmsavelDr. A. Amsavel

IntroductionIntroduction

• Statistics

• Problem solving tool

– Types of Charts

• Process capability

What is Statistics What is Statistics

• Statistics is a science, which deals

with the method of collecting,

classifying, presenting (plots, charts,

diagram or etc.), comparing and

interpreting numerical data to throw

some light on any sphere of inquiry.

Importance of measurement

• Anything measured improves

• Anything measured and recorded

improves more

• Anything measured, recorded and

monitored improves most.

Statistical analysis is problem Statistical analysis is problem solving toolsolving tool

Data and methodData and method

STATISTICS AS DATA

STATISTICS AS METHOD

It is quantitative It is operational technique

It is often in raw state

It helps in processing the raw data

Unprocessed data does not help in decision making

Process is done for analysis and interpretation

We have so much data, align to the required form. Apply statistical tools to turn data into information.

SPC:SPC:

• What causes defects?• How are defective made in the first

place?• Can we make okay?• Are we making it okay?

Why we need Statistical analysis?Why we need Statistical analysis?

• General causes of troubles / problems arises from wrong knowledge and or in-correct operation.

• To discern we have to launch fact-finding process.

• How to eliminate the problem or waste?– Identify– Quantify– Eliminate– Prevent it re-occurrence

QUALITY MANAGEMENT SYSTEMQUALITY MANAGEMENT SYSTEM

• Achieve continues / continual improvement

• Achieve high quality and low cost by eliminating waste in all the work and work process

• By reducing the problems and variation in the process and stabilizing it.

TYPE OF TOOLSTYPE OF TOOLS

• Run chart• Pareto chart• Flow chart• Fish bone / cause and effect diagram• Histograms• Control chart• Process capability, etc.

RUN CHARTRUN CHART

A Run chart shows what happens over a time (period) Visualize the unexpected shift, trend, pattern

• Plot variable vs. time / sequence

• Choose critical elements (key variable) in the process

• Collect the data

• Plot a graph: Time or sequence in X axis and variable in Y axis.

RUN CHARTRUN CHART

RUN CHARTRUN CHART

RUN CHARTRUN CHART

• To monitor process performance.

• % Recovery of solvent Vs Batch / Time

• In determining when a change to a process might have occurred.

RUN CHARTRUN CHARTInformation /recording:

• What is being measured, when it was measured and other information

• Update the chart frequently

• To indicate quality and productivity of an important process

Utilize:

• Monitor the on-going performance

• Monitor the performance of process over time / sequence to detect trends, shift or cycle.

• Investigate the reason and eliminate.

Pareto principlePareto principle

• The Pareto principle (also known as the 80-20 rule) states that, for many events, 80% of the effects come from 20% of the causes. Business management thinker Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who observed that 80% of income in Italy went to 20% of the population.

• 80% of problems usually stem from 20% of the causes.

PARETO CHARTPARETO CHART• This is a simple bar graph ranking in

order of importance the causes, Sources, types or reasons for problems / opportunities.

• It helps to identity the problems that affect greatest potential for improvement.

• Choose the unit of measures and critical elements

• Collect data for the problems• Compare relative cost of each problem

category• Arrange in descending order

Customer complaintCustomer complaint

PARETO CHARTPARETO CHART

Utilize: Setting priorities for action

• Pickup an important areas of waste / opportunities and decide how to measure the various contributors.

– Complaint nature vs. year

– Contribution vs. product

– Cost of failure vs. product

Cause-and-Effect DiagramCause-and-Effect Diagram

• A Cause-and-Effect Diagram (also known as a "Fishbone Diagram") is a graphical technique for grouping people's ideas about the causes of a problem.

Cause-and-Effect DiagramCause-and-Effect Diagram

• Dr. Kaoru Ishikawa, a Japanese quality control statistician, invented the fishbone diagram.

• The fishbone diagram is an analysis tool that provides a systematic way of looking at effects and the causes that create or contribute to those effects.

