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294 Part IV: Quality AssurancePart IV.B.5supplier. More and more manufacturers and suppliers are using PCI as an importantpart of their contract to ensure quality.A process capability analysis is simply the comparison of the distribution of aprocess output with the product tolerances. As noted by Kotz and Lovelace (1998),results of process capability analysis have proven very valuable in many ways.Deleryd (1996) has developed a list of the 13 most common ways of using theresults of process capability analysis:1. As a basis in the improvement process.2. As an alarm clock.3. As specifications for investments. By giving specifications for levelsof process capability indices expected to be reached by new machines,the purchasing process is facilitated.4. As a certificate for customers. The supplier is able to provide theresults from the process capability studies conducted when the actualproducts were produced with the delivery.5. As a basis for new construction. By knowing the capability of theproduction processes, the designer knows how to set reasonablespecifications in order to make the product manufacturable.6. For control of maintenance efforts. By continuously conducting processcapability studies it is possible to see if some machines are graduallydeteriorating.7. As specifications for introducing new products.8. For assessing the reasonableness of customer demands.9. For motivation of coworkers.10. For determining priorities in the improvement process.11. As a base for inspection activities.12. As a receipt for improvement.13. For formulating quality improvement programs.In order to implement a process capability analysis, one needs to consider thefollowing:1. The target value specification, which is usually defined by thecustomer.2. The specification limits, which should be defined by the customer, orby his technical staff, and should be agreed upon by the manufacturer.Furthermore, the specification limits should be such that they allowfor manufacturing variability without jeopardizing proper functionof the product.3. An analysis of the process that allows the manufacturer to determineif his/her product can meet the customer’s specifications.
Chapter 19: B. Statistical Process Control 295Once the production starts, the manufacturer conducts capability studies tocompare the measures of the quality characteristic of the manufactured productwith the specification limits. This is the point where process capability indicesare used.The first generation PCIs were established by the Japanese in the 1970s. Theyused the following indices:C pInherent capability of a processk Position of the process in relation to the target valueC pk Position of the 6s process in relation to the target valueC pl Position of the 6s process in relation to the lowerspecification limitC pu Position of the 6s process in relation to the upperspecification limitIn this section we study these and other capability indices that are frequentlyused in process capability analysis. Here we are not going to address every aspectof these indices. However, an excellent reference for a more detailed study of theseindices is Kotz and Lovelace (1998).Throughout the study of these indices we are going to assume that the processproducing the desired quality characteristic is under control, and thuspredictable.Process Capability Index: C pLet X be the process quality characteristic that we want to monitor. Let USL andLSL be the upper specification limit and lower specification limit, respectively. Theperformance of the process with respect to these limits is defined as follows:Percentage of nonconforming produced by the process at the upper end= P(X > USL).Percentage of nonconforming produced by the process at the lower end= P(X < LSL).Thus, the total percentage of nonconforming produced by the process is definedasP(X < LSL or X > USL) = 1 – P(LSL < X < USL).In the above paragraph we saw the performance of the process with respect to thespecification limits. Now we look into the performance of the process with respectto the natural tolerance limits, that is, the upper natural tolerance limit (UNTL) andthe lower natural tolerance limit (LNTL).The performance of the process with respect to the natural tolerance limits isthe percentage of the product produced by the process with its quality characteristicfalling within the interval (m – 3s, m + 3s), where m and s are respectivelythe mean and the standard deviation of the process quality characteristic. Assumingthat the process quality characteristic is normally distributed and the processPart IV.B.5
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294 Part IV: Quality Assurance
Part IV.B.5
supplier. More and more manufacturers and suppliers are using PCI as an important
part of their contract to ensure quality.
A process capability analysis is simply the comparison of the distribution of a
process output with the product tolerances. As noted by Kotz and Lovelace (1998),
results of process capability analysis have proven very valuable in many ways.
Deleryd (1996) has developed a list of the 13 most common ways of using the
results of process capability analysis:
1. As a basis in the improvement process.
2. As an alarm clock.
3. As specifications for investments. By giving specifications for levels
of process capability indices expected to be reached by new machines,
the purchasing process is facilitated.
4. As a certificate for customers. The supplier is able to provide the
results from the process capability studies conducted when the actual
products were produced with the delivery.
5. As a basis for new construction. By knowing the capability of the
production processes, the designer knows how to set reasonable
specifications in order to make the product manufacturable.
6. For control of maintenance efforts. By continuously conducting process
capability studies it is possible to see if some machines are gradually
deteriorating.
7. As specifications for introducing new products.
8. For assessing the reasonableness of customer demands.
9. For motivation of coworkers.
10. For determining priorities in the improvement process.
11. As a base for inspection activities.
12. As a receipt for improvement.
13. For formulating quality improvement programs.
In order to implement a process capability analysis, one needs to consider the
following:
1. The target value specification, which is usually defined by the
customer.
2. The specification limits, which should be defined by the customer, or
by his technical staff, and should be agreed upon by the manufacturer.
Furthermore, the specification limits should be such that they allow
for manufacturing variability without jeopardizing proper function
of the product.
3. An analysis of the process that allows the manufacturer to determine
if his/her product can meet the customer’s specifications.