Q 564. Multi-vari chart is a graphical representation of ANOVA data. Explain the basics of a Multi-vari chart and how to interpret the results using an example.

 

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If Multiple variables in a process or system can be analgised by using statistical process control tool- Anova, correlation chart or an interaction plot..

Chart on multiple variables give representation of patterns and relationships between them. On X-axis there will be 2 or more variable & on Y-axis measured value.

Multi-vari charts used mostly for manufacturing process to identify potential cause ( Vital x) and  effective ( Response-Y). This chart can be use healthcare and finance analyse the relationships between factor and response. . Interpretation of the chart involves analyzing the patterns and relationships between the variables, and identifying potential areas for improvement or further investigation.

Chart Quality- Variability on a single piece, Piece-to-piece variability Time-to-time variability

Example- We have 3 type of material used for parts. Due to raw material type, different cycle time or process time for production & will give impact strength. So data collection for same. And Raw Material cost(Rs/kg)  ABS>HIPS>PP.

 

Which material to be selected for production and why?

 

Raw Material Type	Cycle Time	Impact Strength
ABS	60	23
ABS	60	20
ABS	60	21
PP	60	22
PP	60	19
PP	60	20
HIPS	60	19
HIPS	60	18
HIPS	60	21
ABS	65	22
ABS	65	20
ABS	65	19
PP	65	24
PP	65	25
PP	65	22
HIPS	65	20
HIPS	65	19
HIPS	65	22
ABS	75	18
ABS	75	18
ABS	75	16
PP	75	21
PP	75	23
PP	75	20
HIPS	75	20
HIPS	75	22
HIPS	75	24

 

Interpreting the results

1.       ABS Material- lower cycle time and higher Impact Strength

2.       HIPS Material – Higher Cycle time- higher Impact Strength

3.       PP Material – Higher strength at Optimum cycle time.

Out of all three Raw material and cycle time.

1.       If Material Selection based on available time- ABS material can be selected for higher number of production for higher strength.

2.       If Cost is factor- PP material can be used for production.

Multi-vari chart is a graphical tool to find the variation and root cause in the data including cyclic variation and interaction. It is also the graphical representation of the relationship between factors and a response. Sources of variation can be found because of following reasons:

1.    Variation within Part (is also called Positional variation).

2.    Part to part variation (is also called cyclic variation).

3.    Time to time variation (is also called Temporal variation)

A multi-Vari is plotted on 2 axis, response (y) is plotted on the vertical axis however Factors are plotted on Horizontal axis. Consecutive measurements are plotted from left to right on horizontal axis.

Example and interpretation of Multi-Vari Charts: -

XYZ water company, A leading supplier of quality water wanted to check the purity of Water.

The following is the Table of Sample taken during different positions to check the Water Purity. A multi-vari chart was drawn using Minitab to check the source of variation in purity of water.

Shift	Piece (Sample)	Position (Sample Location)	% Purity
1	1	1	99
1	1	2	99
1	1	3	99
1	1	4	100
1	2	1	95
1	2	2	97
1	2	3	98
1	2	4	96
2	1	1	100
2	1	2	100
2	1	3	97
2	1	4	100
2	2	1	96
2	2	2	97
2	2	3	100
2	2	4	98

 

 

 

 

Ø  On the Multi-vari charts, Cleary evident that Largest Variation occurs due to Variation in sample hence Part to part variation.

Ø  Within Position variation is also present however it is less compared to part-to-part variation

Ø  Shift to shift (Time to Time) variation is present, however not significant and less than the variation caused by part-to-part variation.

However further analysis of Variation done through ANOVA, and Part-to-part variation was found significant based on the p-values obtained.

 

 

 

 

Multi vari chart is a graphical representation from which we cannot draw statistical inferences. It is  used to identify the multiple sources of common cause variations. We can check variations across piece to piece, variation on single piece and time to time using a multi vari chart

 

Piece to Piece helps identify variations within a part of the product/process

When we want to compare two different process/product, piece to piece can be used. 

Time to time variation is used to compare the variations between the different times of production

 

Interpreting the Multi Vari chart:

Means for each factor must be referred and the interaction of one factor with the other and the impact on the other can be understood by the studying the trend line that passes through the mean.

Introduction – One of six sigma's key objectives is to reduce variation, and comprehending these variations can be aided by using Multi-Vari charts.  Leonard Seder first described Multi-Vari charts in 1950. Later, it was widely used to comprehend stock market fluctuations. Then, Dorian Shainin began utilising it as a root cause analysis tool, which he referred to as Red X.

