Abstract
Quality is a "very talked" subject: many top managers are giving this matter greater attention, due to Quality System Certification (according to ISO 9000:2000 series of Standards); many Gurus are providing their precepts; managers either look for "cooking books" they can apply immediately or look for packaged off-the-shelf solutions. Quality, when it is really appreciated by Customers, entails costs reduction to advantage both to the Customers and to the Company: Quality provides higher earnings to the Company than disquality does. Quality, serious and difficult business has to become an integral part of management, because "low quality can be a very costly luxury for a company".
Many times managers know little about Statistics and Probability Theory; nevertheless they have to make decisions based on few data. Managers do not like to ask themselves whether a method is good or bad especially when a method provides them with results that are appealing. That is true also when optimisation of preventive maintenance is concerned. Replacement problems can be either deterministic or probabilistic. Replacement decisions for probabilistically failing items involve a decision-making in a state of uncertainty. A model is shown which allows the computation of the optimal preventive replacement interval of items during their lifetime. The model can be extended to include all the subsystems comprising a system, in order to minimise the cost of products maintenance (Life Cycle Analysis). The search of optimal replacement interval for wear-out breakdowns of any item is fundamental for all firms. It is management responsibility to find the component reliability, which minimises the working operating cost for customers. The trade-off between the cost of failure c1 and the cost of preventive replacement c0 is an economic decision, which depends on the component cost, maintenance time, lost times and earnings, manpower costs, machine amortisation costs. Reliability has to be considered to find the optimum maintenance interval. We present a model based on the ¡§Reliability Integral Theory (RIT)¡¨, devised by F. Galetto in 1971, a fundamental part of the GIQA (Golden Integral Quality Approach). Let be N0(t,tm) the number of replacements of unfailed items over the interval 0---t, with preventive replacement interval tm and N1(t,tm) the number of failed items: their expectations are M0(t,tm) and M1(t,tm). Let C(t,tm) be the total expected cost over the interval 0---t: C(t,tm)=c0M0(t,tm)+c1M1(t,tm). R(t, tm) is the reliability for the interval 0---t, when items are "renewed" at their "life" tm, b(t,tm) is the pd function.
To optimise the cost over the interval 0---t, we need either to compute M0(t, tm) and M1(t, tm) or to compute the mean cost C(t, tm) from the integral equation derived using the "Integral Theory of Reliability". The optimum time duration for the preventive replacement depends on t, the duration of the interval 0---t, over which we want to optimise and on the cost ratio c0/c1.
Management need to be made fully aware and convinced that "Quality of methods is important": some methods are misleading. "There is no substitute for knowledge" (E. Deming).
Wrong ideas and methods are a huge cost.
Decisions based solely on the (ISO 9000:2000 and 9004:2000) seventh principle ¡§Factual approach to decision making¡¨ are NOT effective: many times they are wrong, IF you do not use a sound theory! Beware of common sense. The so called "practitioners" (either managers or professors) must meditate upon the Table of QUALITY and PRAGMATHEORY (F. Galetto 2000) that states that
á If you teach SCIENTIFIC concepts and ideas, in an EFFECTIVE way, then you get an IDEAL result
á If you teach Wrong concepts and ideas, in an EFFECTIVE way, then you get an VERY DANGEROUS result
á If you teach SCIENTIFIC concepts and ideas, in a NOT effective way, then you get an Almost Useless result
á If you teach Wrong concepts and ideas, in a NOT effective way, then you get an Expensive result taking into account that
Y If I do not Know that I DO NOT Know then I think I Know (F. Galetto, 2000)
Y If I do not Know that I Know then I think I DO NOT Know (F. Galetto, 2000) and that
* facts and figures are useless, if not dangerous, without a SOUND THEORY (Fausto Galetto, 1998)
* The best practical thing is a sound theory (Fausto Galetto, 1970)
* Misleading, if not useless ¡K. (W. E. Deming)
The author acknowledges the support offered by QuASAR (via A. Moro 8, 20090 Buccinasco, Italy).