Control Charts 2

Question 1

What is the difference between specification limits and control limits.

Answer 1

Specification limits are set up taking into account the customer’s requests and the characteristics of the productive process

Control limits are calculated taking into account the variability of the process.

Question 2

What are pros and cons of the 2sigma warning limits (WL)

Answer 2

Pro: The use of warning limits can increase the sensitivity of the control chart.

Con: The use can also result in an increased rist of false alarms

Question 3

By decreasing alpha we increase beta. What does it mean in more practical words?

Answer 3

The power of the test is reduced, thus reducing the sensitivity of the control chart.

Question 4

How to evaluate the ability of Shewart control charts to detect out-of control situations?

Answer 4

The capacity of a CC for detecting an out-of-control situation can be measured by the power of the test (1-beta)

Question 5

What is the Operating Characteristic Curve (OCC)?

Answer 5

A curve that reflects the ability (or sensitivity) of the chart to detect deviations from H0.

The OCC represents the probability that a point is within the control limits, as a function of each possible value of the parameter of the underlying distribution.

Question 6

What is the Average Run Length (ARL)?

Answer 6

The ARL is the expected value of number of samples that we need to gather until having an out of control signal.

Question 7

How to calculate the ARL?

Answer 7

ARL = 1/Pd
Pd = probability of detecting the deviation on the kth sample.

Question 8

How to calculate the ARL when the process is in/out of control:

Answer 8

ARL = 1/alpha
ARL = 1/1-beta

Question 9

What are possible measures to reduce the out of control ARL?

Answer 9

1 Increasing the sample size.
2 Reduce the interval between samples
3 Use more responsive control charts i.e. CUSUM

Question 10

What are Np and p control charts for? (Attributes)

When to use Np and when p?

Answer 10

CC for counting one random variable that only has two possible outcomes: defective and non-defective. (Binomial)

Sample size N constant–> Np Chart
Sample size N variable–> p Chart.

Question 11

What are c and u control charts for? (Attributes)

When to use c and when u?

Answer 11

CC for the number of defects or nonconformaties for a given opportunity area (time or space). (Poisson)

opportunity area constant -> c chart
opportunity are variable -> u chart

Question 12

What are (x,s) and (x,R) control charts for? (Variables)
When to use (x,s) and when (x,R)?

Answer 12

Variables. (Normal-distribution)

Sample size N>8 –> (x,s) chart. Best estimator of sigma is the sample standard deviation

Sample size <= 8 –> (x,R) chart. Best estimator of sigma is the sample range

Question 13

What is the control chart for individual measurements (x,Rmoving) used for? What’s the moving range?

Answer 13

For individual measurements. The moving range is a statistic consisting in the absolute difference between successive values of the variable under analysis.

Question 14

How to calculate p^ for Np charts when no standard given?

Answer 14

p^= total number of defective items / total number of items

Question 15

Name three basic rules for eliminating outliers:

Answer 15

1 Limits must be based on data from a process that is in control.
2 Each of the out of control points has to be examined and discarded if they are linked to assignable causes.
3 The number of discarded samples should not exceed 10% of the total number of samples.

Question 16

What is the difference between defective items and defects per unit?

Answer 16

defective items= Each item is classified into one of two categories: pass/fail.

defects per unit= Each item can have more than one defect, or undesirable characteristics.

Question 17

Name three facts regarding the sensitivity of the control charts for attributes:

Answer 17

1. The sensitivity of the CC is associated with its ability to detect shifts in the process parameters.
   2 The power of the tests with the binomial and poisson distr. is low
   3 CC are not the best tool to control processes with low process capability.

Question 18

CCV are built based on quantitative data. What’s the difference between Average CC’s and Rang CC’s?

Answer 18

ACC: evaluates the process center.
RCC: evaluates the process variation.

Question 19

The Shewart CL highly depend on the variability within subgroups. What happens if assignable causes of variation are present within subgroups?

Answer 19

Inflated limits. CC are insensitive to process shifts.

Question 20

What are two important facts regarding sample variability of X and R charts:

Answer 20

X: monitors the between sample variability (over time)

R monitors the between sample variability (in a given moment)

Question 21

What are three pros and three cons of the (x,MR) charts?

Answer 21

pros: 1 simple interpretaion
2 immediate update
3 direct comparison with the specification limits

cons: 1 less sensitive thatn x,R
2 assumed that observations follow a Normal distr.
3 The successive values of the ranges could be highly correlated.