Quality Control

PRESENTERS

SAADMAN MOSTAFA YASIN ALI RAJU IBRAHIM KHALIL RIDOYAN REZA ASHIKUR RAHMAN

QUALITY CONTROL A process that measures output

relative to a standard, and takes corrective action when output does not meet standards.

The purpose of quality control is to assure that processes are performing in an acceptable manner.

Companies accomplish quality control by monitoring process output using statistical techniques.

HOW QUALITY CONTROL WORKS (EXAMPLE)

Let's assume that Company XYZ makes widgets. The widgets come in blue and pink. To ensure that all the widgets are the same color pink and that the dye department is making the color consistently, it might create a quality control team that takes random samples of widgets and compares them for color consistency. If the team finds any variance, it has the authority to stop the production line until the process is corrected.

• Quality Control is not the same as quality assurance. Quality control usually monitors the finished product; quality assurance monitors the integrity of the production process.

QUALITY ASSURANCE

COVERAGE OF QUALITY ASSURANCE

PHASES OF QUALITY ASSURANCE

Acceptancesampling

Processcontrol

Continuousimprovement

Inspection of lotsbefore/afterproduction

Inspection andcorrective

action duringproduction

Quality builtinto theprocess

The leastprogressive

The mostprogressive

Inspection is an appraisal activity that compares goods or services to a standard.

Inspection can occur at three points: - before production: is to make sure

that inputs are acceptable. - during production: to make sure that

the conversion of inputs into outputs is proceeding in an acceptable manner.

- after production: to make a final verification of conformance before passing goods to customers

INSPECTION

INSPECTION• At the Ericsson mobile

phone company in Kumla, Sweden a technician checks phone board circuits under a microscope. This Visual check can help uncover defects early on, before this component becomes part of an assembled phone.

INSPECTION Inspection before and after production involves

acceptance sampling procedure. Monitoring during the production process is referred

as process control

Inputs Transformation Outputs

Acceptancesampling

Processcontrol

Acceptancesampling

Acceptance sampling and process control

INSPECTION The purpose of inspection is to provide

information on the degree to which items conform to a standard.

• The basic issues of inspection are:1. How much to inspect and how often2. At what points in the process inspection should occur.3. Whether to inspect in a centralized or on-site location.4. Whether to inspect attributes (counts) or variables

(measures)

HOW MUCH TO INSPECT AND HOW OFTEN

• The amount of inspection can range from no inspection to inspection of each item many times.

• Low-cost, high volume items such as paper clips and pencils often require little inspection because:

1. the cost associated with passing defective items is quite low.

2. the process that produce these items are usually highly reliable, so that defects are rare.

• High-cost, low volume items that have large cost associated with passing defective items often require more intensive inspection such as airplanes and spaceships.

• The majority of quality control applications ranges between these two extremes.

• The amount of inspection needed is governed by the cost of inspection and the expected cost of passing defective items.

HOW MUCH TO INSPECT AND HOW OFTEN

• Traditional View: The amount of inspection is optimal when the sum of the costs of inspection and passing defectiveness is minimized.

INSPECTION COSTS

Cost

Optimal

Amount of Inspection

Cost of passingdefectives

Cost of inspection

Total Cost

Inspection always adds to the cost of the product; therefore, it is important to restrict inspection efforts to the points where they can do the most good. In manufacturing, some of the typical inspection points are:

• Raw materials and purchased parts

• Finished products

• Before a costly operation

• Before an irreversible process

• Before a covering process

WHERE TO INSPECT IN THE PROCESS

EXAMPLES OF INSPECTION POINTS IN SERVICE ORGANIZATIONS

Type ofbusiness

Inspectionpoints

Characteristics

Fast Food CashierCounter areaEating areaBuildingKitchen

AccuracyAppearance, productivityCleanlinessAppearanceHealth regulations

Hotel/motel Parking lotAccountingBuildingMain desk

Safe, well lightedAccuracy, timelinessAppearance, safetyWaiting times

Supermarket CashiersDeliveries

Accuracy, courtesyQuality, quantity

• Some situations require that inspections be performed on site such as inspecting the hull of a ship for cracks requires inspectors to visit the ship.

• At other times, specialized tests can best be performed in a lab such as medical tests, analyzing food samples, testing metals for hardness, running viscosity tests on lubricants.

CENTRALIZED VERSUS ON-SITE INSPECTION

CONTROL CHARTS

A Time-ordered Plot Of Sample Statistics, Used To Distinguish Between Random And

Nonrandom Variability.

