Mata kuliah : J0444 - Manajemen Operasional
Tahun : 2010
Quality Control
Pertemuan 12

Learning Objectives
• List and briefly explain the elements of the control process.
• Explain how control charts are used to monitor a process, and the concepts that underlie their use.
• Use and interpret control charts.
• Use run tests to check for nonrandomness in process output.
• Assess process capability.

Phases of Quality Assurance
Inspection of lots before/after production
Acceptance sampling
Inspection and corrective action during production
Process control
Quality built into the process
Continuous improvement
The least progressive
The most progressive

Inspection
• How Much/How Often
• Where/When
• Centralized vs. On-site
Inputs Transformation
Acceptance sampling
Process control
Outputs
Acceptance sampling

• Raw materials and purchased parts
• Finished products
• Before a costly operation
• Before an irreversible process
• Before a covering process

Examples of Inspection Points
Type of business
Inspection points
Fast Food Cashier
Counter area
Eating area
Building
Kitchen
Hotel/motel Parking lot
Accounting
Building
Main desk
Supermarket Cashiers
Deliveries
Characteristics
Accuracy
Appearance, productivity
Cleanliness
Appearance
Health regulations
Safe, well lighted
Accuracy, timeliness
Appearance, safety
Waiting times
Accuracy, courtesy
Quality, quantity

Statistical Control
• Statistical Process Control :
Statistical evaluation of the output of a process during production
• Quality of Conformance:
A product or service conforms to specifications

Control Chart
• Control Chart
– Purpose: to monitor process output to see if it is random
– A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means)
– Upper and lower control limits define the range of acceptable variation

Control Chart
Abnormal variation due to assignable sources
Out of control
UCL
Mean
Normal variation due to chance
Abnormal variation due to assignable sources
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample number
LCL

Statistical Process Control
• The essence of statistical process control is to assure that the output of a process is random so that future output will be random.

Statistical Process Control Steps
Start
Produce Good
Provide Service
Take Sample
Inspect Sample
No
Assign.
Causes?
Yes
Stop Process
Create
Control Chart
Find Out Why

Statistical Process Control
• Variations and Control
– Random variation : Natural variations in the output of a process, created by countless minor factors
– Assignable variation : A variation whose source can be identified

Sampling Distribution
Sampling distribution
Process distribution
Mean

Normal Distribution

Standard deviation
 
Mean
95.44%
99.74%
 

Control Limits
Sampling distribution
Process distribution
Lower control limit
Mean
Upper control limit

SPC Errors
• Type I error
– Concluding a process is not in control when it actually is.
• Type II error
– Concluding a process is in control when it is not.

Type I and Type II Errors
In control
Out of control
In control
No Error
Type II Error
(consumers risk)
Out of control
Type I error
(producers risk)
No error
10-17

Type I Error

/2

Probability of Type I error
LCL
Mean
UCL

/2

UCL
LCL
1 2
Sample number
3 4

Control Charts for Variables
Variables generate data that are measured.
• Mean control charts
– Used to monitor the central tendency of a process.
– X bar charts
• Range control charts
– Used to monitor the process dispersion
– R charts

Sampling
Distribution
UCL x-Chart
LCL
UCL
R-chart
LCL
Mean and Range Charts
(process mean is shifting upward)
Detects shift
Does not detect shift

Sampling
Distribution
UCL x-Chart
LCL
UCL
R-chart
LCL
Mean and Range Charts
(process variability is increasing)
Does not reveal increase
Reveals increase

Control Chart for Attributes
• p-Chart - Control chart used to monitor the proportion of defectives in a process
• c-Chart - Control chart used to monitor the number of defects per unit
Attributes generate data that are counted.

Use of p-Charts
• 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

Use of c-Charts
• Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted.
– Scratches, chips, dents, or errors per item
– Cracks or faults per unit of distance
–
–
Breaks or Tears per unit of area
Bacteria or pollutants per unit of volume
– Calls, complaints, failures per unit of time

Use of Control Charts
• At what point in the process to use control charts
• What size samples to take
• What type of control chart to use
– Variables
– Attributes

Run Tests
• Run test – a test for randomness
• Any sort of pattern in the data would suggest a nonrandom process
• All points are within the control limits - the process may not be random

• Trend
• Cycles
• Bias
• Mean shift
• Too much dispersion

Counting Runs
Counting Above/Below Median Runs (7 runs)
B A A B A B B B A A B
Counting Up/Down Runs (8 runs)
U U D U D U D U U D

NonRandom Variation
• Managers should have response plans to investigate cause
• May be false alarm (Type I error)
• May be assignable variation

Process Capability
• Tolerances or specifications
– Range of acceptable values established by engineering design or customer requirements
• Process variability
– Natural variability in a process
• Process capability
– Process variability relative to specification

Lower
Specification
Process Capability
Upper
Specification
A. Process variability matches specifications
Lower
Specification
Upper
Specification
B. Process variability well within specifications
Lower
Specification
Upper
Specification
C. Process variability exceeds specifications

Process Capability Ratio
If the process is centered use Cp
Process capability ratio, Cp = specification width process width
Cp =
Upper specification – lower specification
6

If the process is not centered use Cpk
C pk
= min


X

3
LTL
 or
UTL
3

X



1. Process may not be stable
2. Process output may not be normally distributed
3. Process not centered but C p is used

Example
Machine
A
Standard
Deviation
0.13
Machine
Capability C p
0.78
0.80/0.78 = 1.03
B
C
0.08
0.16
0.48
0.80/0.48 = 1.67
0.96
0.80/0.96 = 0.83
Cp > 1.33 is desirable
Cp = 1.00 process is barely capable
Cp < 1.00 process is not capable
10-35