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COMM 225: Operations management > chapter 10: statistical quality control > Flashcards

chapter 10: statistical quality control Flashcards

1
Q

Statistical quality control

A

uses statistical techniques and sampling to monitor and test the quality of goods and services

provides an economical way to evaluate the quality of products and meet the expectations of the customers

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2
Q

The part of statistical quality control that occurs during production

A

statistical process control

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3
Q

phases of statistical quality control in a company

from least progressive, to most progressive

A
  1. Inspection
    before and after production

–> Acceptance sampling

  1. Corrective action during production

–> Statistical process
control

  1. Quality built into the
    process

–> Continuous improvement and Six Sigma

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4
Q

locations of use of acceptance sampling and statistical process control within production

A

inputs: acceptance sampling
transformation: statistical process control
outputs: acceptance sampling

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5
Q

Inspection

A

an appraisal activity that compares the quality of a good or service to a standard

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6
Q

Statistical Process Control Planning Steps

A
  1. Define the quality characteristics important to customers, and how each is measured
  2. a. for each characteristic, determine a quality control point
    b. for each characteristic, plan how inspection is to be done, how much to inspect, and whether centralized or on-site
    c. for each characteristic, plan the corrective action
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7
Q

Defining the Quality Characteristics (step 1)

A

define, in sufficient detail, what is to be controlled

Different characteristics may require different approaches for control purposes

–> Only those characteristics that can be measured are candidates for control

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8
Q

the only characteristics candidates for control

A

those hat can be measured

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9
Q

Determine a Quality Control Point (step 2. a.)

what are the typical inspection points?

A

At the beginning of the process

At the end of the process

At the operation where a characteristic of interest to customers is first determined

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10
Q

when is customer satisfaction and company’s image most at stake?

A

At the end of the process

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11
Q

How Inspection Is to Be Done (step 2. b.)

A

usually technical and needs engineering knowledge.

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12
Q

How Much to-Inspect (step 2. c.)

what is the range of inspection?

A

can range from no inspection whatsoever to inspection of each unit

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13
Q

why do low cost, high-volume items such as paper clips, nails, and pencils often require little inspection?

A

(1) the cost associated with passing defective items is quite low
(2) the processes that produce these items are usually highly reliable

–> defects are rare

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14
Q

do items that have large costs associated with passing defective products often require more intensive inspection?

A

yeee

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15
Q

why is the goal in inspection not catch every single defect?

what is the goal then?

A

because it would be mostly economically inefficient to do so

the goal is the see where the equilibrium would be between comparing the total cost of inspection and the cost of passing defectives

–> the equilibrium, on a graph, shows the total minimal cost, and the amount of inspection

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16
Q

operations with a high proportion of human involvement necessitate more or less inspection than mechanical operations?

why’

A

more inspection than mechanical operations

because the latter tend to be more reliable

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17
Q

statistical process control (SPC)

A

concerns itself with statistical evaluation of the product in the production process

the operator takes periodic samples from the process and compares them with predetermined limits

The main task in SPC is to distinguish assignable from random variation

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18
Q

random variation

A

common variability of the process (Deming)

–> if we were to correct, the result would be negligible

natural variation in the output of a process, created by countless minor factors

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19
Q

assignable variation

A

special variation (Deming)

the main sources of assignable variation can usually be identified (assigned to a specific cause) and eliminated

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20
Q

The variability of a sample statistic is described by what?

A

its sampling distribution

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21
Q

the central limit theorem

A

states that as the sample size increases, the distribution of sample averages approaches a Normal distribution regardless of the shape of the sampled population

The larger the sample size, the narrower the sampling distribution

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22
Q

the likelihood that a sample statistic is close to the true value in the population is higher for large samples or for small samples?

why?

