Cpk Only 0.82, Customer Issues an Ultimatum? — A Case Study of Process Capability Improvement in an Automotive Parts Company
1. Introduction: An Audit Report Reveals the True Picture
An automotive parts company specializes in spline shafts, with an annual production of about 1.2 million units. Its customers are two leading domestic original equipment manufacturers (OEMs). In April this year, during the final meeting of the annual supplier audit, the audit team leader presented a statistical chart: a sampling inspection of 125 process inspection data points from the past three months revealed that the process capability index (Cpk) for the key characteristic "spline major diameter" was only 0.82, far below the customer's requirement of Cpk ≥ 1.33. The audit conclusion included a severe nonconformity, with a 90-day corrective action deadline. Failure to close the nonconformity within this period would trigger the supplier elimination process.
When the news reached the factory, everyone felt wronged: the production line had a first-pass yield of 98.6%, a final shipment yield of 99.8% after rework, and the monthly quality reports had met the standards for 12 consecutive months. How could it suddenly be "insufficient process capability"?
Quality Manager Liu did not rush to argue. He obtained the customer's calculation process and found that the data used was the raw data exported from the SPC system, adhering to standard algorithms without any bias. He realized that the real issue was not the customer's strictness but the company's long-term reliance on "yield" as the sole measure of process performance, never seriously calculating the Cpk.
2. What Does Cpk Really Measure: The Contradiction Between 98.6% Yield and 0.82 Cpk
First, let's look at the definition of Cpk. For characteristics with bilateral tolerances like the spline major diameter, Cpk is the smaller of the two one-sided capability indices: Cpk = min((USL - μ) / 3σ, (μ - LSL) / 3σ), where μ is the process mean and σ is the short-term process standard deviation. It answers two questions: how far is the process center from the tolerance center (offset), and how much does the process vary (dispersion). Any deterioration in either of these aspects will lower the Cpk.
Interestingly, the number 0.82 is consistent with the 98.6% first-pass yield: according to the normal distribution, a Cpk of 0.82 corresponds to a theoretical defect rate of about 1.4%, which almost perfectly matches the 1.4% defect rate measured on the production line. In other words, the 1.4% defects are not "random" but a natural product of the process capability—rework masks the defects, making the final shipment yield look good, but the process itself consistently produces defects.
This is precisely the limitation of result metrics like yield: they only tell you "how many bad units are produced" but do not clarify "how much margin the process has left." Cpk, on the other hand, is a process metric. It compares the tolerance band width and process variation on the same coordinate system, directly answering "if the process continues to run this way, how many units per million will exceed the tolerance."
3. Measurement: Clean the Data First
The first action taken by the corrective action team organized by Liu was not to adjust the equipment but to check the data. This is because the calculation of Cpk is entirely dependent on data quality. Dirty data results in a process capability index that is like a castle in the air.
Three issues were identified during the investigation. First, the SPC system included the first article data after tool changes. Operators habitually process three to five "test cuts" after changing tools, and these parts often have dimensions close to the tolerance limits. According to the procedures, they should be judged separately, but they were all recorded in the regular sampling sequence, increasing the variation. Second, data from two precision lathes were mixed together. Machine 1 and Machine 2 have different service years and tool conditions, and combining their data masked the differences between the machines. Third, the measurement process itself had noise: a measurement system analysis (MSA) of three inspectors showed a %GR&R of 21.5%, which, although within the critical range of 10% to 30%, was enough to interfere with the capability assessment due to inconsistent measurement techniques.
The corrective action team redefined the data rules: first article data after tool changes should be recorded separately, data from the two machines should be calculated separately, and inspectors should standardize their measurement techniques and retest the GR&R. After cleaning the data and recalculating, the true Cpk emerged—it was not 0.82 but 0.71. The customer was actually quite lenient.
4. Analysis: Different Sources of Variation and Offset
A low Cpk can result from either high variation, significant offset, or both. The team stratified the data by machine, shift, and tool usage duration.