• The design of the diagram looks much like the skeleton of a fish. Therefore, it is often referred to as the fishbone diagram.

Cause-and-Effect DiagramCause-and-Effect Diagram

FISHBONE CHART:

• Show relationships between causes and an effect (what we want to study). The major categories of cause contributing to the effect are assigned to the major branches.

• Choose a problem to study

• Clearly define the effect

• Gather people that have knowledge / experience

• Try to get diversified group (different perspectives)

• Group may generate more ideas

Cause-and-Effect DiagramCause-and-Effect Diagram

Cause-and-Effect Diagram Cause-and-Effect Diagram (Long Waiting Times)(Long Waiting Times)

BrainstormingBrainstorming

• Brainstorming is a lively technique that helps a group generate as many ideas as possible in a short time period.

• To identify problems, analyze causes, select alternative solutions, do strategic planning, generate ideas for marketing change, and handle many other situations.

• Explain the objective of the session: problems, analyze causes, or generate ideas.

• Explain the technique – looking for a lot of ideas, and – thoughts and ideas to flow freely. – There is no right or wrong answer. – The idea of brainstorming is to produce as many innovative ideas as

possible. • Silent reflection:

– participants to think about the proposed objective or topic for a few minutes.

• Brainstorm: – call out their ideas – Write them on a flip chart in the order – Write down the ideas using the words of the speaker. Get clarity if

required• Once the list is finished, discuss it with the group to:

– Clarify the meaning of some ideas– Combine similar ideas that are worded in different ways– Eliminate those ideas which are not related to the objective of the

session• Do all this by group consensus. At the end reduce the list to

major ideas of the group

Brain stormingBrain stormingConducting brain storming• Get ideas from every one about possible cause• Transfer causes into fishbone chart.• Rank the cause for further study (major impact)• Prioritise• Re-draw fish bone final form• Issue to every one / Notice Board• Assign teams to work on the major causes • Schedule further meeting• Look for causes appeared repeatedly and gather

data• Use the diagram to eliminate possible causes

HISTOGRAM

• A histogram is a graphical display of tabulated frequencies.

• A histogram is a picture of the variation in a process or a product. It shows the capability of process and helps us to understand and analyse what is happening.

• Shows the spread of variation:

• Average (center) and dispersion

• Range – lowest and highest

HISTOGRAM

MAKING OF HISTOGRAMS:• Decide on the process measures • Collect the data• Make a check sheet• Calculate the range or average• Prepare frequency table (Measurement at

interval and frequency)• Draw a bar chart (x – class width; y –

frequency)• Connect the center point and draw line

HISTOGRAM

HISTOGRAM

Types of HistogramsTypes of Histograms

HISTOGRAM

INTERPRETATION:

• Check the shape (symmetrical, cliff like, [either side], skewed)

• Check for normal distribution

• Compare the range with specification

• Check for improvement

• Target the improvement in the process

CONTROL CHARTCONTROL CHART Dr. Walter A. Shewhart Dr. Walter A. Shewhart

• A Control Chart is a tool for use to monitor a process.

• It graphically depicts the average value and the upper and lower control limits of a process.

• A control chart is a moving picture of the variation in a process. This can be used to analyse, stabilize, control and improve the process.

• This is very powerful tool, it tells the current status, capabilities, variation, etc.

CONTROL CHARTCONTROL CHART

MAKING CONTROL CHARTS:

• Decide what factor to be studied

• Measure the value

• Calculate X or R and standard deviation.

• Use 25 or more points

• Plot immediately to discover the problems

• Compute a new average after making process change

• For any out of control point on the control chart, record the reason for it and the action taken.

