Question

A plant is packaging dry products into plastic bags. The product specification states that the force required to open such a bag must be between 40 and 60 Newtons. We have a testing device that can open the bags and measure the opening force. Discuss how we can evaluate the capability of the manufacturing process to consistently meet the specification for that parameter? Which metric or metrics would you present to your manager to answer that question  

Answer 1

In this case, the plant will open a sample number of bags and find the opening forces at some regular interval. Next, the average and ranges of the sample will be computed. The average of the sample means will reflect an estimate for the process mean (μ). The average of sample ranges should be noted and divided by the coefficient d₂ (the value depends on the sample size, n, and the sigma level of the control chart - the 3-sigma values are available in the form of tables) to get the estimate for process standard deviation (σ). Next, using the following formulae, the process capability ratio (C_p) and capability index (C_pk) will be found.

C_p = (USL - LSL) / 6σ

C_pk = Min{(USL - μ) / 3σ, (μ - LSL) / 3σ}

Where USL and LSL stand for the upper and lower specification limits and are given by 60 and 40 Newton respectively.

The process is capable only when the value of C_p and C_pk are at least 1.0 (for 3-sigma capability). For a 4-sigma capability, the minimum value should be 1.333.