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What is SQC?
Statistical Quality Control (SQC)
The term used to describe the set of statistical tools used by quality professionals to evaluate organizational quality.
Statistical Quality Control (SQC)
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3 Categories of SQC
Statistical process control (SPC) inspecting a random sample of an output from process, within range and functioning properly
Descriptive statistics the mean, standard deviation, and range
Involve inspecting the output from a process
Quality characteristics are measured and charted
Helps identify in-process variations
Acceptance sampling used to randomly inspect a batch of goods to determine acceptance/rejection
Does not help to catch in-process problems
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Sources of Variation
Variation exists in all processes.
Variation can be categorized as either:
Common or Random causes of variation
Random causes that we cannot identify
Unavoidable, i.e.; slight differences in process variables like diameter, weight, service time, temperature
Assignable causes of variation
Causes can be identified
Eliminate cause i.e.; poor employee training, worn tool, machine needing repair
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Descriptive Statistics
The Mean- measure of central tendency
The Range- difference between largest/smallest observations in a set of data
Standard Deviation measures the amount of data dispersion around mean
Distribution of Data shape
Normal or bell shaped or
Skewed
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Distribution of Data
Normal distributions
Skewed distribution
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SPC Methods-Developing Control Charts
Control Charts (aka process or QC charts) show sample data plotted on a graph with CL, UCL, and LCL
Control chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, time
Control charts for attributes are used to monitor characteristics that have discrete values and can be counted, e.g. % defective, # of flaws in a shirt, etc.
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Setting Control Limits
Percentage of values under normal curve
Control limits balance risks like Type I error
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7
Control Charts for Variables
Use x-Bar and R-bar charts together
Used to monitor different variables
x-Bar and R-bar charts reveal different problems
What is the statistical control difference from one chart to the next?
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Control Charts for Variables
Use x-Bar charts to monitor the changes in the mean of a process (central tendencies)
Use R-bar charts to monitor the dispersion or variability of the process
System can show acceptable central tendencies but unacceptable variability
System can show acceptable variability but unacceptable central tendencies
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Constructing an x-Bar Chart: A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled. If the standard deviation of the bottling operation is .2 ounces, use the below data to develop control charts with limits of 3 standard deviations for the 16 oz. bottling operation.
| Time 1 | Time 2 | Time 3 | |
| Observation 1 | 15.8 | 16.1 | 16.0 |
| Observation 2 | 16.0 | 16.0 | 15.9 |
| Observation 3 | 15.8 | 15.8 | 15.9 |
| Observation 4 | 15.9 | 15.9 | 15.8 |
| Sample means (X-bar) | 15.875 | 15.975 | 15.9 |
| Sample ranges (R) | 0.2 | 0.3 | 0.2 |
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Center line and control limit formulas
Solution and x-Bar Control Chart
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Control limits for±3σ limits:
Center line (x-double bar):
x-Bar Control Chart
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Control Chart for Range (R)
Center Line and Control Limit formulas:
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Factors for three sigma control limits
Factor for x-Chart
A2
D3
D4
2
1.88
0.00
3.27
3
1.02
0.00
2.57
4
0.73
0.00
2.28
5
0.58
0.00
2.11
6
0.48
0.00
2.00
7
0.42
0.08
1.92
8
0.37
0.14
1.86
9
0.34
0.18
1.82
10
0.31
0.22
1.78
11
0.29
0.26
1.74
12
0.27
0.28
1.72
13
0.25
0.31
1.69
14
0.24
0.33
1.67
15
0.22
0.35
1.65
Factors for R-Chart
Sample Size
(n)
R-Bar Control Chart
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Second Method for the x-Bar Chart Using R-bar & A2 Factor
Use this method, Control limits solution, when sigma for the process distribution is not known:
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Control Charts for Attributes – P-Charts & C-Charts
Attributes are discrete events: yes/no or pass/fail
Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Number of flaws or stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel
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P-Chart Example: A production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Calculate the control limits.
| Sample | Number of Defective Tires | Number of Tires in each Sample | Proportion Defective |
| 1 | 3 | 20 | .15 |
| 2 | 2 | 20 | .10 |
| 3 | 1 | 20 | .05 |
| 4 | 2 | 20 | .10 |
| 5 | 2 | 20 | .05 |
| Total | 9 | 100 | .09 |
Solution:
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P-Charts are used when both the total sample size
and the number of defects can be computed
P- Control Chart
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C-Chart Example: The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below.
| Week | Number of Complaints |
| 1 | 3 |
| 2 | 2 |
| 3 | 3 |
| 4 | 1 |
| 5 | 3 |
| 6 | 3 |
| 7 | 2 |
| 8 | 1 |
| 9 | 3 |
| 10 | 1 |
| Total | 22 |
Solution:
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C-Charts are used when you can compute only
the number of defects but not the proportion
that is defective
C- Control Chart
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Process Capability
Product Specifications
Preset product or service dimensions, tolerances: bottle fill might be 16 oz. ±.2 oz. (15.8oz.-16.2oz.)
Based on how product is to be used or what the customer expects
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±6 Sigma versus ± 3 Sigma
In 1980’s, Motorola coined “six-sigma” to describe their higher quality efforts
Six-sigma quality standard is now a benchmark in many industries
Before design, marketing ensures customer product characteristics
Operations ensures that product design characteristics can be met by controlling materials and processes to 6σ levels
Other functions like finance and accounting use 6σ concepts to control all of their processes
PPM Defective for ±3σ versus ±6σ quality
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Acceptance Sampling
Defined: the third branch of SQC refers to the process of randomly inspecting a certain number of items from a lot or batch in order to decide whether to accept or reject the entire batch
Different from SPC because acceptance sampling is performed either before or after the process rather than during
Sampling before typically is done to supplier material
Sampling after involves sampling finished items before shipment or finished components prior to assembly
Used where inspection is expensive, volume is high, or inspection is destructive
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Acceptance Sampling Plans
Goal of Acceptance Sampling plans is to determine the criteria for acceptance or rejection based on:
Size of the lot (N)
Size of the sample (n)
Number of defects above which a lot will be rejected (c)
Level of confidence we wish to attain
There are single, double, and multiple sampling plans
Which one to use is based on cost involved, time consumed, and cost of passing on a defective item
Can be used on either variable or attribute measures, but more commonly used for attributes
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Implications for Managers
How much and how often to inspect?
Consider product cost and product volume
Consider process stability
Consider lot size
Where to inspect?
Inbound materials
Finished products
Prior to costly processing
Which tools to use?
Control charts are best used for in-process production
Acceptance sampling is best used for inbound/outbound; attribute measures
Control charts are easier to use for variable measures
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SQC in Services
Service Organizations have lagged behind manufacturers in the use of statistical quality control
Statistical measurements are required and it is more difficult to measure the quality of a service
Services produce more intangible products
Perceptions of quality are highly subjective
A way to deal with service quality is to devise quantifiable measurements of the service element
Check-in time at a hotel
Number of complaints received per month at a restaurant
Number of telephone rings before a call is answered
Acceptable control limits can be developed and charted
Statistical Quality Control (SQC)
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15.62
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16.22
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.53
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.233
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.102
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.282
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0.064
20
(.09)(.91)
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100
9
Inspected
Total
Defectives
#
p
CL
p
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2.25
2.2
3
2.2
c
c
LCL
6.65
2.2
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2.2
c
c
UCL
2.2
10
22
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