Chapter 10 Quality Control Management 3620Chapter 10 Quality Control10-2 Acceptance sampling Process control Continuous improvement Inspection before/after

Chapter 10Quality Control

Management 3620 Chapter 10 Quality Control 10-2

Acceptancesampling

Processcontrol

Continuousimprovement

Inspectionbefore/afterproduction

Correctiveaction duringproduction

Quality builtinto theprocess

The leastprogressive

The mostprogressive

Figure 10-1

Phases of Quality Assurance


The Process (1 of 2)

• Over time, the output of any process shows a certain amount of natural or inherent variability

• This is also referred to as random variability

• It is due to countless minor factors and is assumed to be out of management’s control in the short run, i.e., you have to live with it


Processdistribution

Mean

The Process (2 of 2)

• The distribution of a process’ output has a mean, , and a standard deviation, ; it can have a wide variety of shapes


Process Capability (1 of 3)

• When selecting a process to perform an operation, the inherent variability of process output should be compared to the range or tolerances allowed by the designer’s specifications



LowerSpecification

UpperSpecification

A significant portion of the process output falls outside of the specification width

In other words, is the process capable of producing the itemwithin specifications?

Much of the process output fits within specification width

Almost all of the process output fits within the specification width

process distribution



• The process capability index (cp) compares the design specifications with a measure of process variability

σ6

ionspecificat lower-ionspecificat upper =

widthyvariabilit process

widthionspecificat = cp


1350 ppm 1350 ppm

Three-Sigma Quality

Lowerdesign

specification

Upperdesign

specification

+3 Sigma-3 Sigma mean


1350 ppm 1350 ppm

Three-Sigma Quality vs.Six-Sigma Quality

Lowerdesign

specification

Upperdesign

specification

1.7 ppm 1.7 ppm




Process Control (1 of 6)

• Once a process is in operation, a goal is to maintain the status quo, i.e., keep the process “in control”

• What can make the process no longer be in control, i.e., go “out of control”?– The presence of an assignable cause

• The presence of an assignable cause may cause the process distribution to– shift to the left or right, and/or– increase the variability (flatten out)


upper designspecification

Time

lower designspecification


• If the process mean shifts, more of output falls outside the specifications


Time

upper designspecification

lower designspecification


• If the process mean shifts, more of output falls outside the specifications

• If process variance increases, more of the output falls outside of the specifications



• In either case, the process is considered to be out of control

• It should be stopped, investigated (the assignable cause found if present) and corrected (the process brought back to the status quo)



• Examples of assignable causes include– operator

– raw material

– equipment

– environment



• How does management detect the presence of an assignable cause?

• Process output is monitored to detect any changes by inspecting the output of the process

• Inspection means assessing some characteristic of a unit of output


Inputs Transformation Outputs

Acceptancesampling

Processcontrol

Acceptancesampling

Figure 10-2

Inspection Issues

• How Much/How Often

• Where/When

• Centralized vs. On-site


Inspection Effort

Co

st

Optimal Amount of Inspection

Figure 10-3Amount of Inspection

Total Cost

Cost of inspection

Cost of passingdefectives


Where to Inspect in the Operations System

• Raw materials and purchased parts

• Finished products

• Before a costly operation

• Before an irreversible process

• Before a covering process


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

Table 10-1

Examples of Inspection Points


Inspection Options• 100% inspection of the process

output– can be costly and/or time consuming– inspection may alter or destroy unit

• Sample from the process output– referred to as statistical process control

(SPC)– based on the Central Limit Theorem– error possible when deciding if the

process is in control


Overview of the Statistical Quality Control (QC) Process

Sampleof size n

Inspect Each Item in the Sample

SampleInformationCompare

DecisionCriteria

IN CONTROL

OUT OF CONTROL

ProcessOutput


Central Limit Theorem• The distribution of sample means tend to be

normally distributed even though the process distribution is not normal

• The mean of the distribution sample means (x) is equal to the mean of the process distribution( )

• The standard deviation of the distribution of sample means ( ) is equal to the standard deviation of the process distribution( ) divided by

xx

n


Process Distribution

Processdistribution

Measure

lowerdesign

specification

upperdesign

specificationXσ

μ


Sampling Distribution

Samplingdistribution

Processdistribution

lowerdesign

specification

upperdesign

specificationSample Statistic

nσ

X

X


Statistical Process Control (1 of 3)