 

Definition – Multi-Vari charts analyse various sources of variation or classes of variation, according to their definition.  It is useful for early root cause analysis and helps us focus on the inputs that are producing issues.  These are sometimes referred to as multiattribute utility theory charts, and they assist people in comparing numerous options by outlining the advantages and disadvantages of each other.  This is just an another way to narrow down our inputs by analysing the process Xs or the inputs.  Especially in the early stages of data analysis, use a Multi-Vari chart to visually portray Analysis of Variance (ANOVA) data to analyse data, understand potential relationships, and root causes for variation. Multivariate graphs are particularly helpful for comprehending interactions.

 

 

Sources of Variation as we have in ANOVA:

 

Interaction Within Variables – This source let us understand the reasons for variation within a batch.  This is also called positional variation.  For instance, it is comparing within the variables if we observe variation within a batch on a given day.

 

Interaction Between Variables – This source explains the causes of the change between batches.  Additionally known as cyclical variation.  For instance, if we are seeing variation between Batch 1 and Batch 2, it is comparing between the variables.

 

Time-to-time Interaction – This provides the reasons between weeks or days or any time frame we want to analyse.  This is also called temporal or shift-to-shift variation.  For instance, if we are looking to find our variation across the Day 1 and Day 2, then the time factor comes into picture and it is Time-to-Time variation.

 

A Multi-Vari chart is a two-axis plot.  These graphs are used to examine a process's consistency or stability.  Time is represented on the chart's horizontal, or X-axis while the process output or reaction measurement is depicted on the vertical, or Y-axis.

 

The multiple measurements of each unit are plotted together. Consecutive measurements are plotted from left to right over time. A break in the horizontal groupings indicates a break in time during the sampling process.

 

Advantages –

Ø  It gives us access to several sources of variation, such as within, between, and over time, and is comparable to the reproducibility and repeatability of ANOVA.

Ø  Despite the need for additional statistical analysis, it points us in the right path for determining the reasons of variations.

Ø  This is easily illustrable without the aid of any graphic programme.

 

Disadvantages –

Ø  As was already said, Multi-Vari only provides preliminary sources of variations.

Ø  Given that it is merely a graphical tool, a thorough interpretation is not feasible.  ANOVA can be used to undertake statical procedures and uncover the underlying causes of sources of variation.

Ø  With discrete data, it is ineffective.  To measure the variances, we can only use continuously data.

 

Let's look at one of the industry examples of Quality scores broken down by week that was taken from various clients below.

 

 

Interpretation –

·         Client 5: The Multi-Variance chart shows that Client-5 demonstrated strong Quality performance over the course of all four weeks, with very little variations in their weekly results.  

·         Client 2: The Multi-Variance chart shows that Client 2 has higher weekly variations and is also going lower than 90%.

·         Client 1 is performing similarly to Clients 2 and 4 in terms of quality, however there is more variance between the weeks.

·         Client 3: When compared to other clients, this client's quality is inconsistent and shows significant fluctuations.

A multi-vari chart depicts the focuses on the relations between response and factor, this typically shows the variance data analysis in graph manner, majorly during the initial stages of the data observation, relations, and possible root cases of the data variance. This graph basically analyses the process stability.

Multi-Vari chart is mainly used in services and manufacturing sectors. There are two types of multi-vari chart study:

Passive Nested observed without changing the routine of the process, whereas manipulated crossed observation is oriented towards intentional process changes for observation. This is basically a method of analysing the multivariate in statistical way to stimulate and observe the data, each individual data group is analysed on multiple variables and parameters.

Multi-Vari analysis focuses on logical subgrouping of the data set to analyse effects on continuous Y’s of category X’s. This can be measured with nested analysis of variance. Multi-Vari analysis is consist of tow or more dependent components Y1,Y2 together taken for independent variable X1,X2, so on.

This can be used in very structured way to study and implement in statistical control. Helps in finding the causes of process variation and quantify them.

Within shift, Operator to operator, Within operator, shift to shift, between the shifts etc..

This can be used in six sigma projects to analyse the VOC, Brainstorming, 5S systems, Kaizen, process benchmarking, Poka-Yoke and VSM etc.

With this graph we we can interpret the variation by studying pattern of lines and circles, at every variation within each line item, also between cyclical variations. This help in analysing the effect of various category groups input on a continuous output.

Best answer to this question has been given by Moushmi Kandori. Well done.

 

Vijay's answer is also a must read.