Greer Grate and Gate faces a tough challenge this month: Its ISO 9000 registration, secured several years ago, was not
renewed when it failed to pass a recent audit. Hartford Simsack would like to blame the failure on his predecessor, but the auditor, Art Iffax, pointed out that the company's quality management
system documentation had been inadequate since Simsack assumed the position of quality manager. In addition, Iffax noted that the firm's response to customers' requests for capability analysis
had been abysmal. Simsack wrestled with the notion of coming clean about his own inadequate understanding of statistical methods. He didn't really comprehend the meaning of capability,
for example, and had fudged data that would have identified processes that were not capable. "I should just turn myself in," he whimpered to himself, using the same language that had
initiated his own prison sentence several years earlier, before his brother-in-law had given him a chance by hiring him at Greer Grate and Gate. But instead, he visited his old mentor,
Stan Deviation, the statistician who had been Simsack's instructor in the only statistics course he had ever taken. Deviation had often rescued Simsack from his own inadequacies, and here was yet
another chance. Deviation sighed. "Just give me the data, Simsack, and we'll go through this together." Simsack's data related to the capability of an iron fitting used to
secure carnival rides. Simsack had run X-bar and R charts to ensure that the process was in control, and then pursued chi-square testing that indicated a normal distribution for the part. The
fudging of data had occurred when the printout revealed a Cpk of -1.5 in the capability study. Simsack had simply ignored the negative sign and reported a Cpk of 1.5. In addition, the Z USL was
-3.0. Although Deviation usually reacted to his students with infinite patience, this was nearly too much for him. He shifted in his chair and then asked Hartford if he really understood
the implications of his action. Simsack did indeed. At this moment, he pictured hundreds of small children being hurtled through the air on carnival rides where the Greer Grate and Gate
fittings had not held. At Deviation's urging, Simsack picked up his cell phone and called the customer to acknowledge the error in his capability study, promising that the defect would be righted.
To understand whether Simsack's duplicity would actually have resulted in part failure on the carnival ride, it's important to understand the meaning of a negative Cpk. Which of the
following is an accurate interpretation of negative Cpk? a. The process is running to the high side, so no parts will be within specification limits. b. The process is running to the low
side, so no parts will be within specificationlimits. c. A small negative number for Cpk is of no consequence; the process would continue to produce within specification limits.
d. Fifty percent of the parts are outside of specification limits. Answer A is correct. To understand the impact of Cpk, review Simsack's data: The data (Cp = 1, Cpk
= -1.5) reflect a normal distribution, as illustrated in the figure below. Data Outside of Specification Limits
For ease of explanation, assume that the mean is 10 and the standard deviation is 1.
Because Z- USL is a negative value (-3.0), the data would fall outside (to the right) of the upper specification limit.
In order for this outcome to take place, the X-double bar must be greater than the upper specification limit. Simsack's data would appear as follows, with respect to
the specification limits: 
This explanation suggests that the implications of Simsack's "error" could've indeed been grave. Whenever a part is produced out of specification, the design of the
product is compromised. In this case, Hartford's image of children being hurled off the carnival ride is not too farfetched. As demonstrated in last year's attention to tire
safety, the quality of a product can have serious safety implications in the use of that product. About the author
Michael J. Cleary, Ph.D., is professor emeritus, Wright State University, and founder of PQ Systems Inc. He has published articles on quality management and
statistical process control in a variety of academic and professional journals.E-mail Cleary at mcleary@qualitydigest.com . |
