# Differences Between Statistical Process Control & Acceptance Sampling

## Product Quality Control

There are two types of product quality control approaches that are going to be compared and contrasted in this article, namely:

- Acceptance Sampling
- Statistical Process Control. (SPC)

The purpose of acceptance sampling is to determine the disposition of goods or services i.e. accept, reject or screen. The focus being on the product after it has been produced.

SPC can be defined as the application of statistical techniques to control a process. The focus being on the process and the product as it is being produced.

Ref. Sower et al (1993)

It is important to note that any form of quality control can only be provided at a cost. The various methods employed to ensure quality always need to be considered with this aspect in mind and specifically how can required quality be maintained at a minimum cost.

## Acceptance Sampling

When applying acceptance sampling as your approach to quality, a small batch of components are measured or observed and a decision to scrap or accept is made. This approach is dependent on statistical sampling techniques that use the data collected on a small number of samples to be extrapolated to predict the likelihood of large numbers of products meeting the design specification.

The decision to accept or reject is based on the idea that a certain number of defective items can be tolerated.

**When is Acceptance Sampling Effective.**

To consider when acceptance sampling is going to be effective it is necessary to look at 2 possible extremes.

If the cost of 100% inspection > the cost of all defective components, it is cheaper not to inspect.

If the cost of 100% inspection < cost of the customer finding 1 defect, it is cheaper to inspect 100%.

When the cost of inspection lies between these 2 extremes, acceptance sampling is said to become effective. This does however conveniently omit to take into account the possible damage to reputation, legal liability and potential loss of business as a result of the customer receiving defective goods. In other words the qualitative aspects of doing business are ignored in favour of the quantative aspects.

Ref. Edwards & Endean (1990)

**How Does Acceptance Sampling Work**

Acceptance sampling is formed around probability theories from which it can be predicted what percentage of a lot of components will be acceptable given the results from the observations made on a sample batch from that lot.

Batches whose samples show fewer than a specified number of defectives are going to be accepted, so the probability of finding fewer than that number of defectives in the sample needs to be known. This is determined by the sum of probabilities up to that for the number of defectives specified.

For example: -

If we want to find the probability of finding 1 defective component in a lot of 20 given 3 samples then the equation is

P = 1/20 = 0.95, so the probability of finding fewer than 1 defective in a sample of 3 is

0.95x0.95x0.95 =0.8574

This means that rejecting samples which have at least one defective could result in nearly 15% of all acceptable batches being rejected.

However what we want to know is what would be the risk of allowing batches with more than the permissible number of bad components to get through at either threshold of acceptance/rejection.

To find out requires calculating all relevant values of p, the fraction of defective components in the batch.

Rather than calculate this information every time, there are appropriate national and international standards available that provide the information in the form of extensive tables that detail the size of samples and the levels of defectives to accept or reject in order to provide the desired probabilities of detecting bad batches of products.

There is a finite probability of passing unacceptable batches and rejecting acceptable ones. Inspection procedures are arranged to minimise this risk to either manufacturer or customer.

Ref. Edwards & Endean (1990).

## An example of an 'Operating Characteristic Curve' used to establish the national standards

## Statistical Process Control

The basic idea behind SPC is that the products of any manufacturing process vary, one from another, in 2 distinct ways: -

" Variation that is inherent in the process.

" Variation induced by some external factor.

As long as the process chosen is capable of maintaining the tolerances required by the product specification, the first type of variation should not result in defective components.

Externally induced variations are less predictable e.g. a chipped tool may result in sudden deterioration that could affect both surface finish and dimensional accuracy.

SPC puts great emphasis on studying processes to characterise inherent variability so that when variations occur for other reasons they can be detected quickly and adjustments made to the process before defective components are produced.

**Variables & Attributes**

There are 2 different characteristics associated with any product which must be treated differently with respect to product quality. These are variables and attributes.

Variables tend to be thought of as the properties of a material e.g. surface texture, dimensions etc. and these tend to have a range of values which have upper and lower limits.

Attributes can be thought of more as observable defects e.g. surface defects, porosity etc. and these tend to be present or absent, acceptable or unacceptable.

The major difference between variables and attributes is that variables will always be specified as some ideal, whereas it is possible for a customer to specify zero as the only acceptable level for a particular attribute. Ref. Edwards & Endean (1990)

Controlling Product Variables

The first step in meeting this objective is to establish process capability, firstly to determine if the chosen process can produce components to the required standard and secondly to determine the precise nature of the inherent variability.

The tools of SPC are the normal distribution curve used in conjunction with 3 important parameters: -

" The mean or average of the values measured

" The range - difference between highest and lowest readings measured

" The standard deviation, which is derived by formula.

The normal distribution has useful properties which are exploited in process control, i.e.

" The distribution is symmetrical

" The mean coincides with the most frequently occurring reading

" The number of readings falling within any part of the curve is related to the standard deviation.

Knowing the mean and standard deviation of a variable measured on a sample of products provides the function of predicting the number of products that are likely to be made with a value of more than say 2 (standard deviations) above or below the mean.

By taking the initial samples over a very short time frame the effects of any externally induced variability can be considered insignificant. Also an assumption is made that each sample follows a normal distribution curve despite the small sample size.

Taking these factors into account it can be estimated from the areas under the normal distribution, the likelihood of making products outside the specified tolerances, or in other words is the process capable.

Having established the process is capable, the next objective is to look at how future performance of the process can be judged.

This is typically done using control charts or more recently SPC software, the most common of which are based on the mean and range values. The first indicates how the process is behaving relative to initial settings and the second helps detect when additional factors are affecting random variability.

