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Webster chemical company produces mastics

24/11/2021 Client: muhammad11 Deadline: 2 Day

Quality and Performance

Chapter 3

3-‹#›

Quality and Performance

Quality

A term used by customers to describe their general satisfaction with a service or product

Defect

Any instance when a process fails to satisfy its customer

3-‹#›

Costs of Quality

Prevention costs

Costs associated with preventing defects before they happen

Appraisal costs

Costs incurred when the firm assesses the performance level of its processes

Internal Failure costs

Costs resulting from defects that are discovered during the production of a service or product

External Failure costs

Costs that arise when a defect is discovered after the customer receives the service or product

3-‹#›

Total Quality Management and Six Sigma

Total Quality Management

A philosophy that stresses three principles (customer satisfaction, employee involvement and continuous improvement) for achieving high level of process performance and quality

Six Sigma

A comprehensive and flexible system for achieving, sustaining, and maximizing business success by minimizing defects and variability in processes

3-‹#›

Total Quality Management

Figure 3.1

3-‹#›

Total Quality Management

Customer Satisfaction

Conformance to Specifications

Value

Fitness for Use

Support

Psychological Impressions

3-‹#›

Total Quality Management

Employee Involvement

Cultural Change

Quality at the Source

Teams

Employee Empowerment

Problem-solving teams

Special-purpose teams

Self-managed teams

3-‹#›

Total Quality Management

Continuous Improvement

Kaizen

Problem-solving tools

Plan-Do-Study-Act Cycle

3-‹#›

Six Sigma

Process average OK; too much variation

Process variability OK; process off target

Process on target with low variability

Reduce spread

Center process

Figure 3.3

3-‹#›

Six Sigma

Goal of achieving low rates of defective output by developing processes whose mean output for a performance measure is +/- six standard deviations (sigma) from the limits of the design specifications for the service or product.

3-‹#›

Acceptance Sampling

The application of statistical techniques to determine if a quantity of material from a supplier should be accepted or rejected based on the inspection or test of one or more samples.

Acceptable Quality Level

The quality level desired by the consumer.

3-‹#›

Acceptance Sampling

Firm A uses TQM or Six Sigma to achieve internal process performance

Supplier uses TQM or Six Sigma to achieve internal process performance

Yes

Fan motors

Fan blades

Accept blades?

Supplier

Manufactures fan blades

TARGET: Firm A’s specs

Accept motors?

Motor sampling

Blade sampling

Firm A

Manufacturers furnace fan motors

TARGET: Buyer’s specs

Buyer

Manufactures furnaces

Figure 3.4

3-‹#›

Statistical Process Control (SPC)

SPC

The application of statistical techniques to determine whether a process is delivering what the customer wants.

Variation of Outputs

No two services of products are exactly alike because the processes used to produce them contain many sources of variation, even if the processes are working as intended.

3-‹#›

Statistical Process Control (SPC)

Performance Measurements

Variables - Service or product characteristics that can be measured

Attributes - Service or product characteristics that can be quickly counted for acceptable performance

3-‹#›

Statistical Process Control (SPC)

Complete Inspection

Inspect each service or product at each stage of the process for quality

Sampling

Sample Size

Time between successive samples

Decision rules that determine when action should be taken

3-‹#›

Statistical Process Control (SPC)

Figure 3.5

3-‹#›

Statistical Process Control (SPC)

The sample mean is the sum of the observations divided by the total number of observations.

where

xi = observation of a quality characteristic (such as time)

n = total number of observations

= mean

3-‹#›

Statistical Process Control (SPC)

The range is the difference between the largest observation in a sample and the smallest. The standard deviation is the square root of the variance of a distribution.

An estimate of the process standard deviation based on a sample is given by:

where

σ = standard deviation of a sample

3-‹#›

Statistical Process Control (SPC)

Categories of Variation

Common cause - The purely random, unidentifiable sources of variation that are unavoidable with the current process

Assignable cause - Any variation-causing factors that can be identified and eliminated

3-‹#›

Statistical Process Control (SPC)

Control Chart

Time-ordered diagram that is used to determine whether observed variations are abnormal

Controls chart have a nominal value or center line, Upper Control Limit (UCL), and Lower Control Limit (LCL)

3-‹#›

Statistical Process Control (SPC)

Steps for using a control chart

Take a random sample from the process and calculate a variable or attribute performance measure.

If a statistic falls outside the chart’s control limits or exhibits unusual behavior, look for an assignable cause.

Eliminate the cause if it degrades performance; incorporate the cause if it improves performance. Reconstruct the control chart with new data.

Repeat the procedure periodically.

