Which types of quality-control philosophies are generally devided within factories

(p. 2)

Control during production

Real-time control of the production output, to check whether process is in control (use of control charts).

More desirable since it gives the possibility to notice and adjust the process within a short time

Acceptance control

Inspection of the products received by the supplier and decision whether to accept or refuse them

Supplier can be external or internal

At which point of the production process: acceptance control can be performed?

(p. 3)

Outgoing inspection

inspection is performed immediately following production.

Incoming inspection

lots of products are inspected as they are received from the supplier.

Intermediate inspection

semi-finished products can be inspected before moving from one shop to another, within the same factory

What are the purposes of Acceptance control

(p. 4)

Checking the products’ (dimensional and functional) conformity to specifications

Estimate the percentage of defective elements (p).

Acceptance control can be performed by who

Can be performed by

customer

supplier

but inspection cost is generally charged to supplier.

Name the approaches to lot sentencing

100% inspection

Acceptance sampling

Accept with no inspection

Describe the following approache to lot sentencing

inspect every item in the lot, removing all defective units found

The advantage is that we are completely sure of the quality of the production output

Do not require statistics

a sample, which is a subset of the production output, is selected from the lot

then sample units are inspected with respect to a specific quality characteristic

On the basis of the sample information, the lot is then accepted or rejected

Do require statistics

It is useful in situations where the supplier’s process is very good, with almost no defective units

In which situations Acceptance sampling is used

(p. 5)

Testing is destructive

Cost of 100% inspection is extremly high

When a 100% inspection not feasible or require a lot of time

When the supplier has an excelent quality history

When the inspection error rate is high, so that a 100% inspection would cause a higher percentage of defective untis to be passed

Name the disatvanteges of Acceptance sampling

(p. 6)

Risk of accepting bad lots and rejecting good lots

Less information is generated

Requires planning and documentation (100% inspection does not)

Describe Acceptance sampling

the decision whether to accept or refuse the lot is made considering just a portion of the whole lot, using statistical techniques.

It can be interpreted as a hypothesis test

null hypothesis (Hp0) => “the supplier’s lot/material is good”.

Describe Acceptance sampling interpreted as hypothesis test

Null hypothesis (Hp0) => “the supplier’s lot/material is good”.

Type 1 error (alpha)

Player => Supplier

Risk => Seeing good lots being rejacted

alpha => risk of rejection of Hp0 when it is actually true

Type 2 error ( beta)

Player => Customer

Risk => Accepting bad quality lots

beta => risk of failing to reject Hp0 when it is actually false.

Classification of Sampling Plans

(p. 9)

For attributes:

the quality characteristic is expressed through a binary parameter (good/bad, conforming/non-conforming)

Can be classified into sampling plans:

for defectives => product that fail to meet specifications since they have one or more defects

for defects => nonconformities that are serious enough to significantly affect the safe/effective use of the product unit

For variables: the quality characteristic is measured on a continuous numerical scale (e.g., the length of a mechanical component)

Describe the Measuremnet of Attributes

(p. 10)

Measurements of attributes are

quicker and more practical than those of variables

but with lower information content

Example: In order to control the diameter of a metallic bar, we could use a hard gauge to check its conformity to specifications, or a calliper to determine its real diameter.

Definition of a Lot / Batch

(p. 11)

Group of units of the same product, which have been produced under homogeneous conditions

i.e., same machines, same operators, same materials, approximately in the same time

Descibe OC-Curves

(p. 19, 29)

The Operating Characteristic (OC) curve depicts the discriminatory power or severity or protection of the sampling plan, representing the probability of acceptance (Pa) as a function of the lot fraction nonconforming (p).

There are two types of OC curves:

Type-A when Pa is calculated referring to the Hypergeometric distribution;

Type-B when Pa is calculated referring to the Binomial (approx.) distribution.

The OC curve is a monotonically decreasing curve of Pa with respect to p, which asymptotically tends to 0.

The shape of the curve depend on the parameters that characterize the sampling plan (N, n, c).

If n<<N (or n/N ≤ 0.10), the two OC curves are virtually undistinguishable because the hypergeometric distribution is well approximated by the binomial one.

Describe the two perpectives of Sampling Plan designing

(p. 21)

Supplier wants to avoid that lots with relatively high quality are rejected

relatively lower p

Concept of Serverity => Sampling plan should not be too severe

Customer wants to avoid accepting lots with relatively low quality

relatively higher p

Concept of Protection => Sampling plan will need to adequately protect him/her from this risk

Describe the influence of n on the OC-Curve

(p. 22, 24)

The sample size (n) is a parameter affecting the OC curve significantly

While n increases, the curve approaches the ideal “step shape”

Step shape OC curve is acieved when: n → N (100% inspection)

Discriminates “good” and “bad” lots perfectly

for relatively low p values => 𝑃_𝑎 = 1

for larger p values => 𝑃_𝑎 = 0.

Increasing n will also make the sampling plan more expensive and time-consuming

Describe the influence of c on the OC-Curve

(p. 22, 23)

Sampling plans with small c values are more discriminatory for lower p values => OC curve in these cases are said to be more severe

The severity of a sampling plan is the propensity to obtain a relatively low 𝑃_𝑎 value for a given p value (defectiveness)

Describe the concept of severity

In the example, three different OC curves (with different c values) are intersected with a vertical line corresponding to p = 2%.

The 𝑃_𝑎 values of the three OC curve are radically different => 𝑃_𝑎(𝑐=2) >𝑃_y(𝑐=1) >𝑃_a(𝑐=0)

While the curve with c = 0 is relatively severe (fully convex), that one with c = 2 is relatively indulgent.

Describe the influence of N on the OC-Curve

(p. 26)

Nearly no impact

What is a common mistake in desgining Sampling Plans

(p. 27)

The use of a sample size that are a fixed percentage of the lot size (e.g., n/N = constant) is a conceptually wrong practice.

The reason is that n and N differently influence the OC-curve behaviour

Effect of n predominates with respect to that of N.

Consequence => severity of the OC curve vary in an uncontrolled manner

Describe alpha and beta in the OC-Curve

(p. 30)

beta => risk of failing to reject Hp0 when it is actually false

Describe the acceptable quality level (AQL)

(p. 31)

Name the rules of the rectifying inspection plan

(p. 40)

For each rejected lot (N), the inspection is extended from the sample (n) to the rest of the lot (N – n);

Any defective unit found during the inspection, both of the sample (irrespectie of acceptance or rejection) and the rest of the lot (N – n), must be removed from the lot and then replaced with a good/conforming unit.

Describe the of a double sampling Plan

(p. 72)

For double sampling plans two points of the OC-curve (AQL, 1 – a and LTPD, b) are not enough

there are only two equations for four unknown factors to be determined (i.e., n1, c1, n2 and c2).

Two additional equations can be added by imposing some (additional) constraints. The most common ones are

n2 = 2∙n1

c2 = 2∙c1 or c1 + c2 = const.

Describe continous Sampling Plans

(p. 79)

For skip-lot plans only some fractions of the submitted lots are inspected.

Generally, skip-lot sampling plans are used where it is necessary to reduce the average amount of inspection required

(p. 83)

When production is continuous (the product is not formed into lots) a segment of production can be conventionally marked off as a “lot”.

In this case – in order to avoid a 100% inspection – only a fraction of the units can be inspected.

These sample units are selected one at a time at random from the flow of production

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