What is quality

TOTAL QUALITY MANAGEMENT, STATISTICAL PROCESS CONTROL
I. Introduction
-- What is quality?
“The totality of features and characteristics of a product or service that bear on its ability to satisfy stated or implied needs”  -- ASQC

• User-based:
• Product-based:
• Manufacturing-based:

-- Why quality is important?

• Costs and market share
• Company’s reputation
• Product liability
• International implications

-- Two parts of quality management

• Quality Control:
• Quality Assurance:
•  

-- Traditional concept of quality management:

• Responsibility of quality control dept. only
• Rely on the inspection process
• Satisfied with meeting specifications

II. Total Quality Management (TQM)
-- Five TQM concepts:

• Continuous improvement
• Employee Empowerment
• Benchmarking
• Just-in-Time
• Develop proper tools

-- Deming's 14 points:
1. create consistency of purpose
2. lead to promote change
3. quality through design instead of inspection
4. reduce # of suppliers, don’t buy on price alone
5. continuously improve product, quality, and service
6. institute modern training methods
7. emphasize leadership
8. drive out fear
9. break down barriers between departments
10. eliminate numerical goals, slogans, posters for the work force
11. using statistical methods to improve quality and productivity
12. remove barriers to pride of workmanship
13. institute a program for retraining people in new skills
14. put everybody to work on the transformation

III. Tools For TQM

• Quality Function Deployment

-- Translate customer desire to product and process design

•  
• Taguchi Technique

- Quality robustness
- Quality loss function
- Target specification

•  
• Process Flow Charts

-- Standard procedure to decompose and describe a process

•  
• Cause and Effect Diagram

-- Tool to systematically identify quality problems

•  
• Pareto Charts

-- Distinguish major causes and minor causes of quality problems

•  
• Statistical Process Control

    
IV. Statistical Process Control
- graphical presentation of samples of process output over time
- used to monitoring (production) process and detect quality problems

-- Natural and Assignable Variations

                   Natural            Assignable
Charact.:
Causes:
Action:

-- Idea Behind Control Charts:
If (production) process is normal
à only natural variations exist
à samples of output is Normally distributed
à within 3 std. 99.7% of time
Therefore,
à If not within 3 std. ==> assignable variations exist!
UCL and LCL are set to correspond to the 3 std. lines

-- Procedures of using control charts:

• take samples regularly
• calculate proper statistics
• plot the statistics on the control chart
• Analyze the pattern of plots and draw conclusion

-- In control and out of control

• In control: plots Normally distributed, unbiased, no patterns

à indicating no assignable variations exist

• Out of control:
• one plot outside UCL or LCL (for all charts)
• 2 of 3 consecutive plots out of 2 std. Line (for X-chart)
• 7 consecutive plots on one side (for X-chart)

à indicating assignable variations exist, sign of quality problems.

-- Types of control chart:

• Variable Charts: for continuous quality measure
• X-chart: process average
• R-chart: process dispersion and variation

• Attribute Charts: for attribute quality measure
• p-chart: defective rate
• c-chart: number of defectives

 

V. Construct and Use Control Charts
-- Construct X-chart
1. based on some process information:

• CL = specification (target value)
• UCL = CL + 3 std of process /Ön
• LCL = CL - 3 std of process /Ön

- n: sample size

 2. based only on past samples

• CL = average of past samples
• UCL = CL + A2*range average of past samples
• LCL = CL - A2*range average of past samples

- A2: found from the table of your textbook

 3. Differences between 1. and 2.

-- Construct R-chart (based on past samples)

• CL = average range of past samples
• UCL = D4*average range of past samples
• LCL = D3*average range of past samples > 0

- D4 and D3: found from the table of your textbook

-- Example 1
Samples taken from a process for making aluminum rods have an average of 2cm. The sample size is 16. The process variability is approximately normal and has a std. of 0.1cm. Design an X-chart for this process control.

-- Example 2
Five samples of drop-forged steel handles, with four observations in each sample, have been taken. The weight of each handle in the samples is given below (in ounces). Use the sample data to construct an X-chart and an R-chart to monitor the future process.

Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
10.2	10.3	9.7	9.9	9.8
9.9	9.8	9.9	10.3	10.2
9.8	9.9	9.9	10.1	10.3
10.1	10.4	10.1	10.5	9.7

 

-- Use X-chart and R-chart

• Calculate averages and ranges of new samples
• Plot on the X-chart and R-chart, respectively

-- Example 2 (continued)
Five more samples of the handles are taken

Sample 6	Sample 7	Sample 8	Sample 9	Sample 10
10.4	10.5	9.9	10.3	9.9
9.8	9.9	9.9	10.4	10.4
9.9	9.9	9.9	10.6	10.5
10.3	10.5	10.3	10.5	9.9

     Is the process in control (changed)?

