Abstract
This paper develops and illustrates a case in manufacturing management, using the instance of justifying quality improvement of ball bearings—a common precision product whose correct manufacture and assembly greatly affects their efficiency, utility and life. Mass-produced at high speed, bearings extend a fertile domain for benefiting from QA apparatus including Gage R&R, ISO standards, sampling, and SPC to Six Sigma DMAIC (Pyzdek 2000). However, when large investments are involved, it becomes imperative that besides the obvious, the hidden costs of quality be located and sized. This paper provides methods to examine and quantify such shortfalls—many being preventable by reduction of quality variance and/or part variety. Statistical and numerical models have been used. Thus, targeting beyond scrap and rework, this paper invokes modeling methods to quantify such not-so-visible constraints that limit productivity and profits of high-volume high-speed processes.
Introduction
Managing precision manufacturing of specialized products at their highest achievable performance level is anything but trivial, but management frequently finds itself unable to justify the large investment entailed in superior technologies required to do so. We illustrate a procedure for this by using a real case—a firm’s pursuit to upgrade the quality of automotive ball bearings (Figure 1) that it produced. Mounted on skateboards, passenger vehicles, machine tools and even a space shuttle’s engine, bearings have been a major mechanical innovation that reduces surface to surface contact between moving surfaces, thereby reducing friction and saving motive energy requirement and its wasteful loss. Traced to drawings by Leonardo da Vinci around 1500, bearings today help the “bearing” of load typically between a shaft and a rotating surface. Bearings are mass-produced by manual to fully automated machining and assembly. Their precise manufacture greatly affects their efficiency, utility and life. Bearings, as contrasted with appliances, toys, furniture, etc., also are an exceptional domain in which quality assurance methods from Gage R&R, ISO standards, SPC (Montgomery 2005) and sampling to Six Sigma DMAIC (Pyzdek 2000; Evans 2005) can impact business.
A mid-size bearings manufacturer gave this writer an extraordinary opportunity to observe first hand the bearing production process, freely interact with the expert staff manning the machines and work stations and vary process parameters in experiments to observe their effect on product quality. This company had already trained its staff in TQM tools and TPM methods. However, no measurable impact from these on either the bottom line or top line could be discerned by management, as is often the case. Therefore, a rigorous and advanced method that could elevate profits and customer satisfaction was sought. Six Sigma appeared to promise such breakthrough—but, the gains from it could not be projected beforehand. This paper describes the modeling methodologies that led to successfully justifying state-of-the-art technology interventions in this company.
To scope the quality improvement project Cpk was assessed at quality-bottlenecked process steps. The plant ran Orthogonal array experiments (Taguchi and Clausing 1990) to locate process factors speculated to affect quality by the plant. Thus, key quality deviations in need of attention could be identified, but no firm basis could be cited to motivate impacting them. However, such studies led to re-statement of the project’s charter, which became “predict variability of the final bearing assembly based on information available on part variability.” Key parts in question here were the inner and outer rings of the bearing and the rolling balls (Figure 1).
Deductive variance prediction from parts to whole proved too complex as it led to queuing or inventory type models (Bhat 2008) involving random variables discretised (rounded down) from real numbers. General forms of such models (see (1) and (2) later in this paper) have not yet been solved theoretically. Consequently, the process—the assembly of complete bearings from parts separately manufactured by grinding/honing machines with significant variability in them—was first numerically modeled and then studied by Monte Carlo simulation. The objective was to quantify the relationship of high variability (σ) in manufactured ring sizes (outer and inner) and the variety of bearing balls needed to complete the assembly. Till this point, “experience” had guided the creation of the large assortment of ball sizes that the plant used. Producing a wide assortment of ball sizes with frequent machine set up changes (a hidden cost) was a burden for the plant. But management could find no sound method to answer why this practice should be changed. They were “committed to deliver high performance bearings to customers”, so the issue remained stuck there.
Motivation of the current study was to help the manufacturer find economic justification for possible major technology intervention that could cut tangible and intangible COQ (cost of poor quality) (Gitlow et. al. 2005, Gryna et. al. 2008) and delays and raise profits by reducing production of marginal quality bearings. With improved quality, the company could possibly sell to premium bearing markets.
This paper is organized as follows. The next section of this paper outlines the relevant aspects of bearing parts manufacture and assembly, and then states the problem of immediate focus—low yield (proportion of acceptable production) of quality bearings, resulting from parts with high 2 dimensional variability (σ ). The manufacturer wanted to be competitive in both quality and profitability. Subsequently, we portray a key operational bottleneck that the plant faced—the challenge of selecting balls of correct size to match a random pair of outer and inner rings produced by track grinding. Next, we provide a statistical perspective of bearing assembly since all machining operations are subject to random variation yielding rings with considerable variance in their dimensions. Then, we show the steps to numerically determine the dependence of distinct ball size requirements on ring grinding variance, and then relate this to yield.
Subsequently, a simulation procedure is developed to predict process yield within stated precision given specified randomness of outer and inner ring sizes. Typical questions that management will confront that could be successfully tackled by such simulation are presented next. Results of a number of designed simulation experiments indicate that a rising variety is required in distinct ball sizes as grinding variance (σ ) goes up (Figure 4). Next we illustrate one such use of simulation to determine the distinct categories of “standard” ball sizes required in high yield assembly given C ratings of pk track grinding. Subsequently, we use assembly costs and visible COQ (scrap and rework) to help project the justifiable capital expenditure in technology that could improve grinding precision (i.e., reduce σ). The paper ends with a summary of conclusions that management should expect to see in such a study.
