Asked by Alpha Drone on May 12, 2024
Verified
A consultant has been brought in to a manufacturing plant to help apply six sigma principles. Her first task is to work on the production of rubber balls. The upper and lower spec limits are 21 and 19 cm respectively. The consultant takes ten samples of size five and computes the sample standard deviation to be .7 cm and the sample mean to be 19.89 cm. Compute Cp and Cpk for the process. Give the consultant advice on what to do with the process based on your findings.
Sample Standard Deviation
A measure of the dispersion or variability of a set of sample data points around the sample mean.
Spec Limits
Short for "Specification Limits," which are the maximum and minimum values within which a product or process's performance measures must lie to meet customer requirements.
Sample Mean
The average value calculated from a subset of a larger population, used in statistics as an estimate of the population mean.
- Conduct and expound upon the calculations of capability indices (Cp, Cpk) to grasp their critical importance in process capability assessments.
- Examine the stability and capability of processes through the use of statistical instruments.
- Apply six sigma principles to improve quality and performance in manufacturing processes.
Verified Answer
Cpk = min ( (21 - 19.89)/ (3∗.7), (19.89 - 19)/(3∗.7)) = .424
The very low capability metrics mean the process is not controllable within three-sigma limits. The consultant should therefore focus on assignable variation.
Learning Objectives
- Conduct and expound upon the calculations of capability indices (Cp, Cpk) to grasp their critical importance in process capability assessments.
- Examine the stability and capability of processes through the use of statistical instruments.
- Apply six sigma principles to improve quality and performance in manufacturing processes.
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