Quality Control

Quality Control

Quality Control is a testing procedure

performed every hour (or every half hour, etc) in

an ongoing process of production in order to

see whether the process is running properly

(“ is under control” or “not”). If the process is

not under control, the process is halted to

search for the trouble and remove it.

Statistical Process Control

Statistical Process Control (SPC) Monitoring production process

to detect and prevent poor quality

Sample Subset of items produced to

use for inspection Control Charts

Process is within statistical control limits

Quality Measures Attribute

A product characteristic that can be evaluated with a discrete response

good – bad; yes - no Variable

A product characteristic that is continuous and can be measured

weight - length

Process Control Chart

1 2 3 4 5 6 7 8 9 10Sample number

UpperControl

Limit(UCL)

ProcessAverage

(CL)

LowerControl

Limit (LCL)

Out of control

A Process is in Control If …

No sample points outside limits Most points near process average About equal number of points

above and below centerline Points appear randomly distributed

Applying SPC to Service

Hospitals Timeliness and quickness of care, staff responses

to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts

Grocery Stores Waiting time to check out, frequency of out-of-

stock items, quality of food items, cleanliness, customer complaints, checkout register errors

Airlines Flight delays, lost luggage and luggage handling,

waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance

Applying SPC to Service

Fast-Food Restaurants Waiting time for service, customer

complaints, cleanliness, food quality, order accuracy, employee courtesy

Catalogue-Order Companies Order accuracy, operator knowledge and

courtesy, packaging, delivery time, phone order waiting time

Insurance Companies Billing accuracy, timeliness of claims

processing, agent availability and response time

Control Charts for Variables

Mean (x-bar) Charts Tracks the Central Tendency (the

average value observed) over time Range (R) Charts

Tracks the Spread of the Distribution over time (estimates the observed variation)

Control Chart For Mean

nDZUCL

nDZLCL

)(

)(

0

0

If α is not specified, then α be taken as 1%. (Z (1%) = 2.58)

Control Chart For Variance

1

2

12

12

n

CUCL

n

CLCL

Control Chart(For Std Deviation)

1

1

2

1

n

CUCL

n

CLCL

Control Chart For Range

)(

)(3)(

)(3)(

*

**

**

RE

REREUCL

RERELCL

n

n

n

E(R*) = Mean of the Sample Ranges

Problem 1

Suppose a machine for filling cans with

lubricating oil is set, so that it will generate

fillings which form a normal population with

Mean 1 gallon and Standard Deviation 0.03

gallon. Set up a Control Chart for controlling

the mean (that is, find LCL and UCL),

assuming that Sample Size is 6.

Problem 3

What Sample Size should we choose in

Problem 1, if we want LCL and UCL

somewhat closer together, say

UCL – LCL = 0.5

Without changing the Significance Level?

Problem 5

How should we change the Sample Size

in controlling the mean of a Normal

Population, if we want the difference,

UCL – LCL to decrease to half its original

value?

Problem 7Ten Samples of Size 2 were taken from a

production lot of bolts. The values (length in mm) are as following:

Assuming that population is normal with Mean 27.5 and Variance 0.024, set up a Control Chart for the Mean and graph Sample Means on the chart.

Sample No

1 2 3 4 5 6 7 8 9 10

Length 27.4

27.4

27.5

27.3

27.9

27.6

27.6

27.8

27.5

27.3

27.6

27.4

27.7

27.4

27.5

27.5

27.4

27.3

27.4

27.7

Problem 9Graph the ranges of the given sample as Control

Chart for Ranges, assuming that population is normal with Mean 5 and Standard Deviation 1.55.

Time Sample Values Sample Range R

8:00 3 4 8 4

8:30 3 6 6 8

9:00 5 2 5 6

9:30 7 5 4 4

10:00 7 3 6 5

10:30 4 4 3 6

11:00 5 6 4 6

11:30 6 4 6 4

12:00 5 5 6 4

12:30 5 2 5 3

Problem 9Graph the ranges of the given sample as Control

Chart for Ranges, assuming that population is normal with Mean 5 and Standard Deviation 1.55.

Time Sample Values Sample Range R

8:00 3 4 8 4 5

8:30 3 6 6 8 5

9:00 5 2 5 6 4

9:30 7 5 4 4 3

10:00 7 3 6 5 4

10:30 4 4 3 6 3

11:00 5 6 4 6 2

11:30 6 4 6 4 2

12:00 5 5 6 4 2

12:30 5 2 5 3 3

Problem 13

Find formulas for UCL, CL and LCL

(corresponding to 3б Limits) in case of a

Control Chart for the defectives, assuming

that in a state of Statistical Control the

fraction of defectives is p.

Problem 15

A so called C-Chart or Defects Per Unit Chart is used for the control of number of defects per unit (for instance, the number of defects per 10 meters of paper, the number of missing rivets in an airplane wing, etc).

Set up formulas for UCL, CL and LCL corresponding µ ± 3б, assuming that X has a Poisson Distribution.

Compute UCL, CL and LCL in a Control Process of number of imperfections in sheet glass, assume that this number is 2.5 per sheet on average, when process is under control.

Three Sigma Capability

Mean output +/- 3 standard deviations falls within the design specification

It means that 0.26% of output falls outside the design specification and is unacceptable.

The result: a 3-sigma capable process produces 2600 defects for every million units produced

Six Sigma Capability Six sigma capability assumes the

process is capable of producing output where the mean +/- 6 standard deviations fall within the design specifications

The result: only 3.4 defects for every million produced

Six sigma capability means smaller variation and therefore higher quality

Process Control ChartsControl Charts show sample data plotted on a graph with Center Line (CL), Upper Control Limit (UCL), and Lower Control Limit (LCL).

Setting Control Limits

Problem 11

Since the presence of a point outside control

limits for Mean indicates trouble (“the process is out

of control”), how often would we be making the

mistake of looking for nonexistent trouble, if we used:

1 – Sigma Limits

2 – Sigma Limits?

Assume Normality.