Let \(\{X_ n: n\geq 1\}\) be a sequence of i.i.d. random variables and consider a geometric moving average scheme \(S_ n=(1-r)S_{n-1}+rX_ n\), \(n\geq 1\), where \(S_ 0=w\) for some specified initial value w, - \(\infty \leq h^-n)\), \(n\geq 1\); \(p_ n(\cdot)\leq p_{n-1}(\cdot)\) and \(p_ n(\cdot)\) can be computed recursively starting with \(p_ 0(\cdot)=1.\) Next, let \(m^-_ n=\inf \{p_ n(s)/p_{n-1}(s):\) \(h^-n)\leq P(N>n+j)\leq (m^+_ n)^ jP(N>n),\) \[ (ii)\quad (m^-_ n)^{j+1}P(N>n)\leq (m^-_{n+1})^ jP(N>n+1), \] \[ (iii)\quad (m^+_ n)^{j+1}P(N>n)\geq (m^+_{n+1})^ jP(N>n+1). \] Part (i) contains the derived bounds for the distribution of N, Parts (ii) and (iii) guarantee improved bounds at each step of iteration. This scheme is applied in quality control. Some numerical results are illustrating the efficiency of the scheme.