VARIATIONS

Random Variation: Common Natural Variations In The Output Of A Process, Created By Countless Minor Factors. It Would Be Negligible.

Assignable Variation: A Special Variation Whose Source Can Be Identified (It Can Be Assigned To A Specific Cause)

CONTROL LIMITS

The Dividing Lines Between Random And Nonrandom Deviations From The Mean Of

The Distribution.

ERROR TYPE

Type I Error Type I Error Concluding A Process Is Not In

Control When It Actually Is. Type Ii Error

Type II Error Concluding A Process Is In Control When It Is Not.

Type I and Type II errors

AND THE CONCLUSION IS THAT IT IS

IF A PROCESS IS ACTUALLY

IN CONTROL

OUT OF CONTROL

IN CONTROL NO ERROR

TYPE I ERROR

(PRODUCER’S RISK)

OUT OF CONTROL

TYPE II ERROR

(CONSUMER’S RISK)

NO ERROR

TYPES OF CONTROL CHARTS

CONTROL CHARTS FOR VARIABLES

Measured Data, Usually On A Continuous Scale.

Example Amount Of Time Needed To Complete A Task, Length, Width, Weight, Diameter Of A Part.

CONTROL CHARTS FOR ATTRIBUTE

Counted Data Like Number Of Defective Items In A Sample, The Number Of Calls Per Day.

CONTROL CHARTS FOR VARIABLES

Mean Control Chart Control Chart Used To Monitor The Central

Tendency Of A Process.Range Control Chart

Control Chart Used To Monitor Process Dispersion.

Mean Control Charts Used To Monitor The Central Tendency Of A Process. Sometimes Referred To As An (X-bar) Charts x

Example

A quality inspector took five samples, each with four observations, of the length of time for glue to dry. The analyst computed the mean of each sample and then computed the grand mean. All values are in minutes. Use this information to obtain three-sigma (i.e., z = 3) control limits for the means of future time. It is known from previous experience that the standard deviation of the process is 0.02 minute.

1 2 3 4 51 12.1

112.1

512.0

912.1

212.0

92 12.1

012.1

212.0

912.1

012.1

43 12.1

112.1

012.1

112.0

812.1

34 12.0

812.1

112.1

512.1

012.1

212.1

012.1

212.1

112.1

012.1

2

Sample

Observation

x

• The control limits of the mean chart is calculated as follows:

• Upper Control Limit (UCL) =

• Lower Control Limit (LCL) =Where: n = sample size z = standard normal deviation (1,2 and 3; 3 is recommended)

= process standard deviation

= standard deviation of the sampling distribution of the means

= average of sample means

FIRST APPROACH

xzx

xzx

nx

x

x

SOLUTION

08.12402.0311.12:

14.12402.0311.12:

11.125

12.1210.1211.1212.1210.12

LCL

UCL

x

• n = 4• z = 3• = 0.02

Control chart

x

LCL

UCL12.14

12.08

12.11

Sample

1 2 3 4 5

SECOND APPROACH

R

RAxLCL

RAxUCL

2

2

• This approach assumes that the range is in control

• This approach is recommended when the process standard deviation is not known

Where:

A2 = A factor from table given below

= Average of sample ranges

Example

Twenty samples of n = 8 have been taken from a cleaning operations. The average sample range for the 20 samples was 0.016 minute, and the average mean was 3 minutes. Determine three-sigma control limits for this process.

= 3 min. ,

= 0.016,

A2 = 0.37 for n = 8 (table 10.2)

Solution

R

x

994.2)016.0(37.03

006.3)016.0(37.03

2

2

RAxLCL

RAxUCL

Range Control Chart (R-chart)

RDLCL

RDUCL

3

4

• The R-charts are used to monitor process dispersion; they are sensitive to changes in process dispersion. Although the underlying sampling distribution of the range is not normal, the concept for use of range charts are much the same as those for use of mean chart.

