11 - Inspection for faulty components before or after assembly of manufactured items

Summary

Summary

A problem in quality control, supplied by Marks and Spencer pic in the particular context of garment manufacture, is described. A fixed number of components is to be assembled to produce a finished item in the factory. Each component has a small probability of being faulty, and any component can be inspected before the item is assembled, if necessary being replaced by a perfect component. The finished item is checked for faults at the factory, and depending on the outcome of this checking may be sent to the store as perfect, or sold as a second, or repaired. A basic program is described, whose purpose is to help the manufacturer to decide which components, if any, should be inspected before assembly, and to illustrate the process by a simulation. The optimisation and statistical inference aspects of the problem are discussed.

Preamble

I am sure most university statisticians find that the experience of statistical consulting is essential to their professional well-being and sanity, as well as often being great fun, affording a glimpse into other worlds besides their own department or university. Like many statisticians, I find ‘research’ and ‘consulting’ are not readily disentangled, and indeed to separate one's activities into these two areas is probably rather unhealthy. However, there is obviously a danger that if one's research is too much problem-driven, one may be subject to a series of random impetuses, so that the net direction may be rather unclear.