31 May 2011

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, 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.

Other Issues to Consider

A conclusion that can be drawn is that every production scenario must be examined in its own right before a decision on which is the most appropriate quality process to select can be made. 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 and 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 which should be considered 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.

Discussions and publications by John S. Oakland, Crosby, Deming and Juran could be consulted for implementing total quality management systems in an organisation. In particular Deming's 14 point plan.

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