• Control limits:

Where values of D3 and D4 are obtained from table from above

Example

Time Box 1 Box 2 Box 3 Box 4 Range

9 A.M.

9.8 10.4 9.9 10.3 0.6

10 A.M

10.1 10.2 9.9 9.8 0.4

11 A.M

9.9 10.5 10.3 10.1 0.6

Noon 9.7 9.8 10.3 10.2 0.61 P.M 9.7 10.1 9.9 9.9 0.4

• Small boxes of cereal are labeled “net weight 10 ounces.” Each hour, a random sample of size n = 4 boxes are weighted to check process control. Five hours of observation yielded the following:

Solution

0)52.0(0

1865.1)52.0(28.2

52.05

4.06.06.04.06.0

3

4

RDLCL

RDUCL

R

n = 4For n = 4 , D3 = 0 and D4 = 2.28

Since all ranges are between the upper and lower limits, we conclude that the process is in control

USING THE MEAN AND

RANGE CHART

Mean and range charts used together complement each other

1. Obtain 20 to 25 samples. Compute the appropriate sample statistics

(mean and range) for each sample.

2. Establish preliminary control limits using the formulas.

3. Determine if any points fall outside the control limits.

4. If you find no out-of-control signals, assume that the process is in

control. If not, investigate and correct assignable cause of variation.

Then resume the process and collect another set of observations

upon which control limits can be based.

5. Plot the data on a control chart and check for out-of-control signals.

Control Chart for Attributes

Control charts for attributes are used when the process characteristic is counted rather than measured. Two types are available:

• P-Chart - Control chart used to monitor the proportion of defectives items 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

P-Charts

• The theoretical basis for the P-chart is the binomial distribution, although for large sample sizes, the normal distribution provides a good approximation to it.

• A P-chart is constructed and used in much the same way as a mean chart.

• The center line on a P-chart is the average fraction defective in the population, P.

• The standard deviation of the sampling distribution when P is known is:

npp

p)1(

P-Chart

The Control limits

p

p

zpLCL

zpUCL

If p is unknown, it can be estimated from the samples. That estimates , replaces p in the preceding formulas, and replaces p.

= Total number of defectives

Total number of observations

p

p

P-Chart

ExampleAn inspector counted the number of

defective monthly billing statements of a company telephone in each of 20 samples. Using the following information, construct a control chart that will describe 99.74 percent of the chance variation in the process when the process is in control. Each sample counted 100 statements

P-Chart

Sample # of defective Sample # of defective1 4 11 82 10 12 123 12 13 94 3 14 105 9 15 216 11 16 107 10 17 88 22 18 129 13 19 10

10 10 20 16Total 220

Example (cont.)

Solution

P-Chart

SolutionZ for 99.74 percent is 3

03.0100

)11.01(11.0)1(

11.0)100(20

220

^

npp

p

p

Control limits are

02.0)03.0(311.0

20.0)03.0(311.0^

^

p

p

zpLCL

zpUCL

P-Chart

p

Solution (cont.)

Sample number

0.02

0.20

0.11

UCL

LCL

Fraction defective

1 10 20

Use of c-Charts

• Use only when the number of occurrences per unit of measure can be counted; nonoccurrence's 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

C-Chart

• When the goal is to control the number of occurrences (e.g., defects) per unit, a C-chart is used.

• Units might be automobiles, hotel rooms, typed papers, or rolls of carpet.

• The underlying sampling distribution is the Poisson distribution.

• Use of Poisson distribution assumes that defects occur over some continuous region and that the probability of more than one defect at any particular point is negligible.

• The mean number of defects per unit is c and the standard deviation is: c

C-Chart

Control Limits

If the value of c is unknown, as is generally the case, the sample estimate, , is used in place of c. where:

= Number of defects ÷ Number of samples

czcLCL

czcUCL

c

c

C-Chart

Example

Rolls of coiled wire are monitored using c-chart. Eighteen rolls have been examined, and the number of defects per roll has been recorded in the following table. Is the process in control? Plot the values on a control chart using three standard deviation control limit

sample # of defects Sample # of defects1 3 10 12 2 11 33 4 12 44 5 13 25 1 14 46 2 15 27 4 16 18 1 17 39 2 18 1

45

C-Chart

Solution

C-Chart

SolutionAverage number of defects per coil

= c = 45/18 =2.5

024.25.235.2

24.75.235.2

czcLCL

czcUCL

When the computed lower control limit is negative, the effective lower limit is zero. The calculation sometimes produces a negative lower limit due to the use of normal distribution as an approximation to the Poisson distribution

Managerial Consideration Concerning Control Charts

At what point in the process to use control charts: at the part of the process that (1) have tendency to go out of control, (2) are critical to the successful operation of the product or service.

What size samples to take: there is a positive relation between sample size and the cost of sampling.

