Process Capability Process capability For Variables The 6 versus specification limits For attributes Pareto chart Cause and effect diagram

Process Capability There is a difference between a process conforming to the specifications and a process performing within statistical limits A process in statistical control will not necessarily meet specifications as established by the customer The control limits on the charts represent what the process is capable of producing

Process Capability Specifications are set by the customer. These are the “wishes.” Control limits are obtained by applying statistical rules on the data generated by the process. These are the “reality.” Process capability refers to the ability of a process to meet the specifications set by the customer or designer

The 6 Versus Specification Limits It is important to compare the natural tolerances, 6, with the specification range (USL-LSL). Recall that  may be estimated as follows:

The 6 Versus Specification Limits Suppose that process mean = (USL+LSL)/2 Case I: 6 < USL - LSL The specifications will be met even after a slight shift in process mean Case II: 6 = USL - LSL As long as the process remains in control with no change in process variation, the specification will be met Case III: 6 > USL - LSL Although the process may be in statistical control, it is incapable of meeting specifications

The 6 Versus Specification Limits Capability potential The relationship between process mean,  and its target value, is obtained from an index Exercise: If the target mean value = (USL+LSL)/2, is the process capable if

Process Capability Some indices: If the above indices are more than 1, the 3-sigma control limits are within the specification limits, and the process is capable - all but at most 0.27% items meet the specification If CpL < 1, too many items are outside LSL If CpU < 1, too many items are outside USL

The 6 Versus Specification Limits Sometimes, only one of CpL and CpU may be relevant e.g., testing for steel hardness If the process is not capable, actions may be taken to adjust the process mean variation specifications

Problem 9.6: A certain manufacturing process has been operating in control at a mean  of 65.00 mm with upper and lower control limits on the chart of 65.225 and 64.775 respectively. The process standard deviation is known to be 0.15 mm, and specifications on the dimensions are 65.00±0.50 mm. (a) What is the probability of not detecting a shift in the mean to 64.75 mm on the first subgroup sampled after the shift occurs. The subgroup size is four. (b) What proportion of nonconforming product results from the shift described in part (a)? Assume a normal distribution of this dimension. (c) Calculate the process capability indices Cp and Cpk for this process, and comment on their meaning relative to parts (a) and (b).

Pareto Chart 50 100 80 30 60 40 10 20 Cumulative percentage Number of defects 100 80 60 40 20 50 30 10 Cumulative percentage The next sequence translates the data from the checklist to a Pareto chart. 10

Pareto Chart 50 100 80 30 60 C 40 10 20 Cumulative percentage Defect type C D A B Number of defects 100 80 60 40 20 50 30 10 Cumulative percentage The four defect types are charted with the chart height being the relative frequency of occurrence and the defects ordered in descending order of magnitude. This is a discrete chart, one of the two ways Pareto charts are commonly constructed. 11

Pareto Chart 50 100 80 30 60 C 40 10 20 Cumulative percentage Number of defects 100 80 60 40 20 50 30 10 Cumulative percentage Defect type C D A B This chart adds the cumulative line to the chart showing the alternate charting technique. 12

Cause and Effect Diagram Measurement Men/Women Machines Faulty testing equipment Poor supervision Out of adjustment Incorrect specifications Lack of concentration Tooling problems Improper methods Inadequate training Old / worn Quality Problem Inaccurate temperature control Poor process design Defective from vendor Ineffective quality management Not to specifications A cause-and-effect diagram, or fishbone diagram, is a chart showing the different categories of problem causes. Dust and Dirt Material- handling problems Deficiencies in product design Environment Materials Methods

Cause and Effect Diagram Common categories of problems in manufacturing 5 M’s and an E Machines, methods, materials, men/women, measurement and environment Common categories of problems in service 3 P’s and an E Procedures, policies, people and equipment

Reading and Exercises Chapter 9: pp. 324-330 (Section 9.2) 9.1, 9.5