A

large samples

central limit theorem

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23
Q

limits selected within which most values of a sample statistic should fall if its variations are random

A

serves in distinguishing between random and assignable variation of a sampling statistic

typical limits are +2 standard deviations or +3 standard deviations

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24
Q

who developed the control chart

A

Walter Shewhart

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25
Q

control chart

A

a time-ordered plot of a sample statistic, with limits

used to distinguish between random and assignable variation

it has upper and lower limits, called control limits

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26
Q

purpose of a control chart

A

to monitor process output to see if it is random

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27
Q

A necessary (but not sufficient) condition for a process to be deemed “in control,” or stable using a control chart

A

all the data points have to fall between the upper and lower control limits

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28
Q

which proportion of the values will fall within + or - 3 standard deviations of the mean of the distribution?

A

99.7%

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29
Q

control limits

A

The dividing lines between random and assignable deviations from the mean of the distribution

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30
Q

the two control limits in control charts

A

the upper control limit (UCL) which is the largest acceptable value

the lower control limit (LCL) which is the lowest acceptable value

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31
Q

difference between control limits and specification limits

A

Control limits are based on the characteristic of the process

specification limits are based on the desired characteristic of the product

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32
Q

which proportion of the values will fall within + or - 2 standard deviations of the mean of the distribution?

A

95.5%

33
Q

Type I error

A

not finding sample values that fall that outside of the + or - 2 standard deviations

concluding that the process has not shifted, when it has

34
Q

downside of using wider limits (for ex, using + or - 3 standard deviation instead of + or - 2 standard deviation)?

A

make it more difficult to detect assignable variations (i.e., a shift in the process) 扩they are present

35
Q

Type 2 error

A

not finding sample values that fall that outside of the + or - 3 standard deviations

concluding that the process has not shifted, when it has

36
Q

The steps taken to design control charts

A
  1. Determine a sample size n (usually between 2 and 20)
  2. Obtain 20 to 25 samples of size n

–> Compute the appropriate sample statistic for each sample (e.g., sample mean)

  1. Establish preliminary control limits using appropriate formulas and graph them
  2. Plot the sample statistic values on the control chart, and note whether any points fall outside the control limits
  3. If you find no points outside control limits, assume that there is no assignable cause and therefore the process is stable and in control

–> if there are points outside, investigate and correct assignable causes of variation; then repeat the process from Step 2 on

37
Q

the larger the n, the larger or smaller the probability of Type II error?

A

the smaller

38
Q

The sample mean (x_) control chart

A

used to monitor the process mean

control chart for the sample mean

39
Q

how do we find the centre line used in a sample mean (x_) control chart?

A

estimated by taking a few samples, computing their mean, and then averaging these means

called the grand mean

40
Q

calculating the control limits using the standard deviation of the process, σ

A

Upper Control Limit (UCLx_) = x_ + z · (σ of x_ / √n)

Lower Control Limit (LCLx_) = x_ - z · (σ of x_ / √n)

σ of x_: Standard deviation of the sampling distribution of the sample mean

σ: Process standard deviation

n: sample size
z: Standard Normal deviate (usually z = 3)

x_: Average of sample means = Grand mean

41
Q

A second approach to calculating the control limits

A

to use the sample range (i.e., Maximum value - Minimum value in the sample)

42
Q

formulas to find the limits using the sample ranges

A

UCL = x_ + A2R_

LCL: x_ - A2R_

A2: get from the table

R_: average of sample ranges of a few samples

43
Q

The sample range (R) control chart

A

used to monitor process dispersion or spread

44
Q

how to find the limits using the sample range (R) control chart

A

UCLR = D4R_

LCLR = D3R_

D3 and D4 are taken from the table

45
Q

individual unit (X) control chart

A

Control chart for individual unit used to monitor single observations (n = 1)

46
Q

finding the limits for the individual unit (X) control chart

A

UCLx = X_ + zσ

LCLx = X_ - zσ

X_: the mean of a few individual observations (that estimates the process mean)

z: the standard Normal deviate

σ: the process standard deviation

47
Q

moving range (MR) control chart

A

used to calculate the differences between consecutive observations in single unit samples

we want to control the dispersion or spread

48
Q

finding the limits for the moving range (MR) control chart

A

UCLR = D4R_

LCLR = D3R_

D3 and D4 are taken from the table

R_: the average of the moving ranges

49
Q

when are control charts for attributes used?