What type of control chart to use:

Variables: gives more information than attributesAttributes: less cost and time than variables

CONTROL CHART

Run Tests

Run test – a test for randomnessControl charts test for points that are too extreme

to be considered random. However, even if all points are within the control

limits, the data may still not reflect a random process.

Any sort of pattern in the data would suggest a non-random process.

The presence of patterns, such as trends, cycles, or bias in the output indicates that assignable, or nonrandom, cause of variation exist.

Analyst often supplement control charts with a run test, which is another kind of test for randomness.

Nonrandom Patterns in Control charts

Trend: sustained upward or downward movement.

Cycles: a wave patternBias: too many observations on one side of

the center lineMean shift: A shift in the averageToo much dispersion: the values are too

spread out

Figure 10.11

Run Test

A run is defined as a sequence of observations with a certain characteristic, followed by one or more observations with a different characteristic.

The characteristic can be anything that is observable.

For example, in a series AAAB, there are two runs; a run of three A’s followed by a run of one B.

The series AABBBA , indicates three runs; a run of two A’s followed by a run of three B’s, followed by a run of one A.

Run test

There are two types of run test:1. Runs up and down2. Runs above and below the median

In order to count these runs, the data are transformed into a series of U’s and D’s (for up and down) and into a series of A’s and B’s (for above and below the median).

There are three U/D and four A/B runs for the data:

25 29 42 40 35 38 - U U D D UB B A A B A

Where the median is 36.5

Counting Above/Below Median Runs (7 runs)

Counting Up/Down Runs (8 runs)

Figure 10.12

Figure 10.13

Counting Runs

Counting Above/Below Median Runs (7 runs)

Counting Up/Down Runs (8 runs)

U U D U D U D U U D

B A A B A B B B A A B

Figure 10.12

Figure 10.13

Counting Runs

Run test procedure

312)(

12

)(

/

NrE

NrE

du

med

To determine whether any patterns are present in control charts, one must do the following:

1. Transform the data into both A’s and B’s and U’s and D’s, and then count the number of runs in each case.

2. Compare the number of runs with the expected number of runs in a completely random series, which is calculated as follows:

Where: N is the number of observations or data points, and E(r) is the expected number of runs

Run test procedure (cont.)

902916

41

/

N

N

du

med

3. Calculate the standard deviations of the runs as:

Run test procedure (cont.)

testZ

4. Calculate the test statistic (Ztest) as following:

observed number of runs – expected number of runs

standard deviation of number of runs

902916

)3

12(

41

)12

(

N

NrZ

N

NrZ

test

test For the median

Up and downIf the Ztest is within ± 2 or ± 3; then the process is random; otherwise, it is not random

Run test

Example Twenty sample means have been taken from a

process. The means are shown in the following table. Use median and up/down run test with

z = 2 to determine if assignable causes of variation are present. Assume the median is 11.

sample mean sample Mean1 10 11 10.72 10.4 12 11.33 10.2 13 10.84 11.5 14 11.85 10.8 15 11.26 11.6 16 11.67 11.1 17 11.28 11.2 18 10.69 10.6 19 10.7

10 10.9 20 11.9

Run test

sample mean A/B U/D Sample Mean A/B U/D1 10 11 10.72 10.4 12 11.33 10.2 13 10.84 11.5 14 11.85 10.8 15 11.26 11.6 16 11.67 11.1 17 11.28 11.2 18 10.69 10.6 19 10.710 10.9 20 11.9

Solution

Run test

sample mean A/B U/D Sample Mean A/B U/D1 10 B - 11 10.7 B D2 10.4 B U 12 11.3 A U3 10.2 B D 13 10.8 B D4 11.5 A U 14 11.8 A U5 10.8 B D 15 11.2 A D6 11.6 A U 16 11.6 A U7 11.1 A D 17 11.2 A D8 11.2 A U 18 10.6 B D9 10.6 B D 19 10.7 B U10 10.9 B U 20 11.9 A U

Solution

Run test

___3

1(___)23

12)(

___12

___12

)(

/

NrE

NrE

du

med

Solution (cont.)1. A/B: 10 runs and U/D: 17 runs

2. Expected number of runs for each test is:

Run test

133

1)20(23

12)(

1112201

2)(

/

NrE

NrE

du

med

Solution (cont.)1. A/B: 10 runs and U/D: 17 runs

2. Expected number of runs for each test is:

3. The standard deviations are:

___90

29(___)1690

2916

___4

1___4

1

/

N

N

du

med

3. The standard deviations are:

8.190

29)20(1690

2916

18.24

1204

1

/

N

N

du

med

_______

______

_______

______

/

du

med

Z

Z

4. The ztest values are:

observed number of runs – expected number of runs standard deviation of number of runs

testZ

22.28.11317

46.018.2

1110

/

du

med

Z

Z

4. The ztest values are:

Although the median test doesn’t reveal any pattern, because its Ztest value is within ±2, the up/down test does; its value exceed +2. consequently, nonrandom variations are probably present in the data and, hence, the process is not in control