3-‹#›

Control Charts

Samples

Assignable

causes likely

UCL

Nominal

LCL

Figure 3.7

3-‹#›

Nominal

UCL

LCL

Variations

Sample number

Control Charts

(a) Normal – No action

Figure 3.8

3-‹#›

Nominal

UCL

LCL

Variations

Sample number

Control Charts

(b) Run – Take action

Figure 3.8

3-‹#›

Nominal

UCL

LCL

Variations

Sample number

Control Charts

Figure 3.8

3-‹#›

Nominal

UCL

LCL

Variations

Sample number

Control Charts

(d) Exceeds control limits – Take action

Figure 3.8

3-‹#›

Control Charts

Type I error

An error that occurs when the employee concludes that the process is out of control based on a sample result that fails outside the control limits, when it fact it was due to pure randomness

Type II error

An error that occurs when the employee concludes that the process is in control and only randomness is present, when actually the process is out of statistical control

3-‹#›

Control Charts

Variable Control Charts

R-Chart – Measures the variability of the process

-Chart – Measures whether the process is generating output, on average, consistent with a target value

Attribute Control Charts

p-chart – Measures the proportion of defective services or products generated by the process

c-chart – Measures the number of defects when more than one defect can be present in a service or product

3-‹#›

Control Charts for Variables

R-Chart

UCLR = D4R and LCLR = D3R

3-‹#›

Control Charts for Variables

UCL = + A2 and LCL = - A2

where

= central line of the chart, which can be either the average of past sample means or a target value set for the process

A2 = constant to provide three-sigma limits for the sample mean

x-Chart

3-‹#›

Control Charts for Variables

Table 3.1

3-‹#›

Control Charts for Variables

Collect data.

Compute the range.

Use Table 3.1 to determine R-chart control limits.

Plot the sample ranges. If all are in control, proceed to step 5. Otherwise, find the assignable causes, correct them, and return to step 1.

Calculate for each sample and determine the central line of the chart,

Steps to Compute Control Charts:

3-‹#›

Control Charts for Variables

Use Table 3.1 to determine control limits

Plot the sample means. If all are in control, the process is in statistical control. Continue to take samples and monitor the process. If any are out of control, find the assignable causes, correct them, and return to step 1.

Steps to Compute Control Charts:

3-‹#›

Example 3.1

The management of West Allis Industries is concerned about the production of a special metal screw used by several of the company’s largest customers. The diameter of the screw is critical to the customers. Data from five samples appear in the accompanying table. The sample size is 4. Is the process in statistical control?

Sample Number 1 2 3 4 R
1 .5014 .5022 .5009 .5027 .0018 .5018
2 .5021 .5041 .5024 .5020 .0021 .5027
3 .5018 .5026 .5035 .5023 .0017 .5026
4 .5008 .5034 .5024 .5015 .0026 .5020
5 .5041 .5056 .5034 .5047 .0022 .5045
OBSERVATIONS

Average

.0021 .5027

3-‹#›

Example 3.1

Compute the range for each sample and the control limits

UCLR = D4 R =

2.282(0.0021) = 0.00479 in.

0(0.0021) = 0 in.

LCLR = D3 R =

3-‹#›

Example 3.1

Process variability is in statistical control.

Figure 3.9

3-‹#›

Example 3.1

Compute the mean for each sample and the control limits.

= 0.5027 + 0.729(0.0021) = 0.5042 in.

= 0.5027 – 0.729(0.0021) = 0.5012 in.

LCLx = X – A2 R

UCLx = X + A2 R

3-‹#›

Example 3.1

Process average is NOT in statistical control.

Figure 3.10

3-‹#›

Control Charts for Variables

where

σx = σ/ n

σ = standard deviation of the process distribution

n = sample size

x = central line of the chart

z = normal deviate number

If the standard deviation of the process distribution is known, another form of the x -chart may be used:

UCLx = x + zσx and LCLx = x – zσx

3-‹#›

Example 3.2

For Sunny Dale Bank the time required to serve customers at the drive-by window is an important quality factor in competing with other banks in the city.

Mean time to process a customer at the peak demand period is 5 minutes

Standard deviation of 1.5 minutes

Sample size of six customers

Design an -chart that has a type I error of 5 percent

After several weeks of sampling, two successive samples came in at 3.70 and 3.68 minutes, respectively. Is the customer service process in statistical control?

3-‹#›

Example 3.2

x = 5 minutes

σ = 1.5 minutes

n = 6 customers

z = 1.96

The new process is an improvement.

LCLx = x – zσ/n =

5.0 – 1.96(1.5)/6 = 3.80 minutes

The process variability is in statistical control, so we proceed directly to the -chart. The control limits are

UCLx = x + zσ/n =

5.0 + 1.96(1.5)/6 = 6.20 minutes

3-‹#›

Application 3.1

Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped.

Webster is concerned whether the filling process for tubes of caulking is in statistical control. The process should be centered on 8 ounces per tube. Several samples of eight tubes are taken and each tube is weighed in ounces.