-- Construct p-chart

• CL = average defective rate of past samples
• UCL = CL + 3 std of past sample defective rates
• LCL = CL - 3 std of past sample defective rates > 0

-- Use p-chart

• Calculate defective rates of new samples
• Plot on the p-chart

-- Example 3
A good quality lawnmower is supposed to start at the first try. In the third quarter, 50 craftsman lawnmowers are started every day and an average of 4 did not start. In the fourth quarter, the number of lawnmower did not start (out of 50) in the first 6 days are 4, 5, 4, 6, 7, 6, respectively. Was the quality of lawnmower changed in the fourth quarter?

-- Construct c-chart

• CL = average # of defectives in past products
• UCL = CL + 3 std of # of defectives in past products
• LCL = CL - 3 std of # of defectives in past products > 0

-- Use c-chart

• Count # of defective in new products
• Plot on the c-chart

-- Example 4
There have been complaints that the sports page of the Dubuque Register has lots of typos. The last 6 days have been examined carefully, and the number of typos/page is recorded below. Is the process in control?

Day	Mon.	Tues.	Wed.	Thurs.	Fri.	Sat.
Typos	2	1	5	3	4	0

 

VI. Acceptance Sampling
- Accept or reject a lot (input components or finished products) based on inspection of a sample of products in the lot

-- Role of Inspection

• Involved in all stages of production process
• Inspection itself does not improve quality
• Destructive and nondestructive inspection

-- Why sampling instead of 100% inspection?

• Destructive test
• Worker's morale
• Cost consideration

-- Single Acceptance Sampling Plan:

1. Take a sample of size n from a lot with size N

2. Inspect the sample 100%
3. If # of defective > c, reject the whole lot; otherwise, accept it.

• - need to determine n and c.
•  

-- Operating Characteristic (OC) Curves
- to evaluate how well a single acceptance sampling plan
discriminates between good and bad lots

-- Draw OC curve approximately for a sampling plan with n and c
- Idea:
The number of defectives in a sample of size n with defective rate p follows a Poisson distribution approximately with parameter l = np, when p is small, n is large, and N is much larger.

à P(acceptance) = Prob(# def. <= c)
@ Prob(# def. <= c, l) based on Poisson distribution

 - Procedure:

• Create a series of p = 1% to 10%.
• Calculate l = np for each p.
• Use the Poisson table of Appendix B to find P(acceptance) for each l and c.
• Link P(acceptance) to form a curve.

 
-- Example 5:
A single sampling plan with n=100 and c=3 is used to inspect a shipment of 10000 computer memory chips. Draw the OC curve for the sampling plan.

P(%)	1	2	3	4	5	6	7	8	9	10
l = np
P(acceptance)

-- Concepts related to the OC Curve

• AQL: Acceptable quality level, the defective rate that a consumer is happy to accept (considers as a good lot)
• LTPD: Lot tolerance percent defective, the maximum defective rate that a consumer is willing to accept
• Consumer's risk: the probability that a lot containing defective rate exceeding the LTPD will be accepted.
• Producer's risk: the probability that a lot containing the AQL will be rejected. 

-- Example 5 continued:
The buyer of the memory chip requires that the consumer’s risk is limited to 5% at LTPD = 8%. The producer requires that the producer’s risk is no more than 5% at AQL = 2%. Does the single sampling plan meet both consumer and producer’s requirements?

-- Sensitivity of OC curve, consumer's risk, and producer's risk    to N, n, c. 

• Changing n, keeping c constant:

 

• Changing c, keeping n constant:

• Changing both n and c, keeping c/n constant:

 

• Changing N:

-- Average Outgoing Quality(AOQ)
- the quality after inspection (by a single sampling plan), measured in defective rate, assuming all defectives in the rejected lot are replaced
AOQ = p Pa(N-n)/N @ p Pa
Pa = P(acceptance for a lot with defective rate p),             can be found from the OC curve

-- Example 5 continued:
The average defective rate of the memory chip is about 5% (based on the past data). Calculate the AOQ of the memory chip after it is inspected by the sampling plan in Example 5.

-- Other Sampling Plans

• Double sampling plan

 - Given n: sample size
c1: acceptable level of the first sample
c2: acceptable level of both samples
- Procedure:

•  

-- Example:
n = 100, c1 = 4, c2 = 7, # of defective in the first sample = 5.

• Sequential sampling plan

 - Given  n: sample size
upper and lower limits of number of defectives allowed
- Procedure:

• Count # of total defectives found in all previous samples
• If # of defectives > upper boundary, reject the lot
• If # of defectives <= lower boundary, accept the lot
• Otherwise, take a new sample and repeat.

-- Advantages of double and sequential samplings:

• Psychologically:
• Cost: less inspection for the same accuracy

Factors for Computing Control Chart Limits for X and R Charts

Sample Size (n)	Mean Factor (A2)	Upper Range (D4)	Lower Range (D3)
2	1.880	3.268	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.115	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223