A

when the process characteristic is counted rather than measured

50
Q

two types of attribute control charts

A

one for the fraction of defective items in a sample (p-chart)

one for the number of defects per unit (c-chart)

51
Q

when is a p-chart appropriate?

A

when the data consist of two categories of items

When the data consist of multiple samples of n observations each (e.g., 15 samples pf n = 20 each)

52
Q

what is a p-chart?

A

the control chart for the sample proportion of defectives

used to monitor the proportion of defective items generated by the process

53
Q

when is a c-chart appropriate?

A

When only the number of occurrences per unit of measure can be counted

–> non-occurrences cannot be counted

When the goal is to control the number of occurrences of defects per unit product

54
Q

The centre line on a p-chart

A

the average proportion of defectives in the population, p

55
Q

The standard deviation of the p-chart

A

σp = (sqrt(p · (1 - p)) / n

56
Q

control limits for the p chart

A

UCLp = p + z · σp

LCLp = p - z · σp

57
Q

When the goal is to control the number of occurrences of defects per unit product, which chart do we use?

A

the c-chart

58
Q

what is the distribution for the c-chart

A

the poisson distribution

59
Q

the limits using the c-chart

A

UCL = c + z · (c)^(1/2)

LCL = c - z · (c)^(1/2)

c: mean number of defects per unit product
(c) ^(1/2): the standard deviation

60
Q

what must we do after the stability of a process has been established?

A

it is necessary to determine if the process is capable of producing output that is within an acceptable range

–> The capability of a process

61
Q

what are the three focal points we need for process capability

A

Design specification

control limits

Process variability

62
Q

Design specification

A

a range of values into which a product must fall in order to be acceptable

63
Q

Process variability

A

the actual variability in a process for a product

64
Q

process capability

A

he ability of a process to meet the design specification

65
Q

capability analysis

A

measuring the process capability

determines whether the process output falls within the design specification

66
Q

when is a process said to be capable

A

when the process output falls within the design specification

67
Q

process capability ratio

A

Cp = (design specification width) / process width

= (upper design specification - lower design specification ) / 6σ

ratio must be at least 1 for the process to be gyu

68
Q

what measure do we use when the process is not centered between design specification limits, or if there is no design specification limit on one side

A

Cpk

69
Q

Cpk formula

A

Cpk = (Upper design specification - Process mean) / 3σ

and

(Process mean - lower design specification) / 3σ

the smaller of the two ratios is the the Cpk

the Cpk has to be bigger than 1

70
Q

Six Sigma quality

A

refers to the goal of achieving process variability so small that the half width of design specification equals six standard deviations of the process

71
Q

the difference in the objective between Six Sigma quality and Continuous improvement

A

Six Sigma quality: Product and process perfection

Continuous improvement: Product and process improvement

72
Q

the difference in the tools used between Six Sigma quality and Continuous improvement

A

Six Sigma quality: Statistical

Continuous improvement: Simple data analysis

73
Q

the difference in the methodology used between Six Sigma quality and Continuous improvement

A

Six Sigma quality: Define, measure, analyze, improve, control (DMAIC)

Continuous improvement: Plan, do, study, act (PDSA)

74
Q

the difference in the team leaders between Six Sigma quality and Continuous improvement

A

Six Sigma quality: Black belt

Continuous improvement: Champion

75
Q

the difference in the training between Six Sigma quality and Continuous improvement

A

Six Sigma quality: long/formal

Continuous improvement: short/informal

76
Q

the difference in the culture change between Six Sigma quality and Continuous improvement

A

Six Sigma quality: usually enforced

Continuous improvement: sometimes enforced

77
Q

the difference in the project time frame between Six Sigma quality and Continuous improvement

A

Six Sigma quality: moths/years

Continuous improvement: days/weeks

78
Q

Design of experiments

A

involves performing experiments by changing levels of factors to measure their influence on output and identifying best levels for each factor

COMM 225: Operations management (17 decks)

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