Limits are put on the control charts to provide an indication when either the range or mean has moved sufficiently far way from the target to increase the probability of making out of tolerance components. Typically the convention is to set control lines so that the probability of a data point falling outside by chance alone is 1 in 1000.

Ref. Edwards & Endean (1990)

**Controlling Product Attributes**

This can only be done if the customer is prepared to accept a finite number of defective products given a known parameter.

Attribute sampling is similar to acceptance sampling but with a difference that the number of defects is used to decide if the process is still in control rather than whether the lot should be accepted or rejected.

When controlling by attributes, it is a shift in the number of defects in a product or the defective products in a sample that is the trigger for action. There is no upper limit to the number of defects possible so Poisson distribution is used to establish the probability of finding 'x' number of defects in a sample.

Similar to acceptance sampling the relationship established is used to calculate the probability of finding a particular number of defects in a product and from that the probability of finding more or less than a given number. It is this information which is used to decide the positions of control lines on a control chart.

Ref. Edwards & Endean (1990)

## Normal distribution and mean charts

## What approach should be used

Quality Assurance (SPC) versus Quality Control (Acceptance Sampling) is the subject of the debate that examines which approach should be taken when manufacturing products and striving to attain quality levels that are deemed to be acceptable to both manufacturer and customer.

There are no clear cut answers, there are arguments for and against using one or the other, using both or using neither.

As stated earlier quality comes at a cost and generally it is accepted that quality assurance methods which include SPC are more complex and therefore more expensive to set up, but once in place tend to have lower running costs and are geared towards 'zero defects' rather than an acceptable defect level.

Ref. Edwards & Endean (1990)

Does this mean then that SPC is the answer to which quality process to use. Unfortunately it is not as straightforward as that, one factor that cannot be ignored is that SPC is only effective when a process is deemed to be in control i.e. that the process has been set up correctly and is inherently capable of producing components to meet the design specification.

In order to ensure the process is in this condition it is necessary to take early samples of components produced, measure critical features and use the results to make a decision about the process. It has been argued that this is very similar to Acceptance Sampling and that the data could in fact be used for this purpose as well as to establish if the process is under control. In other words it presents a case for combining the 2 methods.

Ref. Taylor (1994)

Edward G Schilling discusses an ABC plan which also supports the view that there is synergy between SPC and acceptance sampling and that they can be combined to present a scenario where there is minimal risk to the consumer.

The ABC plan is subject to several constraints :

" Acceptable quality levels are not utilized

" Acceptance number of zero

" Simplicity

The plan progresses through 3 stages :

" Stage A - control being established

" Stage B - capability being established

" Stage C - capability being maintained

There are various rules associated with the implementation of this plan which are designed to promote continual improvement and learning, but it is accepted that the plan is a prototype and is subject to further development.

Ref. Schilling (1994)

W. Edwards Deming condemns the use of acceptance sampling and proposes all or nothing inspection. Although what he is really objecting to is the misuse of acceptance sampling and the suggestion that a proportion of defective components is acceptable.

In contradiction to this statement it is suggested that Acceptance Sampling is valid for processes that are in a state of chaos and until they reach the point where a process becomes stabilized.

Ref. Sower et al (1993)

## What conclusions can be drawn

There are arguments for both processes either independent of one another or combined. In cases of mass production it is clear to me that dependent on the situation, who the customers, are what agreements have been reached etc. then each and every option could be assessed to be the most appropriate.

The conclusions I have drawn is that every production scenario must be examined in its own right before a decision on which is the most appropriate process to select can be made. I also believe that there will be scenarios where neither SPC, Acceptance Sampling or a combination of the two is appropriate e.g. bespoke small batch production.

If neither acceptance sampling or SPC are appropriate then it needs to be considered what other options are available to try to maintain acceptable quality levels?

An aspect which has not been touched on so far is the need to ensure the specification is correct, clearly if a component is tightly toleranced it will be more difficult to meet the specification. The question must then be asked does the component need to be toleranced so tightly or will it be capable of functioning as required with more open tolerances.

Another aspect I would like to consider is the more modern approach to quality of 'Total Quality Management'. This effectively refers to the workforce at every level of a manufacturing organisation taking individual responsibility over the quality of goods produced.

One of the 14 points proposed by Deming is that the dependence on inspection to achieve quality should be stopped by building quality into the product in the first place. Clearly this point requires the implementation of the other elements of the plan to be effective and cannot be taken in isolation.

The full contents of Deming's 14 point plan can be found here.

What the plan represents is a totally different approach to manufacturing which requires a stepped culture change and a belief in the individual working in a team environment. This is an approach I would tend to subscribe to.

It is my belief that although there may be circumstances when acceptance sampling and or SPC may be totally appropriate, there are other techniques available in modern manufacturing environments that should be considered as viable alternatives to these approaches and require further examination.

This assumption has become more supportable given that manufacturing has had to become ever more flexible and fluid as the demands of society have moved from acceptance of limited choices of mass produced products to a situation where the individual is looking for variability in the choices they are offered to suit their own personal requirements.

Also the advent of CNC machining and manufacturing techniques has provided the means for supporting this level of flexibility. The result of this is smaller production runs and frequent re-tooling to produce the smaller production batches required. Neither SPC or Acceptance Sampling lend themselves to this scenario readily.

## Please feel free to make a contribution to the discussion

While I never worked in a manufacturing environment I am slightly (emphasis on slightly) acquainted with SPC and Acceptance Sampling. Probably, it's from helping my husband study for his Six Sigma black belt or something. My non-engineering mind tends to simplify things; I think of SPC as catching the problem before it results in a bad product and think of it therefore, as superior/preferred. You've taught me otherwise. Your article summarized this nicely for me, and for those hoping to learn about them, should be a great starting point.

SPC, give details of one situation where 100% inspection would be applicable during manufacture