Tube Number
Sample 1 2 3 4 5 6 7 8 Avg Range
1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11 8.040 0.76
2 8.23 8.12 7.98 8.41 8.31 8.18 7.99 8.06 8.160 0.43
3 7.89 7.77 7.91 8.04 8.00 7.89 7.93 8.09 7.940 0.32
4 8.24 8.18 7.83 8.05 7.90 8.16 7.97 8.07 8.050 0.41
5 7.87 8.13 7.92 7.99 8.10 7.81 8.14 7.88 7.980 0.33
6 8.13 8.14 8.11 8.13 8.14 8.12 8.13 8.14 8.130 0.03
Avgs 8.050 0.38
Copyright ©2016 Pearson Education, Inc. All rights reserved.

3-‹#›

Application 3.1

Assuming that taking only 6 samples is sufficient, is the process in statistical control?

UCLR = D4 R =

LCLR = D3 R =

1.864(0.38) = 0.708

0.136(0.38) = 0.052

The range chart is out of control since sample 1 falls outside the UCL and sample 6 falls outside the LCL.

Conclusion on process variability given = 0.38 and n = 8:

3-‹#›

Application 3.1

Consider dropping sample 6 because of an inoperative scale, causing inaccurate measures.

Tube Number
Sample 1 2 3 4 5 6 7 8 Avg Range
1 7.98 8.34 8.02 7.94 8.44 7.68 7.81 8.11 8.040 0.76
2 8.23 8.12 7.98 8.41 8.31 8.18 7.99 8.06 8.160 0.43
3 7.89 7.77 7.91 8.04 8.00 7.89 7.93 8.09 7.940 0.32
4 8.24 8.18 7.83 8.05 7.90 8.16 7.97 8.07 8.050 0.41
5 7.87 8.13 7.92 7.99 8.10 7.81 8.14 7.88 7.980 0.33
Avgs 8.034 0.45
What is the conclusion on process variability and process average?

3-‹#›

Application 3.1

The resulting control charts indicate that the process is actually in control.

Now = 0.45, = 8.034, and n = 8

UCLR = D4 R =

1.864(0.45) = 0.839

LCLR = D3 R =

0.136(0.45) = 0.061

UCL x = x + A2 R =

8.034 + 0.373(0.45) = 8.202

8.034 – 0.373(0.45) = 7.866

LCL x = x – A2 R =

3-‹#›

Control Charts for Attributes

p-charts are used for controlling the proportion of defective services or products generated by the process.

The standard deviation is

p = the center line on the chart

UCLp = + zσp and LCLp = – zσp

3-‹#›

Example 3.3

Hometown Bank is concerned about the number of wrong customer account numbers recorded. Each week a random sample of 2,500 deposits is taken and the number of incorrect account numbers is recorded

Using three-sigma control limits, which will provide a Type I error of 0.26 percent, is the booking process out of statistical control?

3-‹#›

Example 3.3

Sample Number Wrong Account Numbers Sample Number Wrong Account Numbers
1 15 7 24
2 12 8 7
3 19 9 10
4 2 10 17
5 19 11 15
6 4 12 3
Total 147
Copyright ©2016 Pearson Education, Inc. All rights reserved.

3-‹#›

Example 3.3

147

12(2,500)

= = 0.0049

p =

Total defectives

Total number of observations

σp = (1 – )/n

= 0.0049(1 – 0.0049)/2,500 = 0.0014

Calculate the sample proportion defective and plot each sample proportion defective on the chart.

UCLp = p + zσp

= 0.0049 + 3(0.0014) = 0.0091

= 0.0049 – 3(0.0014) = 0.0007

LCLp = p – zσp

3-‹#›

Example 3.3

Fraction Defective

Sample

Mean

UCL

LCL

.0091

.0049

.0007

| | | | | | | | | | | |

1 2 3 4 5 6 7 8 9 10 11 12

The process is NOT in statistical control.

Figure 3.11

3-‹#›

Application 3.2

A sticky scale brings Webster’s attention to whether caulking tubes are being properly capped. If a significant proportion of the tubes aren’t being sealed, Webster is placing their customers in a messy situation. Tubes are packaged in large boxes of 144. Several boxes are inspected and the following numbers of leaking tubes are found:

Sample Tubes Sample Tubes Sample Tubes
1 3 8 6 15 5
2 5 9 4 16 0
3 3 10 9 17 2
4 4 11 2 18 6
5 2 12 6 19 2
6 4 13 5 20 1
7 2 14 1 Total = 72
Copyright ©2016 Pearson Education, Inc. All rights reserved.

3-‹#›

Application 3.2

Calculate the p-chart three-sigma control limits to assess whether the capping process is in statistical control.

The process is in control as the p values for the samples all fall within the control limits.

20(144)

= = 0.025

p =

Total number of leaky tubes

Total number of tubes

p (1 – p )

0.025(1 – 0.025)

144

= 0.01301

σp =

UCLp = p + zσp

= 0.025 + 3(0.01301)= 0.06403

LCLp = p – zσp

= 0.025 – 3(0.01301)= –0.01403 = 0

3-‹#›

Control Charts for Attributes

c-charts – A chart used for controlling the number of defects when more than one defect can be present in a service or product.

The mean of the distribution is and the standard deviation is

UCLc = c + z  c

LCLc = c – z  c

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