The stratification results pointed in two directions. By machine, Machine 1 had a Cpk of 1.21, while Machine 2 had only 0.55—the difference primarily came from the machines. By tool usage duration, the pattern was even clearer: the Cpk was about 0.9 within the first two hours after a tool change, but it plummeted to around 0.4 after two hours. Operators admitted that they relied on "sound and feel" to determine when to change tools, often waiting until the tool was severely worn before making a change. This led to rapid dimensional drift, which was the main source of variation.
The offset came from another source. The team used a tool setter to calibrate the tool setting block and found that the reference surface had worn by 0.012mm. The tolerance band for the spline major diameter is only ±0.025mm, so a 0.012mm wear pushed the entire machining center close to the upper tolerance limit. Combined with tool wear, this led to out-of-tolerance conditions. The root cause was further investigated using the 5Why method: why did the tool setting block wear? Because it was not included in the periodic calibration schedule; why was it not calibrated? Because it was not registered in the metrology ledger. A benchmark that was "off the books" quietly skewed the entire production line.
5. Improvement: Addressing the Root Causes, Not Just the Results
With the root causes identified, the improvement measures were not vague statements like "strengthen inspection, strengthen training" but specific actions targeting each root cause:
Establish tool life management. Conduct a tool life test over two weeks, collect the dimensional drift curves for different tool life segments (based on the number of processed units), and determine that each tool's safe life is 400 units. Force a tool change when the count is reached, and perform a three-point first article inspection and record it separately after each tool change. Change from "changing tools by feel" to "changing tools by data."
Repair and manage the tool setting block. Replace the worn block and include it in the metrology calibration ledger, calibrating it once every quarter. Add a tool setting confirmation step after each changeover to ensure that the machining center always starts from the same reference point.
Standardize program compensation parameters. Previously, each machine maintained its own set of compensation parameters. The team standardized the process parameters and compensation rules, documenting them in the work instruction to prevent "each experienced operator making their own adjustments."
The pilot program was first implemented on Machine 2, the most problematic. After two weeks, Machine 2's Cpk rose from 0.55 to 1.42; after one month, the improvement was rolled out to the entire production line, with the Cpk stabilizing above 1.3.
6. Control: Ensuring a Cpk of 1.55
Improvement is not difficult, but maintaining it is. The team took three steps to solidify the results: first, they changed the Xbar-R control chart from "weekly summary" to "sampling every two hours," automatically marking the tool change points and immediately addressing any abnormal points according to the reaction plan. Second, they established a monthly Cpk review mechanism, rolling Cpk calculations for key characteristics of each machine, triggering an analysis if the Cpk falls below 1.33, and stopping the line if it drops below 1.0. Third, they documented the tool life, tool setting confirmation, and data rules in standardized procedure documents, requiring new employees to pass an assessment before starting work.
At the end of the 90-day corrective action period, the customer conducted a re-evaluation: they re-sampled 125 process data points and found that the Cpk for the spline major diameter was 1.55, the first-pass yield increased from 98.6% to 99.96%, and rework was almost eliminated. The severe nonconformity was closed, and the supplier qualification was retained. According to Six Sigma standards, the sigma level of the production line improved from about 2.5σ to about 4.6σ, reducing the theoretical defect rate from about 14,000 per million to single digits.
7. One Sentence Summary
Cpk is a letter from the process to the management: no matter how good the yield, it cannot hide the deficit in process capability. The journey from 0.82 to 1.55 is not about luck but about "cleaning the data, digging to the root cause, and institutionalizing the improvements"—this is the most straightforward and powerful core of Six Sigma improvement.
Yield is the result, Cpk is the voice of the process; cleaning the data, digging to the root cause, and institutionalizing the results are the steps that ensure process capability can improve from 0.82 to 1.55.
Knowledge code: 6.3.2
Version: v20260817
Author: Quality Think Tank Quality Think Tank is dedicated to providing systematic professional knowledge, methodologies, and practical tools for quality management practitioners, helping companies continuously enhance their quality capabilities.