CONTROL CHARTCONTROL CHART

X Chart for diameter

0 20 40 60 80 100

Observation

1.04

1.043

1.046

1.049

1.052

1.055

1.058

X

CTR = 1.05UCL = 1.06

LCL = 1.04

CONTROL CHARTCONTROL CHARTINTERPRETATION:• A process must be stable before you can use a

control chart effectively for improvement.• Use control chart to help track reason for special

cause and any significant change.

Utilize:• Monitor the performance of process over time /

sequence to detect trends, shift or cycle.• Investigate the reason and eliminate by applying

corrective action.• Compare variables before and after improvement

CONTROL CHARTCONTROL CHART• In control process: process average and standard deviation

are known and predictable, stable, consistent and unchanging

• Out of control process: process average and standard deviation changing, unstable and inconsistent.

OOT / Alarm • Six points consecutive points upward or downward.• Two out of three points in a row in zone A • Four out of five points in a row in zone B or beyond A • Nine ponts in a row on one side of the center line • fourteen points in a row alternate up and down • Two out of three points in a row in zone A

Out Of Trend Out Of Trend

Look for the alarms:• No points outside the control limits (upper or lower).• No run of 7 consecutive points above or below the average line.• No run of 7 consecutive points upward or downward.• No pattern with 2/3 of the points in the middle 1/3 of the control

limits.• No pattern with 2/3 of the points in the outer 2/3 of the control

limits.

If the range is in control then look at the average chartLook for the alarms:• No points outside the control limits (upper or lower).• No run of 7 consecutive points above or below the average line.• No run of 7 consecutive points upward or downward.• No pattern with 2/3 of the points in the middle 1/3 of the control

limits.• No pattern with 2/3 of the points in the outer 2/3 of the control

limits.

Normal distributionNormal distribution

PROCESS CAPABILITY:PROCESS CAPABILITY:

Normal Distribution:µ ± σ = 68.3%µ ± 2σ = 95.4%µ ± 3σ = 99.7%

The capability of the process to meet those specifications is determined by stability of the process, the range of variation and the process aim point:

Normal distributionNormal distribution

NormalMean=114.978Std. Dev.=0.238937

Cp = 1.41Pp = 1.40Cpk = 1.38Ppk = 1.36K = -0.02

Process Capability for strength

LSL = 114.0, Nominal = 115.0, USL = 116.0

114 114.4 114.8 115.2 115.6 116

strength

0

4

8

12

16

20

24

freq

uenc

y

DPM = 30.76

Histogram follows normal distribution process meets the specification

Process capability index can be calculated as below;SU - SL

CP = --------- 6s

One sided specificationSU - x

CP = ---------- 3s

x - SL

CP = --------- 3s

1.33 ≤CP Satisfiable enough1.00 ≤CP < 1.33 AdequateCP < 1.00 Inadequate

Process Capability (Cp)Process Capability (Cp)Yield range: 100 -118 kgStd deviation : 2.5Mean 110

18Cp = ------- = 1.5

6*2.5

METHODOLOGY TOOLS / TECHNIQUES

1. Search for opportunities; decide what to work on.

Identify the area for improvement; Pareto charts; Cause and effect diagrams, flow chart.

2. Clearly define the project; Select the improvement team.

Pareto charts; Brainstorming.

3. Study the current process/ situation.

Check sheet; Run chart; Flow chart; Cause and effect diagram; Histogram; Pareto charts; Control charts

4. Analyse causes; plan the improvement.

Cause and effect diagram; Correlation chart; Pareto charts; Brainstorming; Histogram.

METHODOLOGY TOOLS / TECHNIQUES

5. Carry out the improvement plan.

Run chart; Histogram; flow chart.

6. Study the effect of the changes.

Run chart; Histogram; Control chart.

7. Standardize the improved process.

Flow chart ;Run chart ; Histogram

8. Assess progress and plan for the future.

Cause and effect diagram; Pareto charts; Brain storming

What does not get measured, can not be recorded

What does not get recorded, can not be monitored

What does not get monitored, can not be controlled

What does not get controlled, can not be improved

Thank youThank you