Process Capability

Tolerances or specifications Range of acceptable values established by

engineering design or customer requirementsProcess variability

Natural variability in a processProcess capability

Process variability relative to specification

Capability analysis

Capability analysis is the determination of whether the variability inherent in the output of a process falls within the acceptable range of variability allowed by the design specification for the process output.

If it is within the specifications, the process is said to be “capable.” if it is not, the manager must decide how to correct the situation.

We cannot automatically assume that a process that is in control will provide desired output. Instead, we must specifically check whether a process is capable of meeting specifications and not simply set up a control chart to monitor it.

A process should be both in control and within specifications before production begins.

Process Capability

LowerSpecification

UpperSpecification

A. Process variability matches specifications

LowerSpecification

UpperSpecification

B. Process variability well within specifications

LowerSpecification

UpperSpecification

C. Process variability exceeds specifications

Figure 10.15

Capability analysis

If the product doesn’t meet specifications (not capable) a manager might consider a range of possible solutions such as:

1. Redesign the process.2. Use an alternative process.3. Retain the current process but attempt to

eliminate unacceptable output using 100% inspection.

Process Capability Ratio

Process capability ratio, Cp =specification width

process width

Upper specification – lower specification6

Cp =

Calculate the capability and compare it to specification width. If the capability is less than the specification width, the process is capable.

Where: Capability = 6; where is the process SD

Or calculate

The process is capable if Cp is at least 1.33, this ratio implies only about 30 parts per million can be expected to not be within the specification

Capability analysis

Machine Standard deviation (mm)A 0.13B 0.08C 0.16

Example A manager has the option of using any one

of three machines for a job. The machines and their standard deviations are listed below. Determine which machines are capable if the specifications are 10 mm and 10.8 mm.

Capability analysis

Machine Standard deviation (mm)

Machine capability

Capable

A 0.13B 0.08C 0.16

SolutionCapability = 6

It is clear that machine A and machine B are capable, since the capability is less than the specification width (10.8 – 10 = 0.8)

Capability ratio

Machine Standard deviation

(mm)

Machine capability

6

Cp Capable

A 0.13 0.78B 0.08 0.48C 0.16 0.96

Example Compute the process capability ratio for

each machine in the previous example (specification width is 0.8)

Solution

Only machine B is capable because its ratio exceed 1.33

Processmean

Lowerspecification

Upperspecification

1.350 ppm 1.350 ppm

1.7 ppm 1.7 ppm

+/- 3 Sigma

+/- 6 Sigma

3 Sigma and 6 Sigma Quality

Cpk ratio

If a process is not centered (the mean of the process is not in the center of the specification), a more appropriate measure of process capability is the Cpk ratio, because it does take the process mean into account.

The Cpk is equal the smaller of

Upper specification – process mean 3AndProcess mean – lower specification 3

Cpk Ratio

89.19.07.1

)3(.35.72.9

Example A process has a mean of 9.2 grams and a

standard deviation 0f 0.3 grams. The lower specification limit is 7.5 grams and upper specification limit is 10.5 grams. Compute Cpk

Solution1. Compute the ratio for the lower specification:

2. Compute the ratio for the upper specification: 44.19.3.1

)3.0(32.95.10

The smaller of the two ratios is 1.44 (greater

than 1.33), so this is the Cpk . Therefore, the process is capable

Improving Process Capability

Simplify the processStandardize the processMistake-proofUpgrade equipmentAutomate

Improving Process CapabilityMethod ExamplesSimplify Eliminate steps, reduce number of parts

Standardize use standard parts, standard procedureMake mistake-proof

Design parts that can only be assembled the correct way; have simple checks to verify a procedure has been performed correctly

Upgrade equipment

Replace worn-out equipment; take advantage of technological improvements

Automate Substitute processing for manual processing

Limitations of Capability Indexes

1. Process may not be stable2. Process output may not be normally

distributed3. Process not centered but Cp is used