8. Quality Control

1. (1 - a ) is your level of confidence when you make a claim that a sample in your hand is defective.

a is called significance level (or type I error).

a= chance to observe bad luck

2.  how to claim defective

1)Set your significance level a (the probability that you just have a bad luck)

2)Based on the level of confidence (1- a) you set, the threshold qa can be determined using statistical knowledge

3) Observe samples and claim confidently (under the level of your confidence) that something is wrong in manufacturing process (process is not in control)

3. Objective of Statistical Process Control is to identify whether process is in control or not.

It does not try to catch defectives. As long as an observed spec is within a usual variation, it is fine.

4. Statistical process control:  

A method to evaluate the output of a process to determine its acceptability using a small number of items (samples) taken. These samples are compared with some predetermined standard.

5. Four control charts to monitor qualities

Mean Control Chart, Range Control Chart, p (proportion)-Chart, and c (count)-Chart.

6. Four indices to identity errors in quality control

mean, range, trend, and pattern

7. sample distribution

8. Trade-off Between Type I/II Errors

• Type I error (false positive)

Concluding a process is not in control when it actually is.

-The probability of rejecting the null hypothesis when the null hypothesis is true.

-Manufacturer’s Risk

• Type II error (false negative)

Concluding a process is in control when it is not.

-The probability of failing to reject the null hypothesis when the null hypothesis is false.

-Consumer’s Risk

9. Control Chart: 

A time ordered plot of representative sample statistics obtained from an ongoing process (e.g. sample means), used to cope with both random and nonrandom variabilities

10.  how to use control chart

• Observed data are within control limits, which are set by your confidence level (1-a)

• Observed data do not show trend or pattern

11. Mean Control Chart

12. Range Control Chart

13. p-Chart

When observations can be placed into two categories.

-Good or bad

-Pass or fail

-Operate or don’t operate

When the data consists of multiple samples of several observations each

14. c-Chart

Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted.