18 terms

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ANOVA

Is there any effect of material on uniformity of film thickness of computer chips?

Which material is the best?

Which material is the best?

Single Factor ANOVA

A test to find out whether differences exist among the means of the populations (i.e., materials) of interest.

If the population means are found different, we compare the population means. (i.e., compare means)

If the population means are found different, we compare the population means. (i.e., compare means)

Single Factor ANOVA-First Step

Are the means equivalent?

Partition the total variation in the sample to between and within group variations

Total variance:

= Between group variance + within group variance

In other words, Total sum of squares (SST) =

sum of (Each group mean - Overall mean)2

+ sum (Individual values - Each group mean)2

SST = sum of squares of treatments (SSTR)

+ error sum of squares (SSE)

Partition the total variation in the sample to between and within group variations

Total variance:

= Between group variance + within group variance

In other words, Total sum of squares (SST) =

sum of (Each group mean - Overall mean)2

+ sum (Individual values - Each group mean)2

SST = sum of squares of treatments (SSTR)

+ error sum of squares (SSE)

Single Factor ANOVA: Second Step

Are the means equivalent? Are the between and within group variances are significantly different?

F follows a distribution with degrees of freedom (dof) a - 1, and N - a.

The figure below shows the H0 rejection region for a level of significance where F,a-1,N-a denotes the critical value of F for dof a - 1, and N - a.

F follows a distribution with degrees of freedom (dof) a - 1, and N - a.

The figure below shows the H0 rejection region for a level of significance where F,a-1,N-a denotes the critical value of F for dof a - 1, and N - a.

Logic of ANOVA Test

Both MSTR and MSE estimatevariation in the data (2 )

If the group means are equal, the ratio MSTR/MSE should be close to 1. (statistically, H0 is true)

If the means are unequal (i.e., H0 is not true), the ratio should be significantly larger than 1, since MSTR would tend to over-estimate 2.

The ratio F = MSTR/MSE

Hence, reject H0 if F = MSTR/MSE is too large

F follows an F distribution with numerator d.f. a - 1, and denominator d.f. N - a.

F is too large, if it is larger than a critical value, F,a-1,N-a.

If the group means are equal, the ratio MSTR/MSE should be close to 1. (statistically, H0 is true)

If the means are unequal (i.e., H0 is not true), the ratio should be significantly larger than 1, since MSTR would tend to over-estimate 2.

The ratio F = MSTR/MSE

Hence, reject H0 if F = MSTR/MSE is too large

F follows an F distribution with numerator d.f. a - 1, and denominator d.f. N - a.

F is too large, if it is larger than a critical value, F,a-1,N-a.

Single Factor ANOVA: Excel Steps

Go to Data

Go to Data Analysis

Go to Analysis Tools

Click on ANOVA: Single Factor

Select the input range, group's arrangement (i.e., columns or rows, alpha (i.e., significance level), output range

Press ok

Interpret the results

Go to Data Analysis

Go to Analysis Tools

Click on ANOVA: Single Factor

Select the input range, group's arrangement (i.e., columns or rows, alpha (i.e., significance level), output range

Press ok

Interpret the results

Two Factor ANOVA: Excel Steps

Go to Data

Go to Data Analysis

Go to Analysis Tools

Click on ANOVA: Two Factor with Replication

Select the input range, rows per sample (i.e., number of replication at each factorial level, alpha (i.e., significance level), output range

Press ok

Interpret the results

Go to Data Analysis

Go to Analysis Tools

Click on ANOVA: Two Factor with Replication

Select the input range, rows per sample (i.e., number of replication at each factorial level, alpha (i.e., significance level), output range

Press ok

Interpret the results

Pull System

Customer driven - contains clear customer-supplier connections throughout operations!!!

Problems/wastes are eliminated as they surface

Problems/wastes are eliminated as they surface

Elimination of 7 Forms of Waste (time, effort, material, money)

Overproduction

Waiting (idle time)

Conveyance (material handling)

Processing

Inventory

Defects

Motion

Waiting (idle time)

Conveyance (material handling)

Processing

Inventory

Defects

Motion

Lean Tools & Techniques

Value Stream Process Mapping (VSM)

Kaizen

5S

Line Balancing

Schedule Leveling

Error Proofing (poka-yoke)

Setup Time Reduction (SMED)

Preventive & Predictive Maintenance

Standardized Work

Visual Management

Reduced Lot Sizes (single piece flow)

Kanban (pull inventory management)

Kaizen

5S

Line Balancing

Schedule Leveling

Error Proofing (poka-yoke)

Setup Time Reduction (SMED)

Preventive & Predictive Maintenance

Standardized Work

Visual Management

Reduced Lot Sizes (single piece flow)

Kanban (pull inventory management)

House of Lean: The Toyota Production System

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