Process Capability and Statistical
Review and Discussion Questions
1. The capability index allows for some drifting of the process mean. Discuss what this means in terms of product quality output. When Cpk is larger then 1.33 or 1.5, this means that the mean of the process can drift (up to a limit) while still producing within specifications. This is what is implied by the phrase “a capable process." 2. Discuss the purposes and differences between the P-charts and X-bar and R charts. P-charts are used to monitor the process for attribute data. These are typically binomial “go, no-go” data. An example of a P-chart is percent of pieces nonconforming. X-bar charts are used for charting population values for continuous measurement. X-bar charts operate effectively with smaller sample sizes than P-charts, but it is more involved to analyze the sample for an X-bar chart since a measurement must be taken. A rule of thumb for the sample size of a P-chart is to have at least one defective in each sample. This can require a relatively large sample size in some cases. If the process is slow, an X-bar chart will generally be a better choice since it functions with smaller sample sizes. An example of an X-bar chart is average time to complete a mile run for one person. R charts are used to compute process ranges for variable data, and are generally used in concert with X-bar charts. 3. In an agreement between a supplier and a customer, the supplier must ensure that all parts are within tolerance before shipment to the customer. What would be the effect on the cost of quality to the customer? Before the agreement was made, the customer probably inspected each part to protect against off-spec supplies. This agreement (ideally) eliminates the need for this inspection. Appraisal costs, such as materials and supplies inspection and reliability testing, will be reduced since the agreement would ensure that the supplies are totally within tolerance. This allows the customer to focus attention on quality improvement within his or her own processes, requiring an increase in prevention cost. Scrap and rework costs will initially drop because of the improvement in the quality of the part supply. Once prevention programs are in force, scrap, repair, rework, and downtime costs will drop even further because of improvements in the internal process. External failure costs will drop because of improvement in the product and the process. 4.
In the situation described in Question 3, what would be the effect on the cost of quality to the supplier? If operating under the traditional definition for the quality control function, appraisal costs will increase since all parts, not just a sample, must be inspected before shipment. Coupled with costs associated with internal and external failure, an increase in the appraisal cost could drive up the price of the parts so that they are no longer competitive. 5. Discuss the trade-off between achieving a zero AQL (acceptable quality level) and a positive AQL (e.g., an AQL of 2 percent). The tradeoff involves a cost/precision tradeoff. This is analogous to the service level/cost tradeoff. From a classical economic point of view, if the cost of defects is very high, an AQL of zero is economical. If defect costs are nominal, the cost of achieving near perfect quality can be prohibitive. This assumes that conformance is asymptotic to the cost axis.
Problem| Type of Problem| Difficulty| Check Figure in Appendix D| | Cost of Inspec-tion| P-chart| X-bar and R charts| Accep-tance Sampling| Cpk| | | 1| Yes| | | | | Easy| Yes|
2| | | | | Yes| Moderate| |
3| | Yes| | | | Moderate| |
4| Yes| | | | | Easy| |
5| Yes| | | | | Easy| |
6| | | Yes| | | Moderate| Yes|
7| | | | Yes| | Easy| |
8| | Yes| | | | Moderate| |
9| | | | Yes| | Easy| Yes|...