• Primary purpose is to decide when the process output may be affected by an assignable cause

• The decision is based on– an indicator of the status of the output

of a process (sample statistic)

– the criteria placed on the distribution of the sample statistic (control limits)


Sampling Distribution


Processdistribution

lowerdesign

specification

upperdesign

specification

Lowercontrol

limit

Uppercontrol

limit

Figure 10-4

sample statistic


Control Chart (1 of 5)

• This information is typically displayed as a control chart

Time

SampleStatistic

upper control limit

lowercontrol limit

centralline




• After a sample is taken and inspected, the resulting sample statistic is computed and plotted

Time

SampleStatistic

upper control limit

lowercontrol limit

centralline



• If the sample statistic falls between the control limits, the process is considered to be in control

Time

SampleStatistic

upper control limit

lowercontrol limit

centralline



• If the sample statistic falls outside the control limits, the process is considered to be out of control

Time

SampleStatistic

upper control limit

lowercontrol limit

centralline


upper control limit


• Under this arrangement, there is the possibility of making an error in determining the process’s status

Time

SampleStatistic

lowercontrol limit

Probability of deciding theprocess is out of controlwhen it is still in control

centralline



Possible Errors When Sampling(A Summary)

Decision about the process based on sample information

True state of the process

Process is in control

Process is out of control

Process is actually in

control

Decision is

correct

Type I error

Process is actually out of control

Type II error

Decision is

correct


Statistical Process Control (3 of 3)

• Control charts for the two inspection methods will be examined– Two control charts for variables

inspection• sample means chart (x-bar chart)• sample range chart (R chart)

– One control chart for attributes inspection• sample proportion defective chart (p chart)


• A sample of size n is taken from the process output

• Each unit in the sample is inspected a variables basis– Measurement of the specified value is

taken on a continuous scale

Control Charts for Variables (1 of 3)


• These data are used to calculate two sample statistics – sample mean, x (the sum of

measurement of each unit in the sample divided by n)

– sample range, R, (the highest measurement in the sample minus the lowest measurement in the sample)

Variables (2 of 3)


• In this case two separate control charts are used to monitor two different aspects of the process output– central tendency– variability

• The central tendency of the output is monitored using the x-chart

• The variability of the output is monitored using the R-chart

Variables (3 of 3)


• The central line is x, the sum of a number of sample means collected while the process was considered to be “in control” divided by the number of samples

• The 3 lower control limit is x - A2R• The 3 upper control limit is x + A2R• Factor A2 is based on sample size

x-Chart


• If the process distribution standard deviation, , or variance, is given, the upper and lower control limits can be calculated using

x-Chart

σ 2σ

n

σzx = LCL

n

σz+x = UCL

-


R (range)-Chart

• The 3 lower control limit is D3R

• The 3 upper control limit is D4R

• Factors D3 and D4 are based on sample size


UCL

LCL

x-Chart

UCL

LCL

R-chart

Shift Detected

No shift detected

Figure 10-10Aprocess mean is shifting upward

ProcessDistribution

Mean and Range Charts


UCL

LCL

R-chart

UCL

LCL

x-Chart

Figure 10-10Bprocess variability is increasing

Mean and Range Charts

ProcessDistribution

No shift detected

Increase detected


Control Chart for Attributes(1of 3)

• A sample of size n is taken from the process output

• Each unit in the sample is inspected a attributes basis– A unit is classified in one of two categories

• good or bad• pass or fail• operates or doesn’t operate• does or does not meet design specifications


Attributes (2 of 3)

• These data are used to calculate the sample statistic– sample percentage defective, p (the

number of units found to be defective in that sample divided by n)

• Although the distribution of sample statistic follows a binomial distribution, that distribution can be approximated by a normal distribution with a mean of and a standard deviation of

p)/np(1p


Attributes (3 of 3)

The lower control limit is

The upper control limit is

)/np(1pz + p

)/np(1pz - p


Use of c-Charts• Use only when the number of

occurrences per unit of measure can be counted; nonoccurrences 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

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Chapter 10 Quality Control Management 3620Chapter 10 Quality Control10-2 Acceptance sampling Process control Continuous improvement Inspection before/after