Question

2" (5%) Consider the funnel experiment described by Dr. Deming. The experiment is illustrated as to drop a marble through a funnel with the objective of hitting a target. Imagine that a funnel is fixed on a stand at a certain distance above a target point T on a level surface. A marble is dropped through the funnel. The marble rolls down the funnel and comes to rest at a certain location. This landing point is recorded. This experiment is repeated for 50 drops for each of four different rules which are stated as follows: Rule 1: Leave the funnel fixed over the target and do not make any adjustments. Rule 2: After e very experiment, move the funnel a distance -z from its last position where z is the distance of the landing point from the target. Rule 3: After each expe marble ends up a distance z from the target. Rule 4: Adjust the funnel to be over its last resting position. Which rule is the best? Why? riment, move the funnel a distance -z from the target position where the

Answer 1

The question requires the comparitive study of the four rules from Dr. Deming's funnel experiment and make an inference based on it.

But before that let us try ot understand the experiment first.

The experiment is illustrated as to drop a marble through a funnel with the objective of hitting a target.

A funnel is fixed on a stand at a certain distance above a target point say T on a level surface.

A marble is dropped through the funnel. The marble rolls down the funnel and comes to rest at a certain location.

This landing point is recorded. This experiment is repeated for multiple times say 50 drops for each of four different rules which are stated as follows:

Rule 1: Leave the funnel fixed over the target and do not make any adjustments.

Rule 2: After every experiment, move the funnel a distance say -z from its last position where z is the distance of the landing point from the target.

Rule 3: After each experiment, move the funnel a distance -z from the target position where the marble ends up a distance z from the target.

Rule 4: Adjust the funnel to be over its last resting position.

Now we have to pronounce as to which method is the best .

Now we are not given with any data sets to make an assertion .

Hence we took help of a pre designed and pre conducted funnel experiment as per the four rules and inferred the following .

1. x bar chart

A general observation of the x bar chart as per the four rules is as per the following trends

We can see that observations/output based on the control chart is most disciplined as per rule 1 and least discipines as per rule 4 .

Also it can be noted that the control limit band is very narrow for rule 1 and widest for rule 3.

Thus rule 1 gives us the most reliable observations as per hte contorl chart.

2. R chart

The typical R charts ofr the 4 rules are :-

what do you observe?

The variablity is range for rule 1 and 4 is least and under control while that for rule 2 and 3 is high and not under control.

3. Q-Q plot

The Q Q plot gives us as idea of the degree of variablity explianed by the model

From hte plot above we see that plot under rule 1 has least aberration .

Thus from all the three observations, one this comes out very clearly that rule 1 is the dest method to conduct the funnel experiment .This is so because :-

1. It has least process variablity.

2. It has most reliable process model

3. It has very restricted process